IV. Proraun grede pozicija 207 208 207
IV.I Analiza optereenja: Na gredu djeluje optereenje od ploe pozicija 202-203-203-202. Greda je T presijeka.
Stalno optereenje : Vlastita teina grede : mkNgvt /66,225,0125028,0 Stalno optereenje od ploe pozicija 202-203-203-202 :
-3 ,7 3 k N /m -3 ,7 3 k N /m -3 ,7 3 k N /m -3 ,7 3 k N /m
3 ,9 3 5 m 3 ,9 3 5 m 3 ,9 3 5 m 3 ,9 3 5 mC 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5
-5,7
7 kN
7,87
kN
-6,8
1 kN
8,91
kN
5,77
kN
-7,8
7 kN
-6,8
1 kN8,91
kN
mkNl
gR yg /78,16287,773,3143,1
2143,1
Ukupno stalno optereenje : /203202 /44,1978,1666,2 mkNRgg gvt
Pokretno optereenje : Pokretno optereenje od ploe pozicija 202-203-203-202 :
C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 ,9 3 5 m 3 ,9 3 5 m C 3 5 /4 53 ,9 3 5 m 3 ,9 3 5 m
- 6 ,2 3 k N - 6 ,2 3 k N - 6 ,2 3 k N
15,2
2 kN
-14,
78 k
N
10,8
4 kN
13,6
8 kN
9,73
kN
-9,2
9 kN
0,98
kN
mkNl
qR yq /98,29287,723,6223,1
2223,1
IV.II Statiki proraun Stalno optereenje :
3 0 x 5 03 0 x 5 0 3 0 x 5 0
-1 9 ,4 4 k N /m
120,
10 k
Nm
120,
10 k
Nm
120,
10 k
Nm
120,
10 k
Nm
-1 9 ,4 4 k N /m -1 9 ,4 4 k N /m
7 ,8 6 m 7 ,8 6 m 7 ,8 6 mC 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5
-9 6 ,0 8 k N m
-3 0 ,0 2 k N m
-9 6 ,0 8 k N m
kNmlgM xg 08,9686,744,1908,008,0
22207 kNmlgM xg 02,3086,744,19025,0025,0
22208 kNmlgM xg 10,12086,744,191,01,0
22208207
30x5030x50 30x50
-19 ,44kN /m -19 ,44kN /m -19 ,44kN /m
91,6
8 kN
-61,
12 k
N
-76,
40 k
N
7 ,86 m 7 ,86 m 7 ,8 6 mC 35 /45 C 35 /45 C 35 /45
-61,
12 k
N
76,4
0 kN
91,6
8 kN
08,16886,744,191,11,1208207 xg lgR Polje 207 : Pokretno optereenje
7 ,8 6 m3 0 x 5 0
C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 0 x 5 0
7 ,8 6 m3 0 x 5 0
7 ,8 6 m
92,6
1 kN
m
92,6
1 kN
m
92,6
1 kN
m
- 2 9 ,9 8 k N /m -2 9 ,9 8 k N /m
-1 8 7 ,0 7 k N m -1 8 7 ,0 7 k N m
kNmlqM xq 07,18786,798,29101,0101,022207
Polje 208 : Pokretno optereenje
7 ,86 m30x50
C 35 /45C 35 /45C 35 /4530x50
7 ,86 m30x50
7 ,86 m
92,6
1 kN
m
92,6
1 kN
m
92,6
1 kN
m
92,6
1 kN
m
2 9 ,98kN /m
-138 ,91 kN m
kNmlqM xq 91,13886,798,29075,0075,022208
Leaj 207-208 : Pokretno optereenje
7,86 m30x50
C35/45C35/45C35/4530x50
7,86 m30x50
7,86 m
29,98kN /m 29,98kN /m
-135,76 kNm -98,72 kNm
61,1
2 kN
m
61,1
2 kN
m
216,
70 k
Nm
216,
70 k
Nm
7,86 m30x50
C35/45C35/45C35/4530x50
7,86 m30x50
7,86 m
-29,98kN/m -29,98kN/m
145,
39 k
N
-90,25 kN 137,38 kN
