calcule bapii partea i
TRANSCRIPT
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CalculeCuprins: I - Coeficienti
II - Predimensionare: 1.Distanta intre axele grinzilor secundare
2. Inaltime placa3.Grinda Secundara
4.Grinda Principala
5.Stalpi
III - Calcul Placa: 1.Caracteristicile materialelor
2.Evaluarea incarcarilor
3.Calculul aproximativ in domeniu plastic
4.Aria de armatura
IV - Calcul Grinda secundara: 1. Evaluarea incarcarilor
2.Calcul static in domeniu plastic
3. Latime de calcul in camp
4.Aria de armatura
5.Calcul la forta taietoare
6. Lungimi de ancorare
V - Floricele pe campii
I - Coeficienti
Informatii generale Placa
Distanta intre ax. gr. Sec l1= 2.300
Beton C25/30 Distanta intre gr. Sec ln1= 2.050
Armaturi S400 Grosimea placii hf= 0.090
Plasa sudata S460
fck= 25
KN/m2fcd= 16.67 Armare placa
fyk,arm= 400
fyd,arm= 347.83 sl,1= 0.0071
,beton= 25KN/m3
sl,B= 0.0060
,mozaic= 16.5 sl,2-3-C-D= 0.0056
Incarcarea utila pn= 12KN/m2
fyk,pl1 / fyd,pl1= 440.00 382.61
Incarcarea totala pd= 23.171 fyk,pl2 / fyd,pl2= 440.00 382.61
L= 11.500 fyk,pl3 / fyd,pl3= 440.00 382.61T= 6.000 c,nom= 0.015
Inaltime utila H= 4.000 d,1= 0.071
d,B= 0.072
d,2-3-C-D= 0.072
Valori predimensionare
Grosimea placii hf= 0.090 Eforturi in placa
Inaltime grinda principala hg= 1.200 MEd,A= 0.000 KNm
Latime grinda principala bg= 0.500 MEd,1= 8.852
Inaltime grinda secundara hn= 0.500 MEd,B= 6.955
Latime grinda secundara bn= 0.250 MEd,2=MEd,3 6.086
MEd,C=MEd,D -6.086
Inaltime stalp lo= 4 300 VEd A= 21 375 KN
Distante intre axele stalpilor total:2L*5T
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II - Predimensionare
Se introduc stalpi intermediari deoarece latimea clcadirii depaseste 10 m 2xL=23
Se alege deschiderea grinzilor secundare T=6m
1.Distanta intre axele grinzilor secundare (l1)
Impartim deschiderea placi L la un numar intreg n si alegem l1 respectand conditiile de mai jos
L/l1=2~3(4) L/4=2.875
T/l1 > 2 L/2=5.750
l1< T/2 T/2=3.000
2. Inaltime placa (hf)
Se alege grosimea placii respectand conditile:
Cond. de rigiditate: hf=l1/35 l1/35= 0.066 m
Conditii tehnologige: hf=>50mm
hf mult. de 10mm
Rezistenta la foc: R60; hf=>80mm
3.Grinda Secundara (hn;bn)
Se alege inaltimea si grosimea respectand conditile:
Cond de rigiditate: hn=T/20 T/20= 0.300
Conditii tehnologice: bn=>0,15m
hn mult. de 50mm
hn/bn=1.5~3 hn/1,5= 0.333 hn/3= 0.167
Rezistenta la foc: R60; bn=>120mm
4.Grinda Principala (hg;bg)
Se alege inaltimea si grosimea respectand conditile:Cond. de rigiditate: hg=L/15 L/15= 0.767
Conditii tehnologice: bg=>0,2m
hg mult. de 50mm
hg > hn +100mm (pentru a nu ne suprapune armaturile longitudinale la intersectia grinz
hg/bg=1,5~3 hg/1,5= 0.800 hg/3= 0.400
Rezistenta la foc: R60; bg=>300mm
5.Stalpi
Din conditii de flexibilitate: lc=lo=H+30cm= 4.300
hc=bc=>lo/30 lo/30= 0.143Din conditii tehnologice: mult. de 50mm
bc=hc=>300mm
III - Calcul Placa:
1. Caracteristicile materialelor (rezistente de calcul)
Pentru Beton C25/30:
fck= 25fcd=cc*fck/c= 16.67 cc,placa= 1 c= 1.5
Otel S400 pt armaturi grinzi
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Din greutate proprie:
placa+pardoseala(sapa 5cm + mozaic 2cm)
gk=hf*,bet+h,sapa*,bet+h,moz*,moz
hf= 0.09 ,bet= 25.00 h,sapa= 0.05 h,mox= 0.03 ,moz= 16.50
gk=0,09x25+0,05x25+0,03x16,5= 3.83
Din incarcari variabile:
qk=pn (KN/m2) 12.000
15.830
23.171
3. Calculul aproximativ in domeniu plastic
Deoarece armarea se calculeaza dupa o singura directie, cea scurta, calculul se face pe o fasie de 1 metru liniar
Distanta intre grinzile secundare (ln1)
ln1=l1-(bn/2)*2= 2.050
otelul in clasa B de ductilitate
rap. pe reazem intern si camp= 0,3~2
xn/d = sl= 0.007 Clasa de expunere: XC1, a structurii:S4
c,min,dur= 0.02 c,tol= 0
0.01
Pentru aria de armatura calculam folosind formula, apoi alegem din tabel valoarea s corespunzatoare pentru a o folosi in formul
Calculam separat aria necesara de armatura pentru campurile 1, 2 si 3. rezulatatele din restul campurilor sunt aceleasi cu cele ale c
~Campul 1~
Diametre plasa: sl= 0.0071
0.071
= 0.104 s= 0.1101 Asl(cm2)= 3.427 Ale
~Reazem B~
a) val. caracteristica: pk=gk+qk=
b) val. de calcul: pd=1,35*gk+1,5*qk=
Inalt. utila (d): d=hf-c.nom-Sl/2=
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1. Evaluarea incarcarilor
Placa transmite grinzilor secudare incarcarea sub forma de sarcina uniform distribuita
Incarcari permanente:
din placa: g,pl=gk*l1= 8.81 KN/m
greutate propprie: gn=bn*(hn-hf)*,beton= 2.56 KN/m
total permanente: gkn=g,pl+gn= 11.37 KN/m
Incarcari tehnologice: qkn=qk,pl*l1= 27.6 KN/m
Incarcarilor totale (incarcari permanente + incarcari tehnologice) li se aplica coeficientii partiali de siguranta
Incarcari totale: pd,n=1,35*gkn+1,5*qkn= 56.75 KN/m
2. Calcul static in domeniu plastic
Determinam deschiderilor de calcul cu formulele:
Teff=Tn+2*min(bg/2;hn/2)= 6
Tn=T-2*(bg/2)= 5.5
Momentele pentru cele mai periculoase scheme de incarcare se calculeaza in domeniu plastic folosind relatii simplificate
M=*pd,n*Teff^2
In campurile intermediare, momentele incovoietoare pot deveni negatve in functie de raportul qk/gk
qk/gk= 2.43
Momente Momente reduse,1= 0.09 MEd,2= 185.92 Pe reazeme momente se cons
,B= 0.09 MEd,B= 185.92 130.59 si se poate reduce dupa form
7= -0.02 MEd,7= -49.03 Mi,red=Mi-|Vi,st
7-8= 0.06 MEd,7-8= 127.69
8= -0.02 MEd,8= -36.77
,C= 0.06 MEd,C= 127.69 80.87
12= -0.01 MEd,12= -14.3
12-13= 0.06 MEd,12-13= 127.69
Forte taietoare
Ved,A=0,45*pd,n*Teff= 153.23
Ved,Bst=-0,65*pd,n*Teff= -221.33Ved,Bdr=0,55*pd,n*Teff= 187.28
Ved,Cst=-0,55*pd,n*Teff= -187.28
Ved,Cdr=0,55*pd,n*Teff= 187.28
3. Latime de calcul in camp
Deoarece grinda secundara este turnata monolit cu placa, in camp se calculeaza ca si grinda T si trebuie calculata latimea de placa
Formule: beff=beff,1+beff,2+bn
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Asl=s*b*d*fcd/fyd
