7.20 ćenja za polja (položaj opt. 1)imksus.grf.bg.ac.rs/nastava/BETON/PROJEKTOVANJE I...DONJA ZONA...
18
1 1 Donja zona, q u = 1.6×G+1.8×P (totalno opt.) 5.40 7.20 6.00 6.00 5.40 2.40 1.80 2.40 21.5 22.4 27.4 31.0 23.3 16.1 21.5 22.4 20.3 27.4 26.8 22.4 DONJA ZONA M u [kNm/m] C B A 3 4 1 2 qu = 1.6×6 + 1.8×10 = 27.6 kN/m 2 G+P G 2 Šema opterećenja za polja (položaj opt. 1) 5.40 7.20 6.00 6.00 5.40 C B A 3 4 1 2 2.40 1.80 2.40 C D F G C E B A POS 104 POS 103 POS 105 POS 106 POS 107 POS 102 POS 101 A G+P G
Transcript of 7.20 ćenja za polja (položaj opt. 1)imksus.grf.bg.ac.rs/nastava/BETON/PROJEKTOVANJE I...DONJA ZONA...
-
1
1Donja zona, qu = 1.6×G+1.8×P (totalno opt.)
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40
21.5
22.4
27.431
.023.3
16.1
21.5
22.4
20.3
27.4
26.822
.4
DONJA ZONA
Mu [kNm/m]C
B
A
3 41 2
qu = 1.6×6 + 1.8×10 = 27.6 kN/m2
G+P
G
2Šema opterećenja za polja (položaj opt. 1)
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
C D
F G C
E B
A
POS
104
POS 103
POS
105
POS
106
POS
107
POS 102
POS 101
A
G+P
G
-
2
3
45 150 45
p1 = p2 = 20 kN/mp1 = 20 kN/m
p2 = -20 kN/m
165 75150140.63
M [kNm]
T [kN]
dy [mm]
M [kNm]
T [kN]
dy [mm]
4
2u mkN6.270.108.10.66.1q =×+×=
21u mkN6.18
20.108.10.66.1q =×+×= 22u m
kN0.92
0.108.1q ±=×±=
mkNm5.145.21
6.276.18MC
X,1u=×=
mkNm5.184.27
6.276.18M
...
...m
kNm1.154.226.276.18M
G
C
Y,1u
Y,1u
=×=
=×=
-
3
5Donja zona, qu1 = 1.6×G+1.8×P/2
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40
14.5
15.1
18.5
20.9
15.7
10.8
14.5
15.1
13.7
18.5
18.1
15.1
DONJA ZONA
Mu1 [kNm/m]C
B
A
3 41 2
qu1 = 1.6×6 + 1.8×102 = 18.6 kN/m
2
6
Donja zona, ploče C,E,F: qu2 = ±1.8×P/2
Lx = 5.40
L y =
6.0
0
Mx = 13.7
My
= 12
.0
1.14.50.6
LL
x
y ≈=
mkNm7.130.64.50.9047.0Mxu =×××=
yx2uxu LLq047.0M ×××=
mkNm0.120.64.50.9041.0Myu =×××=
yx2uyu LLq041.0M ×××=
-
4
7
Donja zona, ploče D,G: qu2 = ±1.8×P/2
Lx = 6.00
L y =
7.2
0
Mx = 19.1
My
= 14
.8
2.10.62.7
LL
x
y ==
mkNm1.192.70.60.9049.0Mxu =×××=
yx2uxu LLq049.0M ×××=
mkNm8.142.70.60.9038.0Myu =×××=
yx2uyu LLq038.0M ×××=
8Donja zona, qu2 = ±1.8×P/2
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40
-13.7
-12.
0
14.8
19.1
-13.7
-12.
0
13.7
12.0
-14.8
-19.
1
13.7
12.0
DONJA ZONA
Mu2 [kNm/m]C
B
A
3 41 2
qu2 = 1.8×102 = 9 kN/m
2
+P2
-P2
-
5
9Šema opterećenja za polja (položaj opt. 2)
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
C D
F G C
E B
APO
S 10
4POS 103
POS
105
POS
106
POS
107
POS 102
POS 101
A
+P2
-P2
10Donja zona, ±1.8×P/2
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40
-13.7
-12.
0
14.8
19.1
-13.7
-12.
0
13.7
12.0
-14.8
-19.
