jgw-t1301483-towerb1 b2 vacuum v3 - university of...
Post on 28-Oct-2019
6 Views
Preview:
TRANSCRIPT
Appendix A1
Shell under external pressure 8 Pag 47 EN 13445-3 2002 (E)
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-8 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Geometrical data: overall length 1805mm outer diameter 870mm inner diameter 860mm.
8.5.22 Thori-spherical thickness pag. 81
ea 8 mm Selected analysis torospherical thickness
Rav 1508mm External Crown radius
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts pag 25
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Pye ea
Rav Pressure at the mean circunferential stress reaches the yield point
Py 6.366 105
Pa Py 6.283atm
E 200 109
Pa
8.7 Spherical shell 8.7.1 pag. 80
PmE ea
2 1.21
Rav2
Pm 6.811 106
Pa Pm 68.107bar
RatioPm
Py Ratio 10.698
RPr_Py 0.57
Pr RPr_PyPy Pr 3.629 105
Pa Pr 3.629bar
S 1.5 Safety factor
PacPr
S Pac 2.387atm Pac 2.387atm
With the thicknees of 8mm the external pressure can be 2.34 bar
We can search for the minimum thickness to have a pressure of 1 bar.
ea1 4 mm
Py1e ea1
Rav Pressure at the mean circumferential stress reaches the yield point
Py1 3.183 105
Pa Py1 3.141atm
E 200 109
Pa
Pm1E ea1
2 1.21
Rav2
Pm1 1.703 106
Pa Pm1 17.027bar
Ratio1Pm1
Py1 Ratio1 5.3
RPr_Py1 0.55
Pr1 RPr_Py1Py1 Pr1 1.751 105
Pa Pr1 1.751bar
S 1.5 Safety factor
Pac1Pr1
S Pac1 1.152atm Pac1 1.167bar
With the thickness of 4 mm the external pressure can be 1.16 bar
Appendix A2
Shell under external pressure 8 Pag 47 EN 13445-3 2002 (E) Top vessel end
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4306, X2CrNi19-11 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Geometrical data: overall length 543mm outer diameter 1500mm inner diameter 1484mm.
8.5.22 Cylinder thickness
ea 8 mm Selected analysis cylinder thickness
Ri 742mm Inner radius
Rex Ri ea Rex 750mm Outer radius
RavRi Rex
2 Rav 746 mm Mean cylinder radius
Lcyl 425 mm h1 295 mm h11 0 mm
Lc Lcyl 0.4 h1 0.4 h11 Lc 0.543m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts page 25
Rp01 180106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 1.287 106
Pa Py 12.7atm
Lc 543 mm cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 0.36
Ord1ea
2 Rav Ord1 0.005
0.3 ncy1 4 ncy2 4
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.0124 c2 0.0124 Calculated from formula
From Diagram 8.5.3
ord2Lc
2 Rav ord2 0.364
Curvp2 Rav
ea Curvp 186.5
d 0.0012 From diagram 8.5.3
c1 0.0124 c2 0.0124
E 200 109
Pa
PmE ea c1
Rav Pm 2.658 10
7 Pa Pm 265.781bar
RatioPm
Py Ratio 20.65
RPr_Py 0.959
Pr RPr_PyPy Pr 1.234 106
Pa Pr 12.341bar
S 1.5 Safety factor
PacPr
S Pac 8.12atm Pac 8.12atm
With the thickness of 8 mm the external pressure can be 8.12 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 3.5 mm Selected analysis cylinder thickness
Ri1 746mm Inner radius
Rex1 Ri1 ea1 Rex1 749.5mm Outer radius
Rav1Ri1 Rex1
2 Rav1 747.75mm
e 120106
Pa 8.4.2 8.4.2 for austenitic steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 5.617 105
Pa Py1 5.543atm
Lc 543 mm cylinder length
Z1 Rav1
Lc Z1 4.326
Asc11Lc
2 Rav1 Asc11 0.36
Ord11ea1
2 Rav1 Ord11 0.002
ncy11 14
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0005
