POS 1a, POS 1b L POS 2 L d = 20 cm L g = 2.0 kN/m POS S p...
20
1 1 L 1 POS 2 POS 1a POS S L 2 POS 1b d s ∆g, p POS 1a, POS 1b L 1 = 3.0 m L 2 = 2.0 m d p = 20 cm ∆g = 2.0 kN/m 2 p = 5.0 kN/m 2 POS S λ = 6.0 m b = 25 cm 2 POS 1a sopstvena težina ploče d p ×g b = 0.20×25.0 = 5.0 kN/m 2 dodatno stalno opterećenje: ∆g = 2.0 kN/m 2 ukupno stalno opterećenje: g = 7.0 kN/m 2 povremeno opterećenje: p = = 5.0 kN/m 2 300 M g T g 31.5 21 g = 7.0 kN/m 2 p = 5 kN/m 2 22.5 15 M p T p 300
Transcript of POS 1a, POS 1b L POS 2 L d = 20 cm L g = 2.0 kN/m POS S p...
1
1
L1
POS 2
POS 1a
POS S
L2
POS 1b
ds
∆g, p
POS 1a, POS 1bL1 = 3.0 mL2 = 2.0 mdp = 20 cm∆g = 2.0 kN/m2
p = 5.0 kN/m2
POS Sλ = 6.0 mb = 25 cm
2POS 1asopstvena težina ploče dp×γb = 0.20×25.0 = 5.0 kN/m2
dodatno stalno opterećenje: ∆g = 2.0 kN/m2
ukupno stalno opterećenje: g = 7.0 kN/m2
povremeno opterećenje: p = = 5.0 kN/m2
300
Mg
Tg
31.5
21
g = 7.0 kN/m2 p = 5 kN/m2
22.5
15
Mp
Tp
300
2
3POS 1aMu = 1.6×31.5 + 1.8×22.5 = 90.9 kNm/mpretp. a1 = 3 cm ⇒ h = 20 – 3 = 17 cmMB 30 ⇒ fB = 20.5 MPa
%.‰/./
.
.. 82616
1082525532
052990
17k ab
=µ=εε
⇒==
mcm6614
400521782616A
2
potra ...., =××=
usvojeno: RØ14/10 (15.40 cm2/m)
Aap,potr. = 0.20×14.66 = 2.93 cm2/musvojeno: RØ10/25 (3.14 cm2/m)
4
1 RØ14/10
3 11RØ10/ 25
20
d
b=ds
300 200
A
POS 1a – usvojena armatura
3
5POS 1bsopstvena težina ploče dp×γb = 0.20×25.0 = 5.0 kN/m2
dodatno stalno opterećenje: ∆g = 2.0 kN/m2
ukupno stalno opterećenje: g = 7.0 kN/m2
povremeno opterećenje: p = = 5.0 kN/m2
Mg
Tg
200
1414
p = 5 kN/m2
1010
g = 7.0 kN/m2
200
Mp
Tp
6POS 1bMu = 1.6×14 + 1.8×10 = 40.4 kNm/mpretp. a1 = 3 cm ⇒ h = 20 – 3 = 17 cm
%.‰/./
.
.. 1517
1047518293
052440
17k ab
=µ=εε
⇒==
mcm236
40052171517A
2
potra ...., =××=
usvojeno: RØ14/20 (7.70 cm2/m)
Aap,potr. = 0.20×6.23 = 1.25 cm2/mAap,min. = 0.085×20 = 1.70 cm2/m > Aap,potr.