-98,
03 k
N
7,78
kN
kNmlqM xq 70,21686,798,29117,0117,022208207 kNmlqR xq 77,28286,798,292,12,1
208207 Raunski moment savijanja u polju pozicija 207 :
7,86 m30x50
C35/45C35/45C35/4530x50
7,86 m30x50
7,86 m
-410,33 kNm -410,33 kNm
kNmMMM qgsd 33,41008,1875,108,9635,15,135,1207207207
Raunski moment savijanja u polju pozicija 208 :
7,86 m30x50
C35/45C35/45C35/4530x50
7,86 m30x50
7,86 m
-248,89 kNm
kNmMMM qgsd 89,24891,1385,102,3035,15,135,1
208208208 Raunski moment savijanja na leaju pozicija 207-208 :
7,86 m30x50
C35/45C35/45
487,
19 k
Nm
487,
19 k
Nm
C35/4530x50
7,86m30x50
7,86 m
kNmMMM qgsd 19,48770,2165,110,12035,15,135,1 208207208207208207 Raunski poprena sila na leaju pozicija 207-208 :
kNmRRR qgsd 06,65177,2825,108,16835,15,135,1208207208207208207
IV.III. Dimenzioniranje armature Materijal : C35/45 Armatura : S-400 (RA 400/500)
pretpostavka: mma 22 mmv 8 cmh 50 cmc 0.2 - suhi okoli
udaljenost do teita armature :
cmcd av 9.322,28,02
21
statika visina :
cmdhd 10,4690,3501 Raunska vrsto betona : 22 /33,2/0,20
5,135 cmkNmmN
ff
c
ckcd
Raunska vrstoa armature : 22 /783,34/83,347
15,1400 cmkNmmkN
ff
s
ykyd
Dimenzioniranje armature u polju poz. 207 Sudjelujua irina ploe : cmlbb weff 62,1615
78685,028585,01
cmbblb
l
bb
l
bbbb wwy
wy
w
wy
weff 5,393282282787
22
22
22
2 21
Bezdimenzionalni koeficijent armiranja :
0252,0051,033,210,4662,161
4103322
207
cdeffsd
sd fdbM
odabrano za : 053,0 ; 964,0 ; 095,0 poloaj neutralne osi : cmdx 38,410,46095,0 < 12 cm
Potrebna armatura :
2207
1 55,26783,3410,46964,041033 cm
fdMA
yd
sds
Minimalna armatura :
2min 94,140010,46286,06,0 cm
fdbA
yk
ws
Maksimalna armatura :
2max 23,42410,4662,161783,3433,285,085,0 cmdb
ffA effyd
cds
ODABRANA ARMATURA: 21 64,26227 cmAods
udaljenost od teita armature:
ns
sa
aavsa
v
A
AncAncd
11
11
122
cmd 79,580,37
80,3322,22,22,28,00,280,34
22,28,00,2
1
statika visina:
cmdhd 21,4479,5501
Odreivanje sudjelujue irine ploe : cmlbb weff 62,1615
78685,028585,0
Bezdimenzionalni koeficijent armiranja :
0252,0056,033,221,4462,161
4103322
207
cdeffsd
sd fdbM
odabrano za : 056,0 ; 962,0 ; 099,0 poloaj neutralne osi : cmdx 38,421,44099,0 < 12 cm
Potrebna armatura :
2207
1 74,27783,3421,44962,041033 cm
fdMA
yd
sds
ODABRANA ARMATURA: 21 77,2713,164,26121227 cmAods
Dimenzioniranje armature u polju poz. 208
Odreivanje sudjelujue irine ploe : cmlbb weff 04,1385
7867,02857,0