Diagram 8.5.3
ord111Lc
2 Rav1 ord111 0.363
Curvp12 Rav1
ea1 Curvp1 427.286
c11 0.0005 d1 0.0005
E 200 109
Pa
Py1 5.617 105
Pa Py1 5.617bar
Pm1E ea1 c11
Rav1 Pm1 4.546 10
5 Pa Py1 5.617 10
5 Pa
Ratio11Pm1
Py1 Ratio11 0.81
RPr_Py1 0.3
Pr1 RPr_Py1Py1 Pr1 1.685 105
Pa
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 1.123bar External pressure
The required thickness for only the vacuum can be 3.5mm
Using the mi mum thickness 4 mm we can evaluate the membrane longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea1 3.5mm
LPext Rav
2 ea1 L 10.657 10
6 Pa
CPext Rav
ea1 C 21.314 10
6 Pa
Appendix A3
11.1 Flanges EN13445-3 (E) TOP VESSEL END
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45 )
Rp02t 175 106
Pa Minimum 0.2 % proof strength at the working temp
Rm26 600 106
Pa Minimum tensile strength at the working temp
0.29 Poisson ratio
Al% 35 Elongation to the Breaking point
_________________________________________________________________________________
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts pag 25
Rp01 180 106
Pa Normal operational load cases
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
fd e
11 Flanges page 155 EN 13445-3
Geometrical data
A 1600mm B 1500mm e 46mm g1 16mm
C 1544mm g0 8 mm G 1518mm h 8 mm
11.5.2 Bolts loads and areas
w 10mm Contact width of gasket
bow
2 Basic effective gasket or joint seating width
bo 5 mm bo is less than 6.3 mm b=bo
b bo b is the effective gasket or joint width
When bo is less that 6.3 mm G is the mean diameter of the gasket contact area
G 1518mm Mean diameter of the gasket contact area of gasket
P 0.1106
Pa External pressure
H
44 G
2 P Total hydrostatic Force
H 81.372tonf Total force in ton compressive force
m1 1 m
Hg 2 G m1 P compression load on the gasket to assure the tightness
Hg 107.21tonf
pc 200newton
mm Require compression force for presetting force 200 N/mm
Hg G pc Hg 107.21tonf Total Presetting force
Assembly condition minimum bolt load
ycalpc
b ycal 40 10
6 Pa Pressure contact on sealing
y 54 106
Pa y is the minimum gasket or joint seating pressure
Wa b G ycal
nbHg
52
Wa 107.21tonf
C 1.544 103
mm Bolt pitch circle diameter
Operating condition
Wop H Hg Wop 25.838tonf
Pre-loading during the assembly condition
fa fd Bolt Material nominal design stress at ambient temperature
Rpbolt 700 106
Pa
fbRpbolt
4 fb 175 10
6 Pa 11.4.3 Bolting pag 151
fba fb Normal design stress for assembly temperature
Ab_min maxWa
fba
Wop
fb
Minimum Bolt stress area
Ab_min 5.45 103
mm2
dbe 11.6mm Effective diameter for M12
Adbe12
4dbe
2 Adbe12 105.683mm
2
n12regAb_min
Adbe12 n12reg 51.571
nbused 52
Fpre24 Adbe12 fb Fpre24 18494.556N Fpre24 2.079tonf
Pre-loading Austenitic steel A1-A2-A4 M12 class 70 19100 -29200 Newton torque between 50-88 NewtonXm
The flange has 52 bolts M12. Allowing during the assembly condition to make in contact the other flange. However we limit the preloads at about to 18177 Newton using a torque of 70 NewtonXm
wused 18177newton wused 2.043tonf
Wu nbused wused The total bolts loads
Wu 106.245tonf Total pre loading force
hgC G
2 hg 13mm Arm of the moment during to the pre-loading
Ma Wu hg Max flange momentum during the bolt pre loading