usvojeno: RØ8/25 (2.01 cm2/m)
4
7
1 RØ14/10
3 11RØ10/ 25 4 7RØ8/ 25
2 RØ14/20
20
A
1 RØ14 L=403
50
33815
2 RØ14 L=303
15238
50
POS 1a, 1b – usvojena armatura (varijanta 2)
8
3 11RØ10/ 25
4 7RØ8/ 25230
RØ
14/2
0
160
RØ
14/1
0
160
RØ
14/1
0 L=
403
(60)
50
338
15
230
RØ
14/2
0 L=
303
(30)
15
238
50
300
200
A
5 4
600
POS 1a, 1b – armatura u osnovi (varijanta 2)
5
9
20
A3 11RØ10/ 25 4 7RØ8/ 25
300 200
2 RØ14/20
1 RØ14 L=403
50
33815
2 RØ14 L=526
15 496 15
2 RØ14/201 RØ14/20,
POS 1a, 1b – usvojena armatura (varijanta 1)
1030
020
0
A
5 4
600
3 11RØ10/ 25
4 7RØ8/ 25
130
RØ
14/2
0
130
RØ
14/2
0 L=
403
(30)
50
338
15
230
RØ
14/2
0
230
RØ
14/2
0 L=
526
(30)
15
496
15
POS 1a, 1b – armatura u osnovi (varijanta 1)
6
11POS 2stalno opterećenje:
mTg = 31.5 – 14 = 17.5 kNm/mg = 21 – (–14) = 35.0 kN/m
L1 = 3.0 m
Mg
Tg
L2 = 2.0 m
POS 1a POS 1b
14g(2)
m(2
)Tg
g = 7.0 kN/m2 g = 7.0 kN/m2
21.0
31.5
14
14
21
14.0
A A A
L1 = 3.0 L2 = 2.0
S.T.POS 2
31.5 14.0
12POS 2povremeno opterećenje na POS 1a:
mTp1 = 22.5 – 0 = 22.5 kNm/mp1 = 15 – 0 = 15.0 kN/m
15.0
A A A
L1 = 3.0 L2 = 2.0
22.5
p = 5 kN/m2
p(2)
1m
(2)
Tp1
POS 1bPOS 1a
Mp1
Tp1
0
0
3.0 m 2.0 m
22.5
15
7
13POS 2povremeno opterećenje na POS 1b:
mTp2 = 0 – 10 = –10.0 kNm/mp2 = 0 – (-10) = 10.0 kN/m
L1 = 3.0 m L2 = 2.0 m
POS 1a POS 1bA A A
L1 = 3.0 L2 = 2.0
p(2)
2m
(2)
Tp2
Tp2
Mp2
0
0
p = 5.0 kN/m2
10
10
10.010.0
14POS 2 - dimenzionisanje prema MT
MTg = 17.5×6.0/2 = 52.5 kNmMTp1 = 22.5×6.0/2 = 67.5 kNmMTp2 = –10×6.0/2 = –30 kNm
6.00mTg = 17.5 kNm/m
MTg
6.00mTP1 = 22.5 kNm/m
MTp1
6.00mTp2 = 10 kNm/m
MTp2
52.5
52.5
67.5
67.5
30
30
8
15POS 2 - dimenzionisanje prema MT
MTu = 1.6×52.5 + 1.8×67.5 = 205.5 kNmMB 30 ⇒ τr = 1.1 MPa
r200b
TuMn 4
cmkN440
A2M
T τ==δ××
=τ .
( ) ( )a2da2bdbA 000b −×−=×=
( ) ( )8
a2da2b8
db8
d 00m0
−−===δ
,.min,.min
pretp. a = 4.5 cm, b ≤ d:
( ) ( )9d9bdbA 000b −×−=×=
16
b
Ab0 Ab0 dd 0a
aa b0
b
aδ
δ
a
1 4RØ16
d
1 4RØ16
a b0
13R
Ø16
13R
Ø16
d 0a
a
2 UØ12/10
9
17
( ) ( ) 32
2 cm1868184402
10520589d9b =×
××=−×−
..