1
13.7
12.0
DONJA ZONA
Mu2 [kNm/m]C
B
A
3 41 2
qu2 = 1.8×102 = 9 kN/m
2
+P2
-P2
-
6
11Donja zona, qu1+qu2 (ekstremni uticaji)
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40
28.2
27.0
33.3
39.9
29.4
22.8
28.2
27.0
28.4
37.5
31.8
27.0
DONJA ZONA
Mu [kNm/m]C
B
A
3 41 2
qu = 1.6×6.0 + 1.8×10.0 = 27.6 kN/m2
12Potrebna armatura – donja zona (RA 400/500)
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40 DONJA ZONA
C
B
A
3 41 2
6.12
5.30
7.29
7.97
6.40
4.45
5.30
6.18
7.46
5.30
Aa [cm2/m]
Ø12
/12.
5
6.95 6.12
Ø10/12.5
Ø12/15 Ø10/12.5 Ø10/12.5
Ø12/15 Ø12/15
Ø12
/20
Ø10
/15
Ø12
/20
Ø12
/20
Ø12
/15
-
7
13Potrebna armatura – donja zona (MA 500/560)
5.407.20
6.00
6.00
5.40
2.40
1.80
2.40 DONJA ZONA
C
B
A
3 41 2
4.90
4.24
5.83
6.37
5.12
3.56
4.24
4.95
5.97
4.24
Aa [cm2/m]
Q-636
Q-6365.56 Q-636
Q-524Q-524
4.90 Q-524
14Gornja zona, qu = 1.6×G+1.8×P (totalno opt.)
G+P
G79.5
52.8
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40 GORNJA ZONA
Mu [kNm/m]
52.8
58.1
73.9
63.2
46.5
52.8
63.2
79.5
52.8
79.5
62.6 56.0 56.0 52.8
52.8 69.2 69.2 53.7 53.7 44.7
79.5
55.4
68.6
49.6
79.5
79.5
59.3 54.4
61.0 61.4 44.7
-
8
15Šema opterećenja za oslonac u osi 2 (deo A-B)
G+P
G
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
POS
104
POS 103
POS
105
POS
106
POS
107
POS 102
POS 101
A
-X -X
-X -X
16
2u mkN6.270.108.10.66.1q =×+×=
21u mkN6.18
20.108.10.66.1q =×+×= 22u m
kN0.92
0.108.1q ±=×±=
mkNm4.336.49
6.276.18Y
...
...m
kNm4.374.556.276.18Y
43/B
21/B
1u
1u
=×=−
=×=−
−
−
mkNm7.364.54
6.276.18X
...
...m
kNm1.410.616.276.18X
CB/3
BA/2
1u
1u
=×=−
=×=−
−
−
-
9
17Gornja zona, qu1 = 1.6×G+1.8×P/2
53.6
35.6
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40 GORNJA ZONA
Mu1 [kNm/m]
35.6
39.2
49.8
42.6
31.3
35.6
42.6
53.6
35.6
53.6
42.2 37.8 37.8 35.6
35.6 46.6 46.6 36.2 36.2 30.1
53.6
37.4
46.2
33.4
53.6
53.6
40.0 36.7
41.1 41.4 30.1
18
Gornja zona, X pravac, ploča C1: qu2 = ±1.8×P/2
-XC1
Lx = 5.40
L y =
6.0
0
1.14.50.6
LL
x
y ≈=
mkNm5.240.64.50.9084.0X 2u =×××=−
yx2u2u LLq084.0X ×××=−
-
10
19
Gornja zona, X pravac, ploča D1: qu2 = ±1.8×P/2
-Y D1
Ly = 7.20
L x =
6.0
0
2.10.62.7
LL
x
y ==
mkNm3.322.70.60.9083.0Y 2u =×××=−
yx2u2u LLq083.0Y ×××=−
20Oslonac u osi 2 (deo A-B), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
C1
C1 D1
D1
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
24.5 32.328.4
-24.5 -32.3-28.4
-
11
21Oslonac u osi 2 (deo B-C), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
C1
C1 D1
D1
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
24.5 32.328.4
-24.5 -32.3-28.4
22Oslonac u osi 3 (deo A-B), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
C1
C1D1
D1
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
24.532.328.4
-24.5-32.3-28.4
-
12
23Oslonac u osi 3 (deo B-C), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
C1
C1D1
D1
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
24.532.328.4
-24.5-32.3-28.4
24
Gornja zona, Y pravac, ploča C2: qu2 = ±1.8×P/2
-Y
C2
Lx = 5.40
L y =
6.0
0
1.14.50.6
LL
x
y ≈=
mkNm5.240.64.50.9084.0Y 2u =×××=−
yx2u2u LLq084.0Y ×××=−
-
13
25
Gornja zona, Y pravac, ploča D2: qu2 = ±1.8×P/2
D2
-X
Ly = 7.20
L x =
6.0
0
2.10.62.7
LL
x
y ==
mkNm9.312.70.60.9082.0Y 2u =×××=−
yx2u2u LLq082.0Y ×××=−
26Oslonac u osi A (deo 1-2), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
C2
25.9
24.5
25.9
-
14
27Oslonac u osi B (deo 1-2, 3-4), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
C2 D2
C2 D2
C2
C2
-31.
