Calcule BapII Partea I

8/9/2019 Calcule BapII Partea I

1/23

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


3/23

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=


4/23

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


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


5/23

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-




6/23

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=


7/23

Forte taietoare

Ved,A= -588.39

Ved,B= 829.6


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


8/23


9/23

2.300

0.090

0.500

0.250

1.200

0.500

0.500


10/23


11/23


12/23

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


13/23


14/23

0.0391

0.040

10.745

3.582

11.4

0.1640

0.174

47.257

5.907

1.01

0.13


15/23

Coeficientii pt calculul ariei armaturii pt beton


16/23

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


17/23

50/60

verificare0.003

0.0052


18/23


19/23

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


20/23

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


21/23

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


23/23

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

Documents

Calcule BapII Partea I