15 - greda sa prepustom
TRANSCRIPT
1
1
BETONSKE KONSTRUKCIJE 1
Vežba br.15
2
g = 30 kN/m MB 30
p = 20 kN/m RA 400/500
2
3
4
336
420
252
672
378
3
5
URØ8/204RØ22
5RØ22
2RØ12
B-B2RØ22
2RØ12
2RØ22
2RØ22
URØ10/20
4RØ22C-C
Presek u polju: Presek nad osloncem:
6
336
420
252
672Osiguranje glavnih napona zatezanja:
2l,Cn
l,Cmu cm/kN252.0
7.4735420kN420T =×
=τ⇒=
2An
Amu cm/kN201.0
7.4735336kN336T =×
=τ⇒=
2An
d,Cmu cm/kN151.0
7.4735252kN252T =×
=τ⇒=
4
7
τAn =2.01
τC,ln =2.52
τn
MB30 ⇒ τr=1.1 MPa
8
kN5.657.47352
252.011.03Tbu =××−×
=
kN5.3545.65420TTT bumuRu =−=−=
2RuRu cm/kN212.0
7.47355.354
zbT
=×
=×
=τ
( ) cm45.8a76.1011040212.035785.02e )1(
uu =×=×+××××
=
2C,l C,l 2 rmu n 2
r
0.11 kN / cm420T 420 kN 0.252 kN / cm35 47.7 3 0.33 kN / cm
> τ == ⇒ τ = = × < τ =
pp. URØ10; aa(1)=0.785cm2; m=2
Presek C levo:
5
9
( )θ×α+α×σ×××
=τ ctgsincosebam
vu
)1(u)1(
u,u
cm4.22102.035
785.02b
ame 2.min,uz
)1(u
u =××
×=
µ××
≤ −
cm20e.usvcm25
cm5.262hcm35b
.mine uu =⇒
==
≤
( ) 2)1(u,u cm/kN090.011040
2035785.02
=×+×××
×=τ
Usvojimo: URØ10/20
10
τn
τu,u
6
11
cm11912.290.04.281l,C
Ru
)1(u,u
2 =×=ττ
×λ
MPa22.190.012.2)1(u,u
l,Cmax,Ru
l,CRu =−=τ−τ=τ∆
cm4.1621194.2812 =−=λ∆
pp. URØ12; aa(1)=1.13 cm2; m=2
u2 1.13e 40 21.17 cm
35 0.122×
= × =×
(1) 2u,u
2 1.13 40 0.129 kN / cm35 20
×τ = × =
×
Ukupno usvojeno: URØ10/20 + URØ12/20(1) 2u,u 0.09 0.129 0.219 kN / cmτ = + =
URØ12/20
12
(URØ10/20)
7
13
kN5.348354.1622
090.0212.0H k,vu =×
×
−=
( )θ×α+α×σ=
ctgsincosH
Akkv
k,vuk,a
( )2
a,k348.5 348.5A 6.16 cm
40 0.707 0.707 1.0 40 2= = =
× + × ×
bAH k,vu ×= τ
αk=45o ; θ=90o
Usvojeno 2RØ22 (7.60cm2)
14
τRu-τu,u
8
15
τRu-τu,u τRu-τu,u
16
τRu-τu,u
KOSIM PROFILIMADUŽINA OSIGURANJA DUŽINA OSIGURANJA
KOSIM PROFILIMA
τRu-τu,u
9
17
18
kN5.1077.47352
201.011.03TAbu =××
−×=
2A A 2 rmu n 2
r
0.11 kN / cm336T 336 kN 0.201 kN / cm35 47.7 3 0.33 kN / cm
> τ == ⇒ τ = = × < τ =
kN5.2285.107336TTT bumuRu =−=−=
2Ru cm/kN137.0
7.47355.228
=×
=τ
( ) cm1.13a7.1611040137.035785.02e )1(
uu =×=×+××××
=
pp. URØ10; aa(1)=0.785cm2; m=2
Presek A:
10
19
τAn =2.01
τARu=1.37
τ(1)
u,u
= 0.
90
τ(2)
u,u
= 1.