Bezdimenzionalni koeficijent armiranja :
252.0036.033,210,4604,138
2488922
208
cdeffsd
sd fdbM
odabrano za : 036,0 ; 973,0 ; 074,0 poloaj neutralne osi : cmdx 41,310,46074,0 < 12 cm
Potrebna armatura : 2208
1 95,15783,3410,46973,024889 cm
fdMA
yd
sds
ODABRANA ARMATURA: 21 34,1613,121,15121224 cmAods
Dimenzioniranje armature leaja poz. 207-208
Smanjenje momenta nad leajem :
kNmtRM sd 55,328
40,006,6518
208207
/208207 /64,45455,3219,487 mkNmMMM sdlezajsd
Bezdimenzionalni koeficijent armiranja :
252,0328,033,210,4628
4546422 cdw
lezajsd
sd fdbM
Dvostruko armirani leaj :
1) 252,0250,033,2
64010,4628
45464
6
22
cdw
leajsd
ftdb
M
2) 252,0304,033,210,4628
32554546422
cdw
sdleajsd
fdbMM
Granini moment savijanja : kNmfdbM cdwsdsd 3493933,210,4628252,0 22lim, cmcd av 90,32
2,28,0222
Vlana armatura :
2
2
lim,lim,1
82,3195,487,26783,3490,310,46
34939325545464783,3410,46811,0
34939 cm
fddMMM
fdM
Ayd
sdleajsd
yd
sds
Gdje je : 811.0lim Tlana armatura :
22lim,
2 95,4783,3490,310,4634939325545464
)(cm
fddMMM
Ayd
sdleajsd
s
ODABRANA ARMATURA: Vlana armatura: 21,342291 odsA Tlana armatura: 21 67,5192 cmAods
Dimenzioniranje armature rubnog leaja
Uzima se kNmM sd 58,10233,41025,025,0
207 Bezdimenzionalni koeficijent armiranja :
252,0074,033.210,4628
1025825,022
207
cdw
sdsd fdb
M
odabrano za : 076,0 ; 951,0 ; 123,0 Potrebna armatura :
2207
1 73,6783,3410,46951,01025825,0 cm
fdMA
yd
sds
ODABRANA ARMATURA: 21 60.7222 cmAods
KOMBINACIJE POTREBNE ZA CRTANJE ANVELOPE MOMENTA SAVIJANJA
1. Stalno optereenje :
kNmlgmmm
kNmlgMM
ggg
gC
gB
12,1508
86,744,198
10,12086,744,191,01,022
312111
22
3 0 x 5 03 0 x 5 0 3 0 x 5 0
-1 9 ,4 4 k N /m
120,
10 k
Nm
120,
10 k
Nm
120,
10 k
Nm
120,
10 k
Nm
-1 9 ,4 4 k N /m -1 9 ,4 4 k N /m
7 ,8 6 m 7 ,8 6 m 7 ,8 6 mC 3 5 /4 5 C 3 5 /4 5 C 3 5 /4 5
-9 6 ,0 8 k N m
-3 0 ,0 2 k N m
-9 6 ,0 8 k N m 2. Pokretno optereenje : * 1. kombinacija :
kNmlqm
kNmlqMM
g
qC
q
52,2318
86,798,298
61,9205,022
11
211
7 ,8 6 m3 0 x 5 0
C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 0 x 5 0
7 ,8 6 m3 0 x 5 0
7 ,8 6 m
92,6
1 kN
m
92,6
1 kN
m
92,6
1 kN
m
- 2 9 ,9 8 k N /m -2 9 ,9 8 k N /m
- 1 8 7 ,0 7 k N m -1 8 7 ,0 7 k N m * Anvelopa :
kNmmmm
kNmmmmmkNmMMMMM
qgsd
qgsdsd
qB
gB
gB
Csd
Bsd
66,20205,112,15035,15,135,1
94,54952,2315,112,15035,15,135,1
05,301)61,92(5,1)10,120(35,15,15,135,1
212121,
111131,11,
* 2. kombinacija :
kNmlqm