7068.6658580.860
10097.355125120.150
d usv.db
usvojeno: b / d = 85 / 60 cm
( ) ( )440
89b9d9b2
1052058
9b 2
0 ..=
−×−×−×
×⇒
−=δ
18
10
19
6.0 m
mTg = 17.5 kNm/m
MTg
6.0 m
mTp1 = 22.5 kNm/m
MTp1
6.0 m
mTp2 = 10 kNm/m
MTp2
30
30
67.5
67.5
52.5
52.5
stalno opt. povremeno opt.sa POS 1a
povremeno opt.sa POS 1b
g = 47.8 kN/m
Mg
Tg
p1 = 15 kN/m
Mp1
Tp1
p2 = 10 kN/m
Mp2
Tp2
143.3
143.371.6
143.3 143.3
30
30
45
45
45 45
22.5
30 30
15
20
11
21
22
6.0 m
mTg = 17.5 kNm/m
MTg
6.0 m
mTp1 = 22.5 kNm/m
MTp1
6.0 m
mTp2 = 10 kNm/m
MTp2
30
30
67.5
67.5
52.5
52.5
stalno opt. povremeno opt.sa POS 1a
povremeno opt.sa POS 1b
g = 47.8 kN/m
Mg
Tg
p1 = 15 kN/m
Mp1
Tp1
p2 = 10 kN/m
Mp2
Tp2
143.3
143.371.6
143.3 143.3
30
30
45
45
45 45
22.5
30 30
15
12
23
24
13
25
6.0 m
mTg = 17.5 kNm/m
MTg
6.0 m
mTp1 = 22.5 kNm/m
MTp1
6.0 m
mTp2 = 10 kNm/m
MTp2
30
30
67.5
67.5
52.5
52.5
stalno opt. povremeno opt.sa POS 1a
povremeno opt.sa POS 1b
g = 47.8 kN/m
Mg
Tg
p1 = 15 kN/m
Mp1
Tp1
p2 = 10 kN/m
Mp2
Tp2
143.3
143.371.6
143.3 143.3
30
30
45
45
45 45
22.5
30 30
15
26
14
27
28
1 4RØ16
1 4RØ16
1 2RØ16
4.5
85
2525.54.5 25.5
20
4.5
25.5
25.5
4.5
60
Potencijalni raspored podužne armature (var. 1)
15
29
1 4RØ12
1 4RØ12
1 2RØ12
4.52525.54.5 25.5
4.5
25.5
25.5
4.5
602 3RØ12
2 3RØ12
2 2RØ12
2 2RØ12
85
Potencijalni raspored podužne armature (var. 2)
30
1 4RØ12
1 4RØ12
1 2RØ12
4.52525.54.5 25.5
4.5
25.5
25.5
4.5
60
85
3 3RØ16
16
31
4.5
25.5
25.5
4.5
60
4.5
85
2525.54.5 25.5
1 4RØ12
1 4RØ12
1 2RØ12
6 6RØ22
2 2RØ12
2 2RØ12
3 3RØ16
32Podužni presek POS 2
17
33Usvojeni preseci POS 2 – presek nad osloncem
1 4RØ16
1 4RØ16
1 2RØ16
6 RUØ12/20
5 RUØ12/10
3 5RØ224.
525
.525
.54.
5
60
4.5
85
2525.54.5 25.5
34Usvojeni preseci POS 2 – presek u polju
4.5
25.5
25.5
4.5
60
4.5
85
2525.54.5 25.5
1 4RØ16
1 4RØ16
1 2RØ16
8 RUØ10/20
7 RUØ10/20
4 2RØ16
18
35Proračun stuba POS S
λ
q
λ λ
λ λ
λ
q
q q
λPOS S
POS 2
λ
36
6.0 m
mTg = 17.5 kNm/m
MTg
52.5
52.5
g = 47.8 kN/m
Mg
Tg
143.3
143.371.6
143.3 143.3
6.0 m
mTg = 17.5 kNm/m
MTg
52.5
52.5
g = 47.8 kN/m
Mg
Tg
143.3
143.371.6
143.3 143.3
GP
OS
SM
POS
Sg
19
37
6.0 m
mTg = 17.5 kNm/m
MTg
6.0 m
mTp1 = 22.5 kNm/m
MTp1
6.0 m
mTp2 = 10 kNm/m
MTp2
30
30
67.5
67.5
52.5
52.5
stalno opt. povremeno opt.sa POS 1a
povremeno opt.sa POS 1b
g = 47.8 kN/m
Mg
Tg
p1 = 15 kN/m
Mp1
Tp1
p2 = 10 kN/m
Mp2
Tp2
143.3
143.371.6
143.3 143.3
30
30
45
45
45 45
22.5
30 30
15
38
g
Mg=105
G=286.5
Mp1=135
P1=90
Mp2=60
P2=60
H105
135
60
20
39
40
4.5
1 2RØ14
1 3RØ14
1 2RØ14
22R
Ø12
22R
Ø12
3 RUØ10/20
16
L 1 =
3.0
mL 2
= 2
.0 m
2 2RØ16
1 2RØ16
1 2RØ16
4 RUØ10/20
32R
Ø12
32R
Ø12
4.5
var. Ø14 var. Ø16
25