47
τn
τu,u
τRu
20
cm11937.190.04.181A
Ru
)1(u,u
1 =×=ττ
×λ
MPa047.090.037.1)1(u,u
Amax,Ru
ARu =−=τ−τ=τ∆
cm4.621194.1811 =−=λ∆
u2 0.50e 40 24.3 cm
35 0.047×
= × =×
pp. URØ8; aa(1)=0.50cm2; m=2
(1) 2u,u
2 0.5 40 0.057 kN / cm35 20
×τ = × =
×
Ukupno usvojeno URØ10/20 + URØ8/20
(1) 2u,u 0.09 0.057 0.147 kN / cmτ = + =
URØ8/20
11
21
τnτC,d
n =1.51
τC,dRu =0.61
Presek C desno:
22
kN5.1497.47352
151.011.03T d,Cbu =××
−×=
2C,d A 2 rmu n 2
r
0.11 kN / cm252T 252 kN 0.151 kN / cm35 47.7 3 0.33 kN / cm
> τ == ⇒ τ = = × < τ =
kN5.1025.149252TTT bumuRu =−=−=
2Ru cm/kN061.0
7.47355.102
=×
=τ
(1)u u
2 0.785e 40 37.2 a35 0.061
×= × = ×
×
ue 29.2 cm=
pp. URØ10; aa(1)=0.785cm2
Usvojeno URØ10/20
12
23
ub
auvaau N
zMAZ −=σ×=
aub au u
Mz 0.9 h Z N
0.9 h≈ × ⇒ ≈ −
×
−×+=×+= 1uu1auuau a
2dNMyNMM
au378gornja zona : Z 792.5 kN
0.9 53≈ =
×
au672donja zona : Z 1408.8 kN
0.9 53≈ =
×
Za Nu=0: auau
MZ
0.9 h≈
×
LINIJA ZATEŽUĆIH SILA:
24
C DBA
13
25A B DC
v=40
v=40
v=40v=40
POMERANJE LINIJE ZATEŽUCIH SILA:v = 0.75×h = 0.75×53 = 39.75 ≈ 40 cm
( )( )armaturakosauzengijeh50.0vuzengijeh75.0v
+×=×=
26
6×Z(1
)au
Z(1)
auZ(1
)au
Z(1)
auZ(1
)au
Z(1)
auZ(1
)au
v=40
v=40
v=40
v=40
C DBA
usvojeno u polju: 9RØ22
usvojeno nad osloncem: 6RØ22
14
27
Z(1)
auZ(1
)au
Z(1)
auZ(1
)au
Z(1)
auZ(1
)au
6×Z(1
)au
A B DC
v=40
v=40
v=40
v=40
5
Ls1
UKUPNA DUŽINA ŠIPKE
STATICKI POTREBNA DUŽINA ŠIPKE Ls1
UKUPNA DUŽINA ŠIPKE
Ls2Ls2 STATICKI POTREBNADUŽINA ŠIPKE
DUŽINA SIDRENJA:Ls1 = 70 cm (dobra adhezija)Ls2 = 105 cm (loša adhezija)
28
p
v
pu
vs 8.14
Ø4ØL
τ×σ
×=τ×γ
σ×=
2.802.452.101.751.401.20RA0.980.920.850.760.670.60GA605040302015MB
pprianjanjanaponaVrednosti τ
cm708.6975.18.1
40042.2L 1s ≈=
××=
cm105L5.1L 1s2s =×= (Za uslove loše adhezije sračunato sa 2/3τp)
15
29
DUŽINA SIDRENJA:Ls1 = 70 cm (dobra adhezija)Ls2 = 105 cm (loša adhezija)
POMERANJE LINIJE ZATEŽUCIH SILA:v = 0.75×h = 0.75×53 = 39.75 ≈ 40 cm
UKUPNA DUŽINA ŠIPKE
Ls2Ls2 STATICKI POTREBNA DUŽINA ŠIPKE
Ls1
UKUPNA DUŽINA ŠIPKE
STATICKI POTREBNA DUŽINA ŠIPKE Ls1
C DBA
6
7
8
1
2
3
4
8
1
2
3
4
5
v=40
v=40
v=40
v=40
5