Camp 1
Diametru armatura sl= 0.022 Sus
0.46 Diametru armatura sl=
beff= 1.68 = 0.032
Med,1= 185.918 s= 0.031 bn= 0.000
nr. Armaturi= 3 Asl(cm2)= 10.245 Med.2= 27.880
b,min= 0.17 Asl(cm2) / fir= 3.415 nr. Armaturi= 2
Asleff= 11.4 b,min= 0.04Asleff / fir= 3.8
Camp 2
Jos Sus
Diametru armatura sl= 0.018 Diametru armatura sl=
0.46
beff= 1.5 = 0.024 bn= 0.250
Med.2= 127.691 s= 0.024 Med.2= 49.033
nr. Armaturi= 3 Asl(cm2)= 7.288 nr. Armaturi= 2
b,min= 0.17 Asl(cm2) / fir= 2.429 b,min= 0.11
Asl,eff= 7.62
Asleff / fir= 2.54Camp 3
Jos Sus
Diametru armatura sl= 0.018 Diametru armatura sl=
0.46
bn= 1.500 = 0.024 bn= 0.250
Med.2= 127.691 s= 0.024 Med.2= 14.301
nr. Armaturi= 3 Asl(cm2)= 7.320 nr. Armaturi= 2
b,min= 0.15 Asl(cm2) / fir= 2.440 b,min= 0.1
Asl,eff= 7.62
Asleff / fir= 2.54
Reazem BDiametru armatura sl=
bn= 0.250
Med,B= 130.585
nr. Armaturi= 4
b,min= 0.19
Reazem C
Diametru armatura sl=
bn= 0.250
Med,C= 80.87
nr. Armaturi= 2
b,min= 0.12
Inalt. utila (d): d=hn-c.nom-Sl/2=
Inalt. utila (d): d=hn-c.nom-
Inalt. utila (d): d=hn-c.nom-Sl/2= Inalt. utila (d): d=hn-c.nom-
Inalt. utila (d): d=hn-c.nom-Sl/2= Inalt. utila (d): d=hn-c.nom-
Inalt. utila (d): d=hn-c.nom-
Inalt. utila (d): d=hn-c.nom-
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Distanta maxima longitudinala intre etrieri
Sl,max= 0.3
Reazem A
Se face reducerea fortei taietoare cu formula: Ved,ired=Ved,i-pd*d
VEd,Ared=Ved,A-pd*dw= 126.9
Se determina forta taietoare capabila a elementului fara arm transversala folosind formula:
unde: cp= 0; forta axiala s-a neglijat
1= 1; pentru beton greu
0.12k=1+sqrt(200/dw)= 1.66
1=Asl/bn*dw= 0.01
Rezulta: VRdc= 67.03
Se calculeaza valoarea minima a fortei taietoare capabile fara armatura specifica:
unde: min=0,035*k^(3/2)*sqrt(fck)= 0.37
Verificam daca: VRdc > VRdc,min
Pentru ca Ved,Ared >VRdc; Solicitarea de calcul este mai mare decat capacitatea portanta a grinzii, rezulta ca avem n
Se determina capacitatea portanta a diagonalelor comprimate de beton pt valoarea maxima a ctg =2,5
unde: z=0,9*d= 0
VRd,max= 311.61
Asw=2*28,3 Asw= 56.6
S=(Asw*z*fwd*ctg)/VEd,ared S= 0.13 alegem distanta dintre etri
Se determina capacitatea portanta a diagonalelor comprimate de beton pt valoarea maxima a ctg =2
VRds= 361.46 verificam daca: VRds >VRd,Ared
Calcumal procentul de armare cu formula: w,eff=Asw/S*bn w,eff= 0
***Se procedeaza analog pentru reazemele Bst, Bdr, Cst, Cdr
6. Lungimi de ancorare
Fe=Ved,A*a1/z= 153.23 unde: 0.41 ctg
Efortul unitar de intindere in armaturile longitudinalesd=Fe/Asl,eff= 134.41
Lungimea de ancoraj
0.25 < bg
fbd pt c25/30= 2.7
0.22 unde: 1=3=3= 1
2=1-0,15*(cd-)/= 0.93
5=1-0,04p= 0.93
Reazemul A este singurul pt care trebuie calculata lungimea de ancoraj, restul reazemelor fiind intermediare nu exista problema a
V - Calcul Grinda rinci ala:
1. Evaluarea incarcarilor
