graficki rad 1 beton
TRANSCRIPT
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BETONSKE KONSTRUKCIJE 2
MARKO STOJANOVIĆ K-101/08 List br. 1
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BETONSKE KONSTRUKCIJE 2
1. ODREĐIVANJE DIMENZIJE STEPENIKA I STEPENIŠNE PLOČE
-Preporuka za stepenište
a) b+h=63 cmb) b+h=46 cm (62-65 cm)c) c-h=12 cm
-Predpostavka:
b= 17.5 cmh= 29 cmH= 175 cm
H/b= 10 komc= 270.00 cm
USVAJAM : 10 stepenikab' = c / 10 = 270 / 10 = 27 cmh = H / 10 = 175 / 10 = 17.5 cm
b = b' + 2 cm = 27 + 2 cm = 29 cm
0.64815 a = 32,949 0.839
306.91 cm
l'=a+25/2+c'=140+12,5+306.91= 459.41 cm
min. debljina ploče: dpl=I'/35=13.1261 cm USVAJAM : dpl= 14 cm
MARKO STOJANOVIĆ K-101/08 List br. 2
tg a = H/c= 175/270= cos a =
c'=(c-12,5)/cos a =(270-12,5)/0.839=
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BETONSKE KONSTRUKCIJE 2
2. IZVRŠITI ANALIZU OPTEREĆENJA I SRAČUNATI PRESEČNE UTICAJE
2.1. ANALIZA OPTEREĆENJA2.1.1. STALNA OPTEREĆENJA
- PODEST :
-TERACO 0,04x20,0 = 0.80
-AB PLOČA 0,14x25,0 = 3.50
-MALTER 0,015x19,0 = 0.29
UKUPNO: 4.59
-STEPENIŠNI KRAK
-TERACO (0,04x29,0+0,175x0,03)x20 x 100 /27 = 1.25
-GAZIŠTE (0,175/2)x24= 2.1
-SOPSTVENU TEŽINU PLOČE REDUKOVANU NA HORIZONTALU
4.17
-MALTER: (0,015x19)/0,839= 0.340
UKUPNO: 7.86
MARKO STOJANOVIĆ K-101/08 List br. 3
kN/m2
kN/m2
kN/m2
g1= kN/m2
kN/m2
kN/m2
(0,14x25)/cos a =3,5/0,839= kN/m2
kN/m2
g2= kN/m2
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BETONSKE KONSTRUKCIJE 2
2.1.2. KORISNO OPTEREĆENJA
p=3,5 kN/m2
MARKO STOJANOVIĆ K-101/08 List br. 4
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BETONSKE KONSTRUKCIJE 2
MARKO STOJANOVIĆ K-101/08 List br. 5
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BETONSKE KONSTRUKCIJE 2
MARKO STOJANOVIĆ K-101/08 List br. 6
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BETONSKE KONSTRUKCIJE 2
3. DIMENZIONISANJE
MB 30 (C 25/30) d= 14 cm 2.05
GA 240/360 Gv= 24
1.5 cm predpostavka
Ф = d - 2 cm = 14 - 2 = 12 mm 1.13 cm2)
14 - 1.5 - 1.2/2 = 11.9 cm
0.15 / 100 x 100 x 14 = 2.1
3.1. U POLJU NA MESTU max Mu
Mu= 36.684 kNm
2.8131TAB.
10 / 2.350 ‰13.630 ٪
0.927
13.8543
8.156297
Dobijena armatura je na malom međusobnom rastojanju što treba izbegavati.
Usvajam potreban razmak armature:
e = 20 cm
Na osnovu usvojenog razmaka armature određujem potreban prečnik šipke:
1.13 ≥ 13.914 x 12.5 / 1001.13 ≥ 2.77087 USVAJAM ARMATURU U POLJU: Ф 10/20 + Ф 16/20
Ф 10: 0.79 14
Ф 16: 2.01
MARKO STOJANOVIĆ K-101/08 List br. 7
fb= kN/cm2
kN/cm2
ao=
(Aa1 =
h = d - a0 - Ф/2 =
min Aa1= m / 100 x b x d = cm2/m1
k = h √ ( fb x b / Mu ) = 11.9 √ ( 2.05 x 1.00 / 36.684 ) =
ea / eb =
Aapot.= m1M / 100 x b x h x fb/Gv = 13.630 / 100 x 100 x 11.9 x 2.05 / 24 =
Aapot.= cm2/m1
e = Aa1 / Aa
pot. x 100 = 1.13 / 13.854 x 100 = cm/m1
Aa1 ≥ Aa
pot. x e / 100
Aa1= Aa
stv.= cm2/m1
Aa1=
μ1M=
ζ b=
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BETONSKE KONSTRUKCIJE 2
3.2. PODEONA ARMATURA
2.8 MERODAVNO
≥
2.1
Ф 6: 0.28
10 cm USVAJAM: Ф 6/10
2.8
Rag= 12.05 kNza X = 152.5 cm Rap= 7.175 kN
g1= 4.59 kN/m1p= 3.00 kN/m1
13.04 kNm
7.45 kNm
34.27849 kNm
2.91013TAB.