30P O S 1 - G R ED A SA P R E PU S T O M08 .10 .1998 . L ist 1 /1
16
31
32
POMERENA LINIJA ZATEŽUĆ IH SILA
LINIJA ZATEŽUĆ IH SILA
1
3
5
4
9
8
6
10
6
v = 40
40 40
1Ø22
2Ø22
2Ø22
2Ø22
2Ø22
2Ø22
3 2RØ22
2RØ225
2RØ22108 2RØ22 7 2RØ22 2RØ22711 2RØ12 11 2RØ12
13 6.5
9URØ10/2012
3URØ8/2013
20URØ8/2013 15URØ10/2012 5URØ10/2012 10URØ8/2013
960
45
885
45
1 2RØ22 L=1005
1RØ22 L=9302
2RØ22 L=1026832
325
64105
45.5
45.5
2RØ22 L=6205620654.5
2RØ22 L=360335
9
A1...840x594R 1:20MB 30 RA 400/500
GODIŠNJI ZADATAK - LIST br.6
PLAN ARMATURE POS 1
KOLICINE MATERIJALA
25
16025 25 20 380 28020 80 20 180 5
4.5
2RØ12 L=65011630
55
10
30
3010
55
29URØ10 L=19012
30
33URØ8 L=190
55 55
10
30
10
132
2 3
31
1
6.54.5 4.513 6.5
4.5
35
25.5
60
4.5
4.5 26
5.5
204.
5
URØ10/20
48
2RØ22
9 9
2RØ12
2RØ22
12
37
68
37
68
PRESEK 3-3 R 1:10
4RØ22
3 3
REKAPITULACIJA ARMATURESPECIFIKACIJA ARMATURE
ΣG[kg]
g[m]
LΣ[kg/m]
1g[mm]
Ø
UKUPNO:
25.462.70
23.7
34.9
129.12
26.00
55.10
478.8
394.8
0.4058
3.058
0.911
0.63310
12
22
gL gLΣ
20.10
[m]
n
2
[kom.]
Ø
22
[mm] [cm]
1005
9.30
20.52
15.20
7.10
12.40
1
2
22
22 1026
930
2
2
2
22
22
22
760
355
620
9.40
17.90
7.20
26.00
10.00
2
2
22
22 895
470
2
4
2
22
12
22 500
360
650
2
3
4
6
5
7
8
9
11
10
1
55.10
62.70
29
33
19010
1908
12
13
BETON (MB 30):
ARMATURA (RA 400/500): 478.8
2.573
kg
m3
kg/m478.82.573 = 186.13 3 betona
OPLATA: 16.468 m2
30
1225
86050
63.4
CBA D
4.5
5.5
204.
525
.5
26
4.5 4.5
60
PRESEK 1-1 R 1:10
4x6.5=26
4.54.5
4812
2RØ12
2RØ22
URØ8/204RØ22
5RØ22
PRESEK 2-2 R 1:10
1
4812
60
30
30 285
35
CO
NFI
DEN
TIA
L!
435
2 35
14
10 10
25.5
4.5
205.
54.
5
60
35
6.5
4.5 4.5
88
1 1
67 7
6
4812
2RØ22
2RØ22
26
4.5 4.5
4RØ22
2RØ12URØ10/20
17
33
4.5
5.5
204.
525
.5
26
4.5 4.5
60
PRESEK 1-1 R 1:10
4x6.5=26
4.54.5
4812
2RØ12
2RØ22
URØ8/204RØ22
5RØ22
1
35
435
2 35
14
10 10
34
13 6.5
3 3
PRESEK 2-2 R 1:10
25.5
4.5
205.
54.
5
60
35
6.5
4.5 4.5
88
1 1
67 7
6
4812
2RØ22
2RØ22
26
4.5 4.5
4RØ22
2RØ12URØ10/20
18
35
6.54.5 4.513 6.5
4.5
35
25.5
60
4.5
4.5 26
5.5
204.
5
URØ10/20
482RØ22
9 9
2RØ12
2RØ22
12
37
68
37
68
PRESEK 3-3 R 1:10
4RØ22