Ma 1.229 104
N m
Hd
4B
2 P hd
C B( )
2 hd 22 mm
HT Hd H
ht2C G B( )
4 ht 17.5mm
11.8.2 external pressure
Mop Hd hd( ) HT ht( ) Hg hg Mop 6.711 103
N m
For pair of flange that traps a tube sheet, bolts loads should be calculated at assembly and operating condition for each flange/gasket combination separately. Whop and WA shall be taken the greater of the two calculated values
flange Stresses and limits 11.5.4.1
b 0 mm Nominal gap between the sheet and the loose flange in the lap joint
e 46 mm Minimum flange thickness
db 12mm Is bolts outside diameter
m 1
Cf maxb
2 db6 e
m 0.5
1
Cf 1
A 1.6m B 1.5m
KA
B K 1.067
M MaCf
B M 8.192 10
3 N
m
m for assembly condition
c) Loose hubbed flange method
g1 16mm g0 8 mm
ratiog1
g0 ratio 2
tttB
g0 ttt 187.5
I0 B g0 I0 0.11m
ratio2h
I0 ratio2 0.07 ratio 2
tK
21 8.555246log K( )( ) 1
1.0472 1.9448K2
K 1( )
t 1.889
uK
21 8.55246log K( )( ) 1
1.36136 K2
1 K 1( )
u 32.83
y1
K 10.66845 5.7169
K2
log K( )
K2
1
y 29.876
fl 11 vl 120 From diagram 11.5.7 and 11.5.8
e fl I0
t I0
e3vl
u I0 g02
53.721
hM
g12
h 5.957 105
Pa Longitudinal hub stress
r1.333e fl I0( ) M
e2
I0
r 5.158 105
Pa Radial stress
y M
e2
rK
21
K2
1
107.656 106
Pa Tangential stress
A) Integral method
f 0.90 Fig. 11.5-4
vi .41 Fig. 11.5-5
3 Fig. 11.5-6
u 32.83
Ie f I0
t I0
e3vi
u I0 g02
I 0.903 ratio2 0.073
Hi M
I g12
Hi 106.344 106
Pa
rI1.333e f I0( ) M
I e2
I0
rI 6.449 106
Pa
Iy M
e2
rIK
21
K2
1
I 15.593 106
Pa
Stress limit B is between 1000mm and 2000 mm k = 1.167 see stress limit 11.5.4.2
Kf2
31
B
2000mm
K 1.067 11.5 38( )
stress limit
fh fd Nominal design stress of hub
fl fd Nominal design stress
Verification for loose hubbed flange method
param1 Kf h param1 6.9 105
Pa 11.5.39( )
param2 Kf r param2 6.017 105
Pa 11.5.40( )
param3 Kf param3 125.598 106
Pa 11.5.41( )
param4 0.5Kf h r( ) param4 6.483 105
Pa 11.5.42( )
param5 0.5Kf h ( ) param5 63.147 106
Pa 11.5.43( )
Nbfab3 All parameters are below the stresses limits
fh 120 106
Pa fl 120 106
Pa
Appendix A4
Shell under external pressure 8 Pag. 47 EN 13445-3 2002 (E) Top vessel
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Geometrical data: overall length 440mm outer diameter 1500mm inner diameter 1484mm.
8.5.22 Cylinder thickness
ea 8 mm Selected analysis cylinder thickness
Ri 742mm Inner radius
Rex Ri ea Rex 750mm Outer radius
RavRi Rex
2 Rav 746 mm Mean cylinder radius
Lcyl 440mm
Lc Lcyl Lc 0.44m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts pag 25
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 1.287 106
Pa Py 12.7atm
Lc 440 mm Cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 0.29
Ord1ea
2 Rav Ord1 0.005
0.3 ncy1 11 ncy2 12
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.002 c2 0.0021
c1 0.002 c2 0.0021
E 200 109
Pa
PmE ea c1
Rav Pm 4.282 10
6 Pa Pm 42.822bar
RatioPm
Py Ratio 3.33
RPr_Py 0.9
Pr RPr_PyPy Pr 1.158 106
Pa Pr 11.582bar
S 1.5 Safety factor
PacPr
S Pac 7.62atm Pac 7.62atm
With the thickness of 8 mm the external pressure can be 7.62 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 3 mm Selected analysis cylinder thickness
Ri1 747mm Inner radius
Rex1 Ri1 ea1 Rex1 750mm Outer radius
Rav1Ri1 Rex1
2 Rav1 748.5mm
