Mathcad - calcule echipament sub presiune

8/14/2019 Mathcad - calcule echipament sub presiune

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Material : P235GH

ReH 235MPa Rm 400MPa A 25%

Limita de curgere conventionala la 0.2% se calculeaza prin interpolare:

DESEN INTERPOLARE..........................................................................

T2 100 C T1 50C Tag 60C

Rp100 190MPa Rp50 206MPa

Rp0.2

Rp50 Rp100 T2 Tag Rp100 T2 T1

T2 T1

Rp0.2 202.8 MPa

Valoarea maxim admisibila pt tensiuni nominale de calcul pt partile supuse la presiune:

fd minRp0.2

1.5

Rm

2.4

135.2 MPa

Invelisul cilindric - recipient supus la presiune interioara:

p 1MPa Di 800mm z 0.85 hi 200mm

Grosimea invelisului:

ep Di

2 fd z p 3.496 mm

Se ia:

ea 6mm

Invelisul cilindric - Manta supusa la presiune interioara:

patm 0.1MPa Dmanta 1 00 mm Di z 0.85

Tag 100


2/24

Rp0.2 190MPa Se determina Rp0.2 --> prin interpolare

fmanta minRp0.2

1.5

Rm

2.4

126.667 MPa

Grosimea invelisului:

ep Dmanta

2 fmanta z patm 4.182 mm

Se ia:

ea 6mm

Funduri elipsoidale - recipient supuse la presiune interioara

KDi

2 hi 2

r Di0.5

K

0.08

136 mm

R Di 0.44 K 0.02( ) 720 mm

Grosimea fundurilor elipsoidale:

esp R

2 fd z 0.5 p 3.139 mm

fb

Rp0.2

1.5126.667 MPa

eb 0.75 R 0.2 Di p

111 fb

Di

r

0.825

1

1.5

3.184 mm

h

i

R RDi

2

R

Di

2

2 r

199.078 mm


3/24

Din standard => hi 200mm

pt calc :

Y min e

R0.04

5.808 10 3

Z log 10 1

Y

3.236

X r

Di

0.17 N 1.006 1

6.2 90 Y( )4

0.847

0.1 N 0.1833 Z3 1.0383 Z2 1.2943 Z 0.837 1.1090.2 max 0.95 0.56 1.94 Y 82.5 Y

2 0.5 0.519

10 0.2 X( ) 0.1 X 0.1( ) 0.2 0.696

ey

p 0.75 R 0.2 Di fd

3.602 mm

min es ey eb 3.139 mm

Evaluarea valorii grosimii calculate:

Ps

2 fd z ea

R 0.5 eb 1.911 MPa

Py

fde a

0.75 R 0.2 Di 1.666 MPa

Pb

111 fb

ea

0.75 R 0.2 Di

1.5

r

Di

0.825

2.586 MPa

pmax min Ps Py Pb 1.666 MPa


4/24

Invelis cilindric - recipient supus la presiune exterioara:

Rp0.2 190MPa Hlichid 911.67mm

H 1600mm Hlichid 688.33 mm

e

Rp0.2

1.25152 MPa

Py

eea

R1.267 MPa

E 2.1 105

MPa

Z R

H3.286

din fig 4.1.2:

2 R

ea

240H

2 R 0.478

8 10 4

Pm

E ea

R1.4MPa

Pm

Py

1.105

Pr 0.5 Py 0.633 MPa

S 1.5

Pr

S0.422 MPa > p. atm=0.10MPa => REZISTA


5/24


6/24

0.1 N 0.1833 Z3

1.0383 Z2

1.2943 Z 0.837 1.092

0.2 max 0.95 0.56 1.94 Y 82.5 Y2

0.5 0.52

10 0.2 X( ) 0.1 X 0.1( ) 0.2 0.692

ey

p 0.75 R 0.2 Dmanta fmanta

4.302 mm

efund max es ey eb 4.302 mm

Evaluarea valorii grosimii calculate:

Ps

2 fmanta z efund

R 0.5 eb 1.143 MPa

Py

fmantaefund

0.75 R 0.2 Dmanta 1 MPa

Pb 111 fbefund

0.75 R 0.2 Dmanta

1.5

r

Dmanta

0.825

1.316 MPa

pmax min Ps Py Pb 1 MPa

Invelis cilindric - manta supus la presiune exterioara:

Hlichid 911.67mmRp0.2 190MPa

e

Rp0.2

1.25152 MPa

Py

eea

R1.126 MPa

E 2.1 105

MPa

din fig 4.1.2:

2 R

ea

270Hlichid

2 R 0.563


7/24

4 10 4

Pm

E ea

R 0.622 MPa

Pm

Py 0.553

Pr 0.3 Py 0.338 MPa

Pr

S0.225 MPa > 0.1 MPa => REZISTA

Funduri de invelisuri supuse la presiune exterioara:

pt funduri de forma elipsoidala:

