1
BETONSKE KONSTRUKCIJE 1
Vežba br.15
2
g = 30 kN/m
MB 30
p = 20 kN/m
RA 400/500
1
3
378
336
4
672 252
420
2
Presek u polju:
5
Presek nad osloncem:
B-B
C-C
2RØ22
2RØ12
4RØ22
2RØ22
URØ8/20
URØ10/20 4RØ22
5RØ22
2RØ12
2RØ22
Osiguranje glavnih napona zatezanja: 672 336 252
6
420
A mu
T
336 = 336 kN Þ t = = 0.201 kN / cm 2 35 ´ 47.7 A n
C ,l Tmu = 420 kN Þ tCn,l =
C ,d Tmu = 252 kN Þ t An =
420 = 0.252 kN / cm2 35 ´ 47.7 252 = 0.151 kN / cm 2 35 ´ 47.7
3
MB30 Þ tr=1.1 MPa
7
tn
tA n =2.01
tC,l n =2.52
8
Presek C levo: C,l mu
T
= 420 kN Þ t
C,l n
2 ì 420 2 ï > tr = 0.11 kN / cm = = 0.252 kN / cm í 2 35 ´ 47.7 ïî< 3tr = 0.33 kN / cm
3´ 0.11- 0.252 ´35´ 47.7 = 65.5 kN 2 TRu = Tmu - Tbu = 420- 65.5 = 354.5 kN
Tbu =
tRu =
TRu 354.5 = = 0.212 kN / cm2 b ´ z 35´ 47.7 pp. URØ10; aa(1)=0.785cm2; m=2
eu =
2 ´ 0.785 ´ 40 ´ (0 + 1 ´ 1) = 10.76 ´ a (u1) = 8.45 cm 35 ´ 0.212
4
m ´ a (u1) 2 ´ 0.785 eu £ = = 22.4 cm b ´ m uz ,min. 35 ´ 0.2 ´ 10-2
9
ì b = 35 cm ü ï ï e u £ min .í h 2 = 26.5 cm ý Þ usv.e u = 20 cm ï ï 25 cm î þ
t
(1) u ,u
m ´ a (u1) = ´ s v ´ (cos a + sin a ´ ctgq) b ´ eu
Usvojimo: URØ10/20
t(u1,)u =
2 ´ 0.785 ´ 40 ´ (0 + 1 ´ 1) = 0.090 kN / cm 2 35 ´ 20
10
tn tu,u
5
11
t(1) 0.90 l 2 ´ uC,,ul = 281.4 ´ = 119 cm 2.12 t Ru
Dl 2 = 281.4 - 119 = 162.4 cm DtCRu,l = tCRu,l,max - t(u1,)u = 2.12 - 0.90 = 1.22 MPa pp. URØ12; aa(1)=1.13 cm2; m=2
eu =
2 ´ 1.13 ´ 40 = 21.17 cm 35 ´ 0.122
t(1) u,u =
URØ12/20
2 ´ 1.13 ´ 40 = 0.129 kN / cm 2 35 ´ 20 Ukupno usvojeno: URØ10/20
+
URØ12/20
2 t(1) u,u = 0.09 + 0.129 = 0.219 kN / cm
12
(URØ10/20)
6
13
H vu ,k = A t ´ b æ 0.212 - 0.090 ö H vu ,k = ç ´ 162.4 ÷ ´ 35 = 348.5 kN 2 è ø
A a ,k =
H vu ,k s v ´ (cos ak + sin a k ´ ctgq)
ak=45o ; q=90o A a,k =
348.5 348.5 = = 6.16 cm 2 40 ´ ( 0.707 + 0.707 ´1.0 ) 40 ´ 2 Usvojeno 2RØ22 (7.60cm2)
14
tRu-tu,u
7
15
tRu-tu,u
tRu-tu,u
DUŽINA OSIGURANJA
DUŽINA OSIGURANJA
KOSIM PROFILIMA
KOSIM PROFILIMA
tRu-tu,u
16
tRu-tu,u
8
17
18
Presek A: A = 336 kN Þ tAn = Tmu
TbuA =
2 336 ïì > tr = 0.11 kN / cm = 0.201 kN / cm 2 í 2 35 ´ 47.7 ïî< 3tr = 0.33 kN / cm
3 ´ 0.11 - 0.201 ´ 35 ´ 47.7 = 107.5 kN 2
TRu = Tmu - Tbu = 336- 107.5 = 228.5 kN
tRu =
228.5 = 0.137 kN / cm2 35´ 47.7 pp. URØ10; aa(1)=0.785cm2; m=2
eu =
2 ´ 0.785 ´ 40 ´ (0 + 1 ´ 1) = 16.7 ´ a (u1) = 13.1 cm 35 ´ 0.137
9
19
tn
A tRu =1.37
t(1) u,u = 0.90