e 120 106
Pa 8.4.2 8.4.2 for austenitic steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 4.81 105
Pa Py1 4.747atm
Lc 440 mm Cylinder length
Z1 Rav1
Lc Z1 5.344
Asc11Lc
2 Rav1 Asc1 0.29
Ord11ea1
2 Rav1 Ord1 0.005
ncy11 11
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0005
E 200 109
Pa
Py1 4.81 105
Pa Py1 4.81bar
Pm1E ea1 c11
Rav1 Pm1 4.115 10
5 Pa Py1 4.81 10
5 Pa
Ratio1Pm1
Py1 Ratio1 0.86
RPr_Py1 0.959
Pr1 RPr_Py1Py1 Pr1 4.612 105
Pa
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 3.075bar External pressure
The required thickness for only the vacuum can be 4mm
Using the minimum thickness 4 mm we can evaluate the menbranal longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea1 3 mm
LPext Rav
2 ea1 L 12.433 10
6 Pa
CPext Rav
ea1 C 24.867 10
6 Pa
Appendix A5
Flat top plate
10.5 Un pierced bolted circular Flat ends EN13445-3 (E)
Material X2CRNI18-9 1.4307
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
fd e
Flat gasket with narrow face b) type raised face page 138 EN 13445-3 page. 137
C 1544mm Bolt pitch circle
G 1518mm Gasket circle (mean contact surface for our case
fa fd Bolt Material nominal design stress at ambient temperature
pset 200N
mm Pre setting pressure sealing gasket
pavg G Average perimeter
TpreF pavg pset TpreF 9.538 105
N TpreF 107.21tonf
f fd nominal design stress
nb 52 number of bolts
boltloadTpreF
nb boltload 18.342 10
3 N
boltps 20000newton pre loading of each bolt
W nb boltps Total pre loading force M12 A4 property class 70
b 10 mm
P 0.1106
Pa
W 1040000N W 116.901tonf Total pre loading force
ypset
b
Wa b G y presetting assembly condition
Wa 9.538 105
newton Wa 107.21tonf
Thickness of the plate without holes
The minimum thickness within the Gasket
0.3 m 1
ep 33
32 G
2 3
G
42 b m
C G( )
P
f ep 24.901mm
ea3 C G( )
G
W
fa
ea 11.906mm
e maxea ep( )
e 24.901mm
10.5.2.2 The minimum thickness for the flange extension Pag 137
ep1 3G
42 b m
C G( )P
f
e1 maxea ep1( )
e1 11.906mm
For a single opening central hole 890mm dia
d1 890mm Di 1600mm
j1 Di
Y21j1
j1 d1 e1r Y21e e1r 37.38mm
For a single hole
d2 125mm J2 Di
Y22J2
J2 d2
e2r Y22e e2r 25.934mm
Bolted flat end (see fig 10-6-1 and 10.6-2)
j 605.5mm mean distance between holes see Fig 10.6-2 equal to k
ds 125mm small opening
di 890 mm eb 3 mm
eab 46.5mm Flange radial thickness
lr 0.8 di eb( ) eb Ap lr eab eb( )
dl di 2Ap
e dl 745.329mm
ddl ds
2 mean diameters of holes
Y2j
j d eo e
e Y2 eo e 46.948mm
Verification of rule 10.5.1.3 pag 137
db 890mm maximum opening hole
calp 2 db6 e1
0.5 m calp 1827.624mm
tb 2164mm mean bolt circle in a bolted flat end
tb is is less than calp so it is satisfied 10.5.1.3
ASME verification solid plate
adm fd
Thick1 C0.3P
adm Thick1 24.413mm
hgC G
2 hg 13mm distance between the bolt and the gasket reaction
Thick2 C0.3P
adm1.9
W hg
adm C3
Thick2 27.104mm
_____________________________________________________________________________________
Analytical calculation Roark pag 393 sixth Edition
Note: The formulas in this table are only valid if the equations in Table 24 yielded deflections greater than one-half the plate thickness, i.e. ymax>t/2.
Provides a description of Table 24a and the notation used.