Dm Dmanta ea 906 mm

RDm

2

4 hi 912.04 mm

Py

2 e ea

R2 MPa

Pm

1.21 E ea2

R2

10.997 MPa

Pm

Py

5.499

Pr

0.58 Py

1.16 MPa

Pr

S0.773 MPa > p.atm=0.1 MPa => REZISTA


8/24

Calculul geometriei si lichidului in recipient:

hc 25mm 0.6 H 1600mm

a 0.5 Di b 0.25 Di apa 1000 10 9

kg

mm3

l 1600 10 9

kg

mm3

OL 7800 10 9

kg

mm3

g 9.81 103

mm

s2

Vapa

Di2

4H 2 hc

4

3 a

2 b 9.634 10

8 mm

3

Gapa Vapaapa g 9.451 kN

Vlichid Di

2

4H 2 hc

1

2

4

3 a

2 b

1

2

4

3 a

2 b 4.708 10

8 mm

3

Glichid Vlichidl g 7.39 kN

Hlichid

Vlichid

Di2

4hc

Di

2

4

911.667 mm

Dmanta 1 00 mm Di 900 mm emanta 6mm e 6mm

Hmanta Hlichid hcDi

4 1.137 10

3 mm

Vmaterial 2 Di

2 e H 2 1.09 Di

2 e 2

Dmanta

2 emanta Hmanta 1.09 Dmanta

2 emanta

1

Vmaterial 7.135 107

mm3

Gmaterial VmaterialOL g 5.459 kN

Gt Gmaterial Gapa 14.911 kN

Gpicior

Gt

43.728 kN


9/24

Flanse

Flansa 1:

Dimensiuni flansa: B 800mm

D 975mm K 920mm L 29.5mm A 813mm

C2 26mm H1 70mm H2 16mm

N1 842mm R 12mm S 6.3mm n 24

wK L N1

224.25 mm

w 25mm

b0w

212.5 mm

Daca b>6.3 atunci:

b 2.52 b0 8.91 mm0.5

b 8.91mm

G K L

2

w

2 892.75 mm

H

4G

2 patm 62.596 kN

Pt elastomeri cu inserie de bumbac: m 1.25 y 2.8MPa

HG 2 G m p b 62.474 kN

Presiunea de strivire a garniturii:

WA b G y 69.971 kN

Wop H HG 125.07 kN

fB.A

Rp0.2

363.333 MPa

fB

Rm

4100 MPa


10/24

AB.min maxWA

fB.A

Wop

fB

1.251 10

3 mm

2 arie necesara

AB L

2

4n 1.64 10

4 mm

2 arie totala efectiva

Momente in flansa:

HD

4patm B( )

2 50.265 kN

HT H HD 12.331 kN

hG K G 27.25 mm

hDL

2w

N1 B

2 60.75 mm

hTG B

4hG 50.437 mm

a) situatia de strangere initiala

W AB.minRp0.2 237.633 kN

MA W hG 6.476 106 Nmm

b) situatia de functionare

Mop HDhD HThT HGhG 5.378 106

Nmm

Tensiuni in flanse si l imite ale tensiunilor:

L0 B S 70.993 mm

k D

B1.219

b 2 K sin

n

240.168 mm

CF max 1b

2 L6 C2

m 0.5

1.273


11/24

Tk

21 8.55246 log k( )( ) 1

1.0472 1.9448 k2

k 1( )1.831

Uk

21 8.55246 log k( )( ) 1

1.36136 k2

1 k 1( )10.909

Y1

k 1 0.66845 5.7169

k2

log k( )

k2

1

9.927

M pt strangerea initiala:

M MA

CF

B 10.306 kN

a) calcul ca flansa integrala

.F , .V si se obtin din fig. 11.5-4, 11.5-5, 11.5-6

N1 B

2S3.333

H1 H2

L0

0.761

1.1 F 0.67 V 0.3

C2 F L0

TL0

C23V

UL0 S2

0.852

Tensiunea longitudinala in gat:

HM

N1 A S 2

2

103.344 MPa

Tensiunea radiala in taler:

r

1.333 C2 F L0 M

C22

L0

23.759MPa


12/24

Tensiunea tangentiala in taler:

YM

C22

rk

21

k2

1

29.686 MPa

Limite ale tensiunilor:

1.5 fd 202.8 MPa

H 1.5 fd

r fd

fd

0.5 H r 63.551 MPa

0.5 H r fd

0.5 H 66.515 MPa

0.5 H fd

M pt situatia de functionare:

M Mop

CF

B 8.559 kN



N1 B

2S

3.333

H1 H2

L0

0.761

1.1 F 0.67 V 0.3

C2 F L0

TL0

C23V

UL0 S2

0.852


13/24


HM

N1 A S 2

2

85.828 MPa


r

1.333 C2 F L0 M

C22

L0

19.732 MPa


YM

C22 r

k2

1

k2

1 24.654 MPa


1.5 fd 202.8 MPa

H 1.5 fd

r fd

fd

0.5 H r 52.78 MPa

0.5 H r fd

0.5 H 55.241 MPa

0.5 H fd


14/24

Flanse

Flansa 2:

Dimensiuni flansa: B 40mm

D 130mm K 100mm L 14mm A 48.3mm

C2 16mm H1 26mm H2 38mm

N1 62mm R 5mm S 2.3mm n 4

w

K L N1

2 12mm

w 12mm

b0w

26 mm

Daca b


15/24

AB.min maxWA

fB.A

Wop

fB

72.501 mm

2 arie necesara

AB L

2

4n 615.752 mm


Momente in flansa:

HD

4p B( )

2 1.257 kN

HT H HD 0.662 kN

hG K G 13mm

hTG B

4hG 24.75 mm

hDL

2w

N1 B

2 30mm


W AB.minRp0.2 13.775 kN

MA W hG 1.791 105

Nmm



Nmm


L0A S( )

2S 7.273 mm

k DA S

2.826

Tk

21 8.55246 log k( )( ) 1

1.0472 1.9448 k2

k 1( )1.249


16/24

Uk

21 8.55246 log k( )( ) 1

1.36136 k2

1 k 1( )2.177

Y1

k 1 0.66845 5.7169 k

2

log k( )

k2

1

1.981


M MA

CF

A S 4.957 kN



N1 S A

S4.957

H1 H2

L0

1.65

0.6 F 0.51 V 0.23

C2 F L0

TL0

C23V

UL0 S2

12.948


HM

N1 A S

2

2

7.069 MPa


r1.333 C2 F L0 M

C22

L0

3.732 MPa


YM

C22

rk

21

k2

1

33.552 MPa


17/24


1.5 fd 202.8 MPa

H

1.5 fd

r fd

fd

0.5 H r 5.401 MPa

0.5 H r fd

0.5 H 20.311 MPa

0.5 H fd


M Mop

CF

A S 0.737 kN



N1 S A

S4.957

H1 H2

L0

1.65

1.1 F 0.67 V 0.3

C2 F L0

TL0

C23V

UL0 S2

16.654



18/24

HM

N1 A S

2

2

1.499 MPa


r

1.333 C2 F L0 M

C 22

L0

0.513 MPa


YM

C22

rk

21

k2

1

5.046 MPa


1.5 fd 202.8 MPa

H 1.5 fd

r fd

fd

0.5 H r 1.006 MPa

0.5 H r fd

0.5 H 3.272 MPa

0.5 H fd

Flanse


19/24

Flansa 3:

Dimensiuni flansa:

D 190mm K 150mm L 18mm A 88.9mm

C2 18mm H1 42mm H2 34mm

N1 102mm R 6mm S 2.9mm n 4

wK L N1

215mm

w 15mm

b0w

27.5mm

Daca b>6.3 atunci:

b 2.52 b0 6.901 mm0.5

b 6.901mm

G N1w

2

109.5 mm

H

4G

2 p 9.417 kN

Pt elastomeri cu inserie de bumbac: m 1.25 y 2.8MPa

HG 2 G m p b 5.935 kN

Presiunea de strivire a garniturii:

WA b G y 6.647 kN

Wop H HG 15.352 kN

fB.A

Rp0.2

363.333 MPa

fB

Rm

4100 MPa


20/24

AB.min maxWA

fB.A

Wop

fB

153.521 mm

2 arie necesara

d.1 este diametrul interior al filetului urubului => extras din STAS 510-74n este numarul suruburilor

d1 13.853mm

AB

d12

4n 602.889 mm


Momente in flansa:

HD

4p A S( )

2 5.809 kN

HT H HD 3.608 kN

hT

K N1

224mm

hD

N1 A S

25.1mm


hGw L

216.5 mm

WAB AB.min

2Rp0.2 71.859 kN

MA W hG 1.186 106

Nmm



Nmm


L0A S( )

2S 11.167 mm

k D

A S 2.209

CF K

n 2 L C2 1.477


21/24

Tk

21 8.55246 log k( )( ) 1

1.0472 1.9448 k2

k 1( )1.432

Uk2 1 8.55246 log k( )( ) 1

1.36136 k2

1 k 1( )2.857

Y1

k 1 0.66845 5.7169

k2

log k( )

k2

1

2.6


M MA

CF

A S 20.364 kN



N1 S A

S3.517

H1 H2

L0

0.716

1.5 F 0.75 V 0.1

C2 F L0

TL0

C23V

UL0 S2

3.716


HM

N1 A S 2

2

315.998 MPa


r

1.333 C2 F L0 M

C22

L0

44.165MPa



22/24

YM

C22

rk

21

k2

1

96.46 MPa


1.5 fd 202.8 MPa

H 1.5 fd

r fd

fd

0.5 H r 180.081 MPa0.5 H r fd

0.5 H 206.229 MPa

0.5 H fd


M Mop

CF

A S 3.678 kN



N1 S A

S3.517

H1

H2

L0

0.716

2.5 F 0.75 V 0.1

C2 F L0

TL0

C23V

UL0 S2

3.716


23/24


HM

N1 A S

2

2

95.124 MPa


r

1.333 C2 F L0 M

C 22

L0

7.977 MPa


Y

M

C22

r k

2

1k

21

17.422 MPa


1.5 fd 202.8 MPa

H 1.5 fd

r fd

fd

0.5 H r 51.55 MPa

0.5 H r fd

0.5 H 56.273 MPa

0.5 H fd


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Date post:	04-Jun-2018
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Mathcad - calcule echipament sub presiune

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