Placa transmite grinzilor secudare incarcarea sub forma de sarcina uniform distribuita
Incarcari permanente:
G1=T*gkn= 68.229
G1=T*gkn/2= 34.11
Incarcari variabile:
G1=T*gkn= 165.600G1=T*gkn/2= 82.8
Sl,max=min(0,75*d(1+ctg);300mm
V,Rdc=[C,Rdc*1*
C,Rdc=0,18/c=
VRdc,min=(min
VRd,max(ctg =2,5)=cv*bn*z*1*fcd*1/(ctg+tg)
alegem ctg=2
>
a1=0,5*z*(ctg -ctg )=
lbd,req=0,25*sl*sd/fbd=
lbd,eff=1*2*3*4*5*lbd,rqd=
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Forte taietoare
Ved,A= -588.39
Ved,B= 829.6
3. Latime de calcul in camp
Deoarece grinda principala este turnata monolit cu placa, in camp se calculeaza ca si grinda T si trebuie calculata latimea de placa
Formule: beff=beff,1+beff,2+bg
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2.300
0.090
0.500
0.250
1.200
0.500
0.500
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0.027
0.028
1.657
0.828
2.26
1.13
0.055
0.057
2.829
1.415
3.08
1.54
0.016
0.016
0.899
0.449
1.01
0.51
0.147
0.185
10.227
2.557
10.16
2.54
0.09
0.11
6.18
3.089
6.28
3.14
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0.0391
0.040
10.745
3.582
11.4
0.1640
0.174
47.257
5.907
1.01
0.13
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Coeficientii pt calculul ariei armaturii pt beton
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0.245 0.3573 0.2859
0.250 0.3661 0.2929
0.255 0.3750 0.3000
0.260 0.3840 0.3072
0.265 0.3930 0.3144
0.270 0.4022 0.3218
0.275 0.4115 0.3292
0.280 0.4208 0.33670.285 0.4303 0.3443
0.290 0.4399 0.3519
0.295 0.4496 0.3597
0.300 0.4594 0.3675
0.305 0.4694 0.3755
0.310 0.4794 0.3836
0.315 0.4897 0.3917
0.320 0.5002 0.4002
0.328 0.5169 0.4135
0.330 0.5211 0.4169
0.335 0.5319 0.4255
0.340 0.5429 0.43430.345 0.5540 0.4432
0.347 0.5585 0.4468
0.350 0.5653 0.4523
0.355 0.5769 0.4615
0.360 0.5886 0.4708
0.365 0.6005 0.4804
0.370 0.6126 0.4901
0.372 0.6175 0.4940
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50/60
verificare0.003
0.0052
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Tabel plase armate
arii
7.58
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.514
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
19.520
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78.54 113.1 153.94 201.06 254.47 314.16 380.13 452.39
5 6 7 8 9 10 11 12
2.62 3.77 5.13 6.70 8.48 10.47 12.67 15.082.45 3.53 4.81 6.28 7.95 9.82 11.88 14.14
2.31 3.33 4.53 5.91 7.48 9.24 11.18 13.31
2.18 3.14 4.28 5.59 7.07 8.73 10.56 12.57
2.07 2.98 4.05 5.29 6.70 8.27 10.00 11.90
1.96 2.83 3.85 5.03 6.36 7.85 9.50 11.31
1.87 2.69 3.67 4.79 6.06 7.48 9.05 10.77
1.78 2.57 3.50 4.57 5.78 7.14 8.64 10.28
1.71 2.46 3.35 4.37 5.53 6.83 8.26 9.83
1.64 2.36 3.21 4.19 5.30 6.54 7.92 9.42
1.57 2.26 3.08 4.02 5.09 6.28 7.60 9.05
1.51 2.17 2.96 3.87 4.89 6.04 7.31 8.70
1.45 2.09 2.85 3.72 4.71 5.82 7.04 8.381.40 2.02 2.75 3.59 4.54 5.61 6.79 8.08
1.35 1.95 2.65 3.47 4.39 5.42 6.55 7.80
1.31 1.88 2.57 3.35 4.24 5.24 6.34 7.54
1.27 1.82 2.48 3.24 4.10 5.07 6.13 7.30