10 / 2.225 ‰12.747 ٪
0.93
12.9568
USVAJAM ARMATURU U POLJU: Ф 10/20 + Ф 16/20
Ф 10: 0.79 14
Ф 16: 2.01
MARKO STOJANOVIĆ K-101/08 List br. 8
0.2 x Aastv.= cm2/m1
Aap
min mpxAb= cm2/m1
(Aa1= cm2)
e £ Aa1/Aap
pot x 100 =
Aastv.= cm2/m1
3.3. DIMENZIONISANJE U POLJU NA MESTU Mu I
MxgI = Rag x 1.525 - 4.59 x 1.5252 / 2 =
MxpI = Rap x 1.525 - 3.00 x 1.5252 / 2 =
MuI = 1.6 x Mxg
I + 1.8 x MxpI =
k = h √ ( fb x b / MuI ) = 11.9 √ ( 2.05 x 1.00 / 34.278 ) =
ea / eb =
Aapot.= m1M / 100 x b x h x fb/Gv = 12.747 / 100 x 100 x 11.9 x 2.05 / 24 =
Aapot.= cm2/m1
Aa1= Aa
stv.= cm2/m1
Aa1=
μ1M=
ζ b=
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BETONSKE KONSTRUKCIJE 2
4. PODATCI ZA DIJAGRAM POKRIVANJA I PLAN ARMATURE
4.1. DUŽINA SIDRENJA ARMATURE
MB 30 0.76 Mpa
GA 240/360 Gv= 24 0.076
1.8
43.8596 Ф
29.2398 Ф
Ф 10: 29.2398 Ф 29.24 1.0 29.24 cm
Ф 16: 29.2398 Ф 29.24 1.6 46.78 cm
USVOJENA DUŽINA SIDRENJA ZA:
Ф 10: 30 cm
Ф 16: 50 cm
4.2. U POLJU NA MESTU max Mu h= 14 cm
1.5 cm0.927
11.55 cm
0.10707 m
max Mu= 36.684 kNm
342.622
POMERANJE LINIJE ZATEŽUĆIH SILA:
n= 0.75 x h n= 8.66 cmna razmaku
SILA KOJU PRIHVATA ARMATURA : Ф 10: 20 0.79
Ф 16: 20 2.01
Ф 10: 0.79 / 20 x 100 x 24 = 94.8
Ф 16: 2.01 / 20 x 100 x 24 = 241.2
MARKO STOJANOVIĆ K-101/08 List br. 9
tp =
kN/cm2 tp = kN/cm2
gu =
ls = ( Ф x Gv ) / ( 4 x tp x gu) = ( Ф x 24 ) / ( 4 x 0.076 x 1.8) =
ls (ef) = 2/3 x ls =
Ф cm
ls (ef) = ls (ef) = ls (ef) =
ls (ef) = ls (ef) = ls (ef) =
ls (ef) =
ls (ef) =
ao=
hstv= h-ao-(Ф16-((Ф10/2+Ф16/2)/2)) hstv=
kN/m1
AaI= cm2
AaII= cm2
Zau I = AaI x Gv = kN/m1
Zau II = AaII x Gv = kN/m1
Zb=ζb xhstv=
ζ b=
maxM u
Zb=
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BETONSKE KONSTRUKCIJE 2
336 < 342.622
Da se ne bih mnogo mlatio oko mešovite armature predpostavio sam F 16 na 12.5 rastojanjeu i tako izvršio novi proračun
MARKO STOJANOVIĆ K-101/08 List br. 10
Zau= kN/m1 kN/m1
Zbog dobijene stvarne statičke visine h stv dolazi do povećanja dobijene sile koja treba da bude manja od sile koju treba da prihvati armatura. Zbog toga moramo izvršiti proveru dobijene armature ali sa dobijenom stvarnom statičkom visinom h stv. DIMENZIONISATI PONOVO OD TAČKE 3. !!!!
maxM u
Zb=
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BETONSKE KONSTRUKCIJE 2
3. DIMENZIONISANJE
MB 30 (C 25/30) d= 14 cm 2.05
GA 240/360 Gv= 24
1.5 cm predpostavka
predpostavka Ф = 16 mm 2.01 cm2)
14 - 1.5 - 1.6/2 = 11.7 cm
0.15 / 100 x 100 x 14 = 2.1
3.1. U POLJU NA MESTU max Mu
Mu= 36.684 kNm
2.766TAB.
