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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
a) calcul ca flansa integrala
.F , .V si se obtin din fig. 11.5-4, 11.5-5, 11.5-6
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
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Tensiunea longitudinala in gat:
HM
N1 A S 2
2
85.828 MPa
Tensiunea radiala in taler:
r
1.333 C2 F L0 M
C22
L0
19.732 MPa
Tensiunea tangentiala in taler:
YM
C22 r
k2
1
k2
1 24.654 MPa
Limite ale tensiunilor:
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
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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
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AB.min maxWA
fB.A
Wop
fB
72.501 mm
2 arie necesara
AB L
2
4n 615.752 mm
2 arie totala efectiva
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
a) situatia de strangere initiala
W AB.minRp0.2 13.775 kN
MA W hG 1.791 105
Nmm
b) situatia de functionare
Mop HDhD HThT HGhG 2.664 104
Nmm
Tensiuni in flanse si l imite ale tensiunilor:
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
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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 pt strangerea initiala:
M MA
CF
A S 4.957 kN
a) calcul ca flansa integrala
.F , .V si se obtin din fig. 11.5-4, 11.5-5, 11.5-6
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
Tensiunea longitudinala in gat:
HM
N1 A S
2
2
7.069 MPa
Tensiunea radiala in taler:
r1.333 C2 F L0 M
C22
L0
3.732 MPa
Tensiunea tangentiala in taler:
YM
C22
rk
21
k2
1
33.552 MPa
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Limite ale tensiunilor:
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 pt situatia de functionare:
M Mop
CF
A S 0.737 kN
a) calcul ca flansa integrala
.F , .V si se obtin din fig. 11.5-4, 11.5-5, 11.5-6
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
Tensiunea longitudinala in gat:
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HM
N1 A S
2
2
1.499 MPa
Tensiunea radiala in taler:
r
1.333 C2 F L0 M
C 22
L0
0.513 MPa
Tensiunea tangentiala in taler:
YM
C22
rk
21
k2
1
5.046 MPa
Limite ale tensiunilor:
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
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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
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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
2 arie totala efectiva
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
a) situatia de strangere initiala
hGw L
216.5 mm
WAB AB.min
2Rp0.2 71.859 kN
MA W hG 1.186 106
Nmm
b) situatia de functionare
Mop HDhD HThT HGhG 2.142 105
Nmm
Tensiuni in flanse si l imite ale tensiunilor:
L0A S( )
2S 11.167 mm
k D
A S 2.209
CF K
n 2 L C2 1.477
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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 pt strangerea initiala:
M MA
CF
A S 20.364 kN
a) calcul ca flansa integrala
.F , .V si se obtin din fig. 11.5-4, 11.5-5, 11.5-6
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
Tensiunea longitudinala in gat:
HM
N1 A S 2
2
315.998 MPa
Tensiunea radiala in taler:
r
1.333 C2 F L0 M
C22
L0
44.165MPa
Tensiunea tangentiala in taler:
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YM
C22
rk
21
k2
1
96.46 MPa
Limite ale tensiunilor:
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 pt situatia de functionare:
M Mop
CF
A S 3.678 kN
a) calcul ca flansa integrala
.F , .V si se obtin din fig. 11.5-4, 11.5-5, 11.5-6
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
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Tensiunea longitudinala in gat:
HM
N1 A S
2
2
95.124 MPa
Tensiunea radiala in taler:
r
1.333 C2 F L0 M
C 22
L0
7.977 MPa
Tensiunea tangentiala in taler:
Y
M
C22
r k
2
1k
21
17.422 MPa
Limite ale tensiunilor:
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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.25