1.23 1.77 2.41 3.14 3.98 4.91 5.94 7.07
1.19 1.71 2.33 3.05 3.86 4.76 5.76 6.85
1.15 1.66 2.26 2.96 3.74 4.62 5.59 6.65
1.12 1.62 2.20 2.87 3.64 4.49 5.43 6.46
1.09 1.57 2.14 2.79 3.53 4.36 5.28 6.28
1.06 1.53 2.08 2.72 3.44 4.25 5.14 6.11
1.03 1.49 2.03 2.65 3.35 4.13 5.00 5.95
1.01 1.45 1.97 2.58 3.26 4.03 4.87 5.800.98 1.41 1.92 2.51 3.18 3.93 4.75 5.65
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530.93 615.75 706.86 804.25 907.92 1017.88 1134.11 1256.64
13 14 15 16 17 18 19 20
17.70 20.53 23.56 26.81 30.26 33.93 37.80 41.8916.59 19.24 22.09 25.13 28.37 31.81 35.44 39.27
15.62 18.11 20.79 23.65 26.70 29.94 33.36 36.96
14.75 17.10 19.63 22.34 25.22 28.27 31.50 34.91
13.97 16.20 18.60 21.16 23.89 26.79 29.85 33.07
13.27 15.39 17.67 20.11 22.70 25.45 28.35 31.42
12.64 14.66 16.83 19.15 21.62 24.24 27.00 29.92
12.07 13.99 16.06 18.28 20.63 23.13 25.78 28.56
11.54 13.39 15.37 17.48 19.74 22.13 24.65 27.32
11.06 12.83 14.73 16.76 18.92 21.21 23.63 26.18
10.62 12.32 14.14 16.08 18.16 20.36 22.68 25.13
10.21 11.84 13.59 15.47 17.46 19.57 21.81 24.17
9.83 11.40 13.09 14.89 16.81 18.85 21.00 23.279.48 11.00 12.62 14.36 16.21 18.18 20.25 22.44
9.15 10.62 12.19 13.87 15.65 17.55 19.55 21.67
8.85 10.26 11.78 13.40 15.13 16.96 18.90 20.94
8.56 9.93 11.40 12.97 14.64 16.42 18.29 20.27
8.30 9.62 11.04 12.57 14.19 15.90 17.72 19.63
8.04 9.33 10.71 12.19 13.76 15.42 17.18 19.04
7.81 9.06 10.39 11.83 13.35 14.97 16.68 18.48
7.58 8.80 10.10 11.49 12.97 14.54 16.20 17.95
7.37 8.55 9.82 11.17 12.61 14.14 15.75 17.45
7.17 8.32 9.55 10.87 12.27 13.76 15.33 16.98
6.99 8.10 9.30 10.58 11.95 13.39 14.92 16.53
6.81 7.89 9.06 10.31 11.64 13.05 14.54 16.116.64 7.70 8.84 10.05 11.35 12.72 14.18 15.71
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Grinda secundara:
Distanta [ Nod Vz [kN] My [kNm]
L=6,000
0 -1 -167.61 00.6 -125.15 -87.83
1.2 -82.69 -150.18
1.8 -40.23 -187.06
2.4 2.24 -198.45
3 44.7 -184.37
3.6 87.16 -144.82
4.2 129.62 -79.78
4.8 172.08 10.73
5.4 214.55 126.72
6 -2 257.01 268.18
L=6,0000 -2 -223.48 268.18
0.6 -181.02 146.83
1.2 -138.56 50.95
1.8 -96.1 -19.44
2.4 -53.64 -64.36
3 -11.17 -83.81
3.6 31.29 -77.77
4.2 73.75 -46.26
4.8 116.21 10.73
5.4 158.67 93.19
6 -3 201.14 201.14
L=6,000
0 -3 -212.31 201.14
0.6 -169.85 86.49
1.2 -127.39 -2.68
1.8 -84.92 -66.38
2.4 -42.46 -104.59
3 0 -117.33
3.6 42.46 -104.59
4.2 84.92 -66.38
4.8 127.39 -2.68
5.4 169.85 86.49
6 -4 212.31 201.14
L=6,000
0 -4 -201.14 201.14
0.6 -158.67 93.19
1.2 -116.21 10.73
1.8 -73.75 -46.26
2.4 -31.29 -77.77
3 11.17 -83.81
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3.6 53.64 -64.36
4.2 96.1 -19.44
4.8 138.56 50.95
5.4 181.02 146.83
6 -5 223.48 268.18
L=6,0000 -5 -257.01 268.18
0.6 -214.55 126.72
1.2 -172.08 10.73
1.8 -129.62 -79.78
2.4 -87.16 -144.82
3 -44.7 -184.37
3.6 -2.24 -198.45
4.2 40.23 -187.06
4.8 82.69 -150.18
5.4 125.15 -87.83
6 -6 167.61 0