kNmlqMM
g
qC
q
52,2318
86,798,298
61,9205,022
11
211
7 ,86 m30x50
C 35 /45C 35 /45C 35 /4530x50
7 ,86 m30x50
7 ,86 m
92,6
1 kN
m
92,6
1 kN
m
92,6
1 kN
m
92,6
1 kN
m
2 9 ,98kN /m
-138 ,91 kN m *Anvelopa :
kNmmmm
kNmmmmmkNmMMMMM
qgsd
qgsdsd
qB
gB
gB
Csd
Bsd
94,54952,2315,112,15035,15,135,1
66,20205,112,15035,15,135,1
05,301)61,92(5,1)10,120(35,15,15,135,1
212121,
111131,11,
* 3. kombinacija :
kNmlqmm
kNmlqMkNmlqMM
qg
qC
qC
qB
52,2318
86,798,298
12,61033,0;70,216117,022
2111
22
7,86 m30x50
C35/45C35/45C35/4530x50
7,86 m30x50
7,86 m
29,98kN /m 29,98kN /m
-135,76 kNm -98,72 kNm
61,1
2 kN
m
61,1
2 kN
m
216,
70 k
Nm
216,
70 k
Nm
* Anvelopa :
* 4. kombinacija :
kNmlqmm
kNmlqMkNmlqM
qB
qC
52,2318
86,798,298
12,61033,0;70,216117,022
3121
22
29,98kN /m216,
70 k
Nm
216,
70 k
Nm
29,98kN /m
61,1
2 kN
m
61,1
2 kN
m
30x507,86 m
-135,76 kNm
C 35/45C35/45
-98,72 kN m
30x507,86 mC 35/457,86 m
30x50
* Anvelopa :
kNmmmm
kNmmmm
kNmmmmkNmMMM
kNmMMMM
qgsd
qgsd
qgsd
qC
gC
Csd
qB
gB
gB
Bsd
66,20205,112,15035,15,135,1
94,54952,2315,112,15035,15,135,1
94,54952,2315,112,15035,15,135,1
82,253)12,61(5,1)10,120(35,15,135,1
19,487)70,216(5,1)10,120(35,15,15,135,1
313131,
212121,
111111,
kNmmmm
kNmmmm
kNmmmmkNmMMM
kNmMMMM
qgsd
qgsd
qgsd
qC
gC
Csd
qB
gB
gB
Bsd
94,54952,2315,112,15035,15.135.1
94,54952,2315,112,15035,15,135,1
66,20205,112,15035,15,135,1
19,487)70,216(5,1)10,120(35,15,135,1
82,253)12,61(5.1)10,120(35,15,15,135,1
313131,
212121,
111111,
* 5. kombinacija :
7 ,8 6 m3 0 x 5 0
C 3 5 /4 5C 3 5 /4 5C 3 5 /4 53 0 x 5 0
7 ,8 6 m3 0 x 5 0
7 ,8 6 m
-2 9 ,9 8 k N /m -2 9 ,9 8 k N /m -2 9 ,9 8 k N /m
185,
22 k
Nm
185,
22 k
Nm
185,
22 k
Nm
185,
22 k
Nm
- 1 4 8 ,1 7 k N m -1 4 8 ,1 7 k N m
-2 7 ,7 8 k N m
* Anvelopa :
kNmmmmmmkNmMMMM
qgsdsdsd
qB
gB
Bsd
Csd
94,54952,2315,112,15035,15,135,1
97,439)22,185(5,1)10,120(35,15,135,1
111131,21;11,
kNmlqmmm
kNmlqMM
qqg
qC
qB
52,2318
86,798,298
22,1851,022
312111
2
* 6. kombinacija :
kNmlqm
kNmlqMkNmlqM
q
qC
qB
52,2318
86,798,298
49,31017,0;09,124067,022
11
22
31x50 31x50 31x50
124,09
kNm
124,09
kNm
-31,49
kNm
-31,49
kNm
-166,69kNm
-29,98kN/m
7,86m 7,86m 7,86mC35/45 C35/45 C35/45
* Anvelopa :
kNmmmmm
kNmmmmkNmMMMkNmMMM
qgsdsd
qgsd
qC
gC
Csd
qB
gB
Bsd
66,20205,112,15035,15,135,1
94,54952,2315,112,15035,15,135,1
37,20949,315,1)10,120(35,15,135,1
27,348)09,124(5,1)10,120(35,15,135,1
212131,21,
111111,
* 7. kombinacija :