t(2) u,u = 1.47
tA n =2.01
tu,u
tRu
t(u1,)u 0.90 l1 ´ A = 181.4 ´ = 119 cm t Ru 1.37
20
Dl1 = 181.4 - 119 = 62.4 cm
Dt ARu = t ARu ,max - t(u1,)u = 1.37 - 0.90 = 0.047 MPa pp. URØ8; aa(1)=0.50cm2; m=2
eu = t(1) u,u
2 ´ 0.50 ´ 40 = 24.3 cm 35 ´ 0.047 2 ´ 0.5 = ´ 40 = 0.057 kN / cm 2 35 ´ 20
URØ8/20
Ukupno usvojeno URØ10/20
+
URØ8/20
2 t(1) u,u = 0.09 + 0.057 = 0.147 kN / cm
10
21
Presek C desno:
tC,d n =1.51
tn
tC,d Ru =0.61
C,d = 252 kN Þ tAn = Tmu
TbuC,d =
ìï > tr = 0.11 kN / cm2 252 = 0.151 kN / cm 2 í 2 35 ´ 47.7 ïî< 3tr = 0.33 kN / cm
22
3 ´ 0.11 - 0.151 ´ 35 ´ 47.7 = 149.5 kN 2
TRu = Tmu - Tbu = 252 - 149.5 = 102.5 kN tRu =
102.5 = 0.061 kN / cm2 35´ 47.7
eu =
2 ´ 0.785 ´ 40 = 37.2 ´ a (1) u 35 ´ 0.061 pp. URØ10; aa(1)=0.785cm2
eu = 29.2 cm
Usvojeno URØ10/20
11
23
LINIJA ZATEŽUĆIH SILA:
Zau = A a ´ s v =
M au - Nu zb
æd ö M au = M u + N u ´ y a1 = M u + N u ´ ç - a 1 ÷ è2 ø M au z b » 0.9 ´ h Þ Zau » - Nu 0.9 ´ h Za Nu=0:
Zau »
M au 0.9 ´ h
gornja zona : Zau »
378 = 792.5 kN 0.9 ´ 53
donja zona : Zau »
672 = 1408.8 kN 0.9 ´ 53
24
A
B
C
D
12
A
B
D 25
C
v=40 v=40
v=40
v=40
POMERANJE LINIJE ZATEŽUCIH SILA:
v = 0.75×h = 0.75×53 = 39.75 » 40 cm
v = 0.75 ´ h (uzengije) v = 0.50 ´ h (uzengije + kosa armatura )
26
usvojeno nad osloncem: 6RØ22 B
C
D
Z(1) au Z(1) au Z(1) au
v=40
Z(1) au
v=40
Z(1) au
6×Z(1) au
Z(1) au
A
v=40
v=40
usvojeno u polju: 9RØ22
13
UKUPNA DUŽINA ŠIPKE
27 Ls2 B
Ls2
C
D
Z(1) au
6×Z(1) au
Z(1) au
Z(1) au
A
STATICKI POTREBNA DUŽINA ŠIPKE
Z(1) au
v=40
Z(1) au
Z(1) au
v=40
v=40
v=40
5 DUŽINA SIDRENJA: Ls1
Ls1
STATICKI POTREBNA DUŽINA ŠIPKE
Ls1 = 70 cm (dobra adhezija) Ls2 = 105 cm (loša adhezija)
UKUPNA DUŽINA ŠIPKE
28
sv sv Ø Ø = ´ Ls = ´ 4 g u ´ t p 4 1.8 ´ t p
Vrednosti napona prianjanja t p MB
15
20
30
40
50
60
GA
0.60
0.67
0.76
0.85
0.92
0.98
RA
1.20
1.40
1.75
2.10
2.45
2.80
L s1 =
2.2 400 ´ = 69.8 » 70 cm 4 1.8 ´ 1.75
L s 2 = 1.5 ´ L s1 = 105 cm
(Za uslove loše adhezije sračunato sa 2/3tp)
14
29
UKUPNA DUŽINA ŠIPKE
STATICKI POTREBNA DU ŽINA ŠIPKE
Ls2
A
B
Ls2
C
D
6
7
v=40 v=40
8
8
1
1
v=40
2
2 3
3 v=40
4
4
POMERANJE LINIJE ZATE ŽUCIH SILA:
v = 0.75×h = 0.75×53 = 39.75 » 40 cm
5
Ls1
5
STATICKI POTREBNA DU ŽINA ŠIPKE
DUŽINA SIDRENJA :
Ls1 = 70 cm (dobra adhezija) Ls2 = 105 cm (loša adhezija)
Ls1
UKUPNA DUŽINA ŠIPKE
0 8 .1 0 .1 9 9 8 .