9-3
1.9
-31.
9
24.5
24.5
24.5
24.5
24.5
24.5
28Oslonac u osi B (deo 2-3), qu2 = ±1.8×P/2
Mu2 [kNm/m] qu2 = 1.8×102 = 9 kN/m2
+P2
-P2
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
C2 D2
C2 D2
C2
C2
31.9
31.9
31.9
-24.
5-2
4.5
-24.
5
-24.
5-2
4.5
-24.
5
-
15
29Oslonac u osi C (deo 2-3), qu2 = ±1.8×P/2
Mu2 [kNm/m]
qu2 = 1.8×102 = 9 kN/m
2
+P2
-P2
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
D2 C2
31.9
25.9
25.9
-24.
5-2
4.5
-24.
5
30Oslonac u osi C (deo 3-4), qu2 = ±1.8×P/2
Mu2 [kNm/m]
qu2 = 1.8×102 = 9 kN/m
2
+P2
-P2
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40
C2D2
25.9
24.5
25.9
-31.
9-2
5.9
-25.
9
-
16
31Gornja zona, qu2 = ±1.8×P/2
25.9
24.5
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40 GORNJA ZONA
Mu2 [kNm/m]
24.5
24.5
31.9
31.9
24.5
24.5
31.9
25.9
24.5
25.9
24.5 32.3 32.3 24.5
24.5 32.3 32.3 24.5 24.5 14.6
25.9
24.5
31.9
24.5
25.9
25.9
28.4 28.4
28.4 28.4 14.6
32Gornja zona, qu1+qu2 (ekstremni uticaji)
79.5
60.1
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40 GORNJA ZONA
Mu [kNm/m]
60.1
63.7
81.7
74.5
55.8
60.1
74.5
79.5
60.1
79.5
66.7 70.0 70.0 60.1
60.1 78.9 78.9 60.7 60.7 44.7
79.5
61.9
78.1
57.9
79.5
79.5
68.4 65.0
69.5 69.8 44.7
-
17
33Potrebna armatura – gornja zona
5.407.20
6.00
6.00
5.40
C
B
A
3 41 2
2.40
1.80
2.40 GORNJA ZONA17.7
0
Aa [cm2/m]
13.0
1
16.9
8
12.1
0
(17.76) 17.76 10.52
RØ
16/1
0
17.7
0 RØ16
/10
17.7
0 RØ16
/10
RØ
16/1
0
RØ
16/1
5
RØ
16/1
5
RØ16/10RØ16/10
(17.76)
RØ16/10
16.32RØ16/10
RØ12/10
34Šema armiranja – donja zona
C
B
A
3 41 2
720540 540
600
600
240
180
240
Ø12/15 Ø12/15Ø10/12.5
Ø10/12.5 Ø10/12.5Ø12/15
Ø12
/12.
5
Ø12
/20
Ø10
/15
Ø12
/20
Ø12
/20
Ø12
/15
-
18
35Šema armiranja – gornja zona
C
B
A
3 41 2
720540 540
600
600
240
180
240
Ø16/10
Ø16
/10
Ø16
/15
Ø16
/15
Ø16
/10
Ø16
/10
Ø16
/10
Ø16/10
Ø16/10
Ø16/10 Ø12/10
36Šema armiranja – gornja zona
C
B
A
3 41 2
720540 540
600
600
240
180
240
Ø16/10
Ø16
/10
Ø16
/15
Ø16
/15
Ø16
/10
Ø16
/10
Ø16
/10
Ø16/10
Ø16/10
Ø16/10 Ø12/10
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