10 / 2.425 ‰14.152 ٪
0.924
14.1432
Ф16: 2.01 14.21182
Usvajam potreban razmak armature:
Ф16: e = 12.5 cm
Na osnovu usvojenog razmaka armature određujem potreban prečnik šipke:
2.01 ≥ 14.2118 x 12.5 / 1002.01 ≥ 1.76789
USVAJAM ARMATURU U POLJU: Ф 16/12.5
Ф 16: 2.01 16.08
MARKO STOJANOVIĆ K-101/08 List br. 7
fb= kN/cm2
kN/cm2
ao=
(Aa1 =
h = d - a0 - Ф/2 =
min Aa1= m / 100 x b x d = cm2/m1
k = h √ ( fb x b / Mu ) = 11.70 √ ( 2.05 x 1.00 / 36.684 ) =
ea / eb =
Aapot.= m1M / 100 x b x h x fb/Gv = 13.152 / 100 x 100 x 11.70 x 2.05 / 24 =
Aapot.= cm2/m1
Аа1= cm2 e = Aa
1 / Aapot. x 100 = 2.01 / 14.301 x 100 = cm/m2
Aa1 ≥ Aa
pot. x e / 100
Aa1= Aa
stv.= cm2/m1
μ1M=
ζ b=
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BETONSKE KONSTRUKCIJE 2
3.2. PODEONA ARMATURA
3.216 MERODAVNO
≥
2.1
Ф 8: 0.5
15.5473 cm e = 15 cm USVAJAM: Ф 8/15
3.216
Rag= 12.05 kNza X = 152.5 cm Rap= 7.175 kN
g1= 4.59 kN/m1p= 3.50 kN/m1
13.04 kNm
6.87 kNm
33.23196 kNm
2.906TAB.
10 / 2.225 ‰12.747 ٪
0.930
12.739
USVAJAM ARMATURU U POLJU: Ф 16/12.5
Ф 16: 2.01 16.08
MARKO STOJANOVIĆ K-101/08 List br. 8
0.2 x Aastv.= cm2/m1
Aap
min mpxAb= cm2/m1
(Aa1= cm2)
e £ Aa1/Aap
pot x 100 =
Aastv.= cm2/m1
3.3. DIMENZIONISANJE U POLJU NA MESTU Mu I
MxgI = Rag x 1.525 - 4.59 x 1.5252 / 2 =
MxpI = Rap x 1.525 - 3.50 x 1.5252 / 2 =
MuI = 1.6 x Mxg
I + 1.8 x MxpI =
k = h √ ( fb x b / MuI ) = 11.7 √ ( 2.05 x 1.00 / 33.232 ) =
ea / eb =
Aapot.= m1M / 100 x b x h x fb/Gv = 12.747 / 100 x 100 x 11.7 x 2.05 / 24 =
Aapot.= cm2/m1
Aa1= Aa
stv.= cm2/m1
μ1M=
ζ b=
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BETONSKE KONSTRUKCIJE 2
4. PODATCI ZA DIJAGRAM POKRIVANJA I PLAN ARMATURE
4.1. DUŽINA SIDRENJA ARMATURE
MB 30 0.76 Mpa
GA 240/360 Gv= 24 0.076
1.8
43.8596 Ф
29.2398 Ф
Ф 16: 29.2398 Ф 29.24 1.6 46.78 cm
USVOJENA DUŽINA SIDRENJA ZA:
Ф 16: 50 cm
4.2. U POLJU NA MESTU max Mu h= 14 cm
1.5 cm0.924
11.7 cm
0.10811 m
max Mu= 36.684 kNm
339.327
POMERANJE LINIJE ZATEŽUĆIH SILA:
n= 0.75 x h n= 8.77 cm
SILA KOJU PRIHVATA ARMATURA : na razmaku
Ф 16: 12.5 2.01
Ф 16: 2.01 / 12.5 x 100 x 24 = 385.92
385.92 > 339.33
tp =
kN/cm2 tp = kN/cm2
gu =
ls = ( Ф x Gv ) / ( 4 x tp x gu) = ( Ф x 24 ) / ( 4 x 0.076 x 1.8) =
ls (ef) = 2/3 x ls =
Ф cm
ls (ef) = ls (ef) = ls (ef) =
ls (ef) =
ao=
hstv= h-ao-Ф16/2 hstv=
kN/m1
Aa= cm2
Zau = Aa x Gv = kN/m1
Zau= kN/m1 kN/m1
Zb=ζb xhstv=
ζ b=
maxM u
Zb=
maxM u
Zb=
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MARKO STOJANOVIĆ K-101/08 List br. 9
BETONSKE KONSTRUKCIJE 2
h= 14 cm
1.5 cm0.930
11.7 cm
0.10881 m
max Mu'= 33.232 kNm
305.413
POMERANJE LINIJE ZATEŽUĆIH SILA:
n= 0.75 x h n= 8.77 cm
SILA KOJU PRIHVATA ARMATURA : na razmaku
Ф 16: 12.5 2.01
Ф 16: 2.01 / 12.5 x 100 x 24 = 385.92
385.92 > 305.41
4.3. U POLJU NA MESTU max MuI
ao=
hstv= h-ao-Ф16/2 hstv=
kN/m1
Aa= cm2
Zau = Aa x Gv = kN/m1
Zau= kN/m1 kN/m1
Zb=ζb xhstv=
ζ b=
maxM u '
Zb=
maxM u '
Zb=
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MARKO STOJANOVIĆ K-101/08 List br. 10
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