kNmlqm
kNmlqMkNmlqM
q
qC
qB
52,2318
86,798,298
09,124067,0
49,31017,0
22
31
2
2
31x50
-166,69kNm
7,86mC35/45
-29,98kN/m
124,09
kNm
124,09
kNm
C35/457,86m
-31,49
kNm
-31,49
kNm
31x50
7,86mC35/4531x50
* Anvelopa :
kNmmmmm
kNmmmmkNmMMM
kNmMMM
qgsdsd
qgsd
qC
gC
Csd
qB
gB
Bsd
66,20205,112,15035,15,135,1
94,54952,2315,112,15035,15,135,1
27,348)09,124(5,1)10,120(35,15,135,1
37,209)49,31(5,1)10,120(35,15,135,1
212121,11,
111131,
ANVELOPA MOMENTA SAVIJANJA
DULJINA SIDRENJA ARMATURE
min,,
,, b
provs
regsbanetb IA
AlI
gdje su:
a=1.0 - za ravne ipke Ib,min - minimalna duljina sidrenja
As,reg - potrebna povrina armature
lb - duljina prianjanja
Duljina prianjanja se dobije iz uvjeta da sila kojom se odupire prionjivost betona i armature
bude vea od sile koja djeluje u armaturi ( vidi sliku ) :
bd
ydb
bdydb
ydbbd
sydbbd
bd
ff
l
ffl
flf
AflfPP
4
14
42
2
Minimalna duljina prianjanja : cmll bb 10153,0min, vrstou prianjanja uzimamo iz tablice na str. 493 za odreenu klasu betona:
- za C 35/45 22 /34,0/4,3 cmkNmmNfbd
Duljinu sidrenja raunamo za svaki profil armature koji smo odabrali kod prorauna : Profil = 22cm:
227,5634,0783,34
42,2
4cm
ff
lbd
ydb
2, 28,31 cmA regS ; 2, 21,34 cmA provS
2
,
,, 45,5121,34
28,3127,560,1 cmAA
lIprovs
regsbanetb
cmcmcmll bb 100,332,21513,1927,5634,034,0min,
mjerodavno lb,net=52cm
Profil = 19cm:
259,4834,0783,34
49,1
4cm
ff
lbd
ydb
2, 95,4 cmA regS ; 2, 67,5 cmA provS
2
,
,, 42,4267,5
95,459,480,1 cmAA
lIprovs
regsbanetb
cmcmcmll bb 105,289,11552,1659,4834,034,0min,
mjerodavno lb,net=43cm
Profil = 12cm:
269,3034,0783,34
42,1
4cm
ff
lbd
ydb
2, 55,26 cmA regS ; 2, 64,26 cmA provS
2
,
,, 59,3064,26
55,2669,300,1 cmAA
lIprovs
regsbanetb
cmcmcmll bb 100,182,11543,1069,3034,034,0min,
mjerodavno lb,net=31cm
Horizontalni pomak anvelope momenata savijanja 1) PBABcmda 69.3425.4675.075.0 2) 27.253925.469.05.09.05.05.0 ECcmctgctgdctgza mjerodavno a = 26cm
PODACI POTREBNI ZA POKRIVANJE MOMENTNOG DIJAGRAMA
Odabrana armatura slA ydslsl fAF dz zFM sl*sl *sls MkomM sdM redSdM
Polje 207
722 112
3.80 1.13
132.18 39.30 0.964 42.62
5633.51 1674.97
39434.57 1674.97 41033
Polje 208
422 112
2.84 1.13
98.78 39.30 0.973 44.86
4431.27 1763.00
17725.08 1763.00 24889
Leaj 207-208 922 3.80 132.18 0.811 34.22 4523.20 40708.80 45464 42209 Rubni leaj 222 3.80 132.18 0.951 43.84 5794.77 11589.54 10258
4Proraun grede 207-208-2075Anvelope