PO S 1 - G R ED A SA PR EPU STO M
L ist 1 /1
30
15
C O N FID EN TIA L !
31
A
B
C
D
32
11 2RØ12 L=650 630 13 3URØ8/20
8 2RØ22
1
10 2RØ22
2
7 2RØ22
63.4
10
10
55
3 2RØ22
11 2RØ12
7 2RØ22
48
55 30
55
3
12
10
60
30
10
30
30
55
11 2RØ12
12 29URØ10 L=190
13 33URØ8 L=190
30
30
12 9URØ10/20
13 20URØ8/20
12 15URØ10/20
1 25
25
160
20
12 5URØ10/20
2
5 2RØ22
380
20
50
13 10URØ8/20
3
280
80
860
20
180
30
5
285
1225
5 2RØ22 L=620 4.5
620
65
25
45.5
64
105
3 2RØ22 L=1026 832
45
45.5
2 1RØ22 L=930
4.5
25
45
885
9 2RØ22 L=360 1 2RØ22 L=1005
335
960
6
6
POMERENA LINIJA ZATEŽUĆ IH SILA LINIJA ZATEŽUĆ IH SILA
2Ø22
1
40 8
9
2Ø22
1Ø22
2Ø22
40 10
SPECIFIKACIJA ARMATURE
3
Lg
n
SLg
Ø
g1
[mm]
[cm]
[kom.]
[m]
[mm]
[kg/m]
[m]
[kg]
1
22
1005
2
20.10
8
0.405
62.70
25.4
2
22
930
1
9.30
10
0.633
55.10
34.9
3
22
1026
2
20.52
12
0.911
26.00
23.7
2
15.20
22
3.058
129.12
394.8
2
12.40
UKUPNO:
478.8
Ø
2Ø22
v = 40
2Ø22
4
5
4 5
4.5
4.5 6.5
13
6.5 4.5
35
4.5
12
5.5 4.5 8 7 6
7 8 6
1 3
3 1
22 22
760 620
22
355
2
7.10
7
22
470
2
9.40
8
22
895
2
17.90
KOLICINE MATERIJALA OPLATA: 16.468 m 2
2
7.20
BETON (MB 30):
2
10.00
ARMATURA (RA 400/500): 478.8 kg
9
22
360
10
22
500
11
12
650
4
26.00
12
10
190
29
55.10
13
8
190
33
62.70
478.8 2.573
26 35
4.5
= 186.13
2.573 m 3
kg/m3 betona
2RØ22 URØ10/20
2RØ12
8 7 6 3
7 8 3 6
GODIŠNJI ZADATAK - LIST br.6 9
2RØ22 4.5
SG
6
25.5
2RØ12
60
2RØ22 URØ10/20
5RØ22 4x6.5=26
20
12
5.5 4.5 60
20 5 4 4 5 1 3 2 3 1
4.5
6.5 4.5 4RØ22
25.5
20 4.5 5.5
10
48
60
10
4RØ22
4.5
25.5
2RØ12
URØ8/20
13
4RØ22
12
4.5
2RØ22
4.5 6.5
4.5
26
PRESEK 3-3 R 1:10
48
4.5
PRESEK 2-2 R 1:10
SLg
48
PRESEK 1-1 R 1:10
REKAPITULACIJA ARMATURE
9
2RØ22 4.5
26
4.5
PLAN ARMATURE POS 1
35
MB 30 RA 400/500
R 1:20
A1...840x594
16
33
PRESEK 1-1 R 1:10 4.5
26
4.5
25.5
12
4.5
2RØ22
2RØ12
4.5 5.5
20
4RØ22
10
48
60
10
URØ8/20
5 4 4 5 1 3 2 3 1
5RØ22 4.5
4x6.5=26
4.5
35
PRESEK 2-2 R 1:10 4.5 6.5
13
34
6.5 4.5
2RØ22 URØ10/20
7 8 6
1 3
3 1
4.5
25.5
2RØ12
8 7 6
48
60
20
12
5.5 4.5
4RØ22
2RØ22 4.5
26
4.5
35
17
PRESEK 3-3 R 1:10 4.5 6.5
13
35
6.5 4.5
2RØ22 URØ10/20
7 8 3 6
4.5
25.5
2RØ12
8 7 6 3
48
60
20
12
5.5 4.5
4RØ22
9
9
2RØ22 4.5
26
4.5
35
18