Plate dimensions:
Notation file
Enter dimensions, properties
and loading
thickness:
tp 45mm av radius of contact radius:
ra 772mm Applied uniform pressure:
pd 0.1106
Pa
Modulus of elasticity: Em 200 10
9 Pa
Poisson's ratio:
m 0.3
Calculation procedure The maximum deflection, ymax, and stress, max are solved for by the following expressions:
DplEm tp
3
12 1 m2
Plate constant
Dpl 1.669 106
J pd 1 105
Pa
dmaxpd ra
4
64 Dpl
5 m
1 m max deflection
dmax 1.356 mm
Mmaxpd ra
2
163 m( )
Mmax 1.229 104
N
max6 Mmax
tp2
max 36.421 106
Pa maximum stress
Appendix A6
11.1 Flanges EN13445-3 (E) TOP VESSEL END
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45 )
Rp02t 175 106
Pa Minimum 0.2 % proof strength at the working temp
Rm26 600 106
Pa Minimum tensile strength at the working temp
0.29 Poisson ratio
Al% 35 Elongation to the Breaking point _________________________________________________________________________________
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts pag 25
Normal operational load cases Rp01 180 10
6 Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
fd e
11 Flanges page 155 EN 13445-3
A 983 mm B 890mm e 35mm g1 16mm
C 950mm g0 8 mm G 924mm h 8 mm
11.5.2 Bolts loads and areas
w 10mm Contact width of gasket
bow
2 Basic effective gasket or joint seating width
bo 5 mm bo is less than 6.3 mm b=bo
b bo b is the effective gasket or joint width
When bo is less that 6.3 mm G is the mean diameter of the gasket contact area
G 0.924m Mean diameter of the gasket contact area of gasket
P 0.1106
Pa External pressure
H
44 G
2 P Total hydrostatic Force
H 30.149tonf Total force in ton
m1 0.04m
Hg 2 G m1 P Compression load on the gasket to assure the tightness
Hg 2.61tonf
pc 200newton
mm Compression force for sealing 200N/mm
Hg G pc Hg 65.258tonf Presetting force
Assembly condition minimum bolt load
ycalpc
b ycal 40 10
6 Pa Pressure contact on sealing
y 54 106
Pa y is the minimum gasket or joint seating pressure
Wa b G y
nbHg
42
Wa 88.099tonf
C 950mm Bolt pitch circle diameter
Operating condition
Wop H Hg Wop 35.109tonf
Possible Prealoaging during the assembly condition
fa fd Bolt Material nominal design stress at ambient temperature
Rpbolt 700 106
Pa
fbRpbolt
4 fb 175 10
6 Pa 11.4.3 Bolting page 151
fba fb Normal design stress for assembly temperature
Ab_min maxWa
fba
Wop
fb
Minimum Bolt stress area
Ab_min 4.479 103
mm2
dbe 11.6mm Effective diameter for M12
Adbe12
4dbe
2 Adbe12 105.683mm
2
n12regAb_min
Adbe12 n12reg 42.378
nbused 42
Fpre24 Adbe12 fb Fpre24 18494.556N Fpre24 2.079tonf
Pre-loading Austenitic steel A1-A2-A4 M12 calss 70 19100 -29200 Newton torque between 50-88 NewtonXm
The flange has 42 bolts M12. allowing during the assembly condition to make in contact the other flange. However we limit the preload at about to 19000 Newton using a torque of 60 NewtonXm
wused 14070newton wused 1.582tonf
Wu nbused wused The total bolts loads
Wu 66.424tonf Total pre loading force
hgC G
2 hg 13mm Arm of the moment during to the pre-loading
Ma Wu hg Max flange momentum during the bolt pre loading
Ma 7.682 103
N m
Hd
4B
2 P hd
C B( )
2 hd 30 mm
HT Hd H
ht2C G B( )
4 ht 21.5mm
11.8.2 External pressure
Mop Hd hd( ) HT ht( ) Hg hg Mop 4.984 103
N m
For pair of flange that traps a tube sheet, bolts loads should be calculated at assembly and operating condition for each flange/gasket combination separately. Whop and WA shall be taken the greater of the two calculated values
Flange Stresses and limits 11.5.4.1
b 0 mm Nominal gap between the sheet and the loose flange in the lap joint
e 35 mm Minimum flange thickness
db 12mm Area bolts outside diameter
m 1
Cf maxb
2 db6 e
m 0.5
1
Cf 1
A 0.983m B 0.89m
KA
B K 1.104
M MaCf
B M 8.632 10
3 N
m
m For assembly condition
c) Loose hubbed flange method
g1 16mm g0 8 mm
ratiog1
g0 ratio 2
tttB
g0 ttt 111.25
I0 B g0 I0 0.08m
h 8 103
m
ratio2h
I0 ratio2 0.09 ratio 2
tK
21 8.555246log K( )( ) 1
1.0472 1.9448K2
K 1( )
t 1.876
uK
21 8.55246log K( )( ) 1
1.36136 K2
1 K 1( )
u 21.425
y1
K 10.66845 5.7169
K2
log K( )
K2
1
y 19.497
fl 8.5 vl 100 From diagram 11.5.7 and 11.5.8
e fl I0
t I0
e3vl
u I0 g02
39.468
hM
g12
h 8.543 105
Pa Longitudinal hub stress
r1.333e fl I0( ) M
e2
I0
r 1.018 106
Pa Radial stress
y M
e2
rK
21
K2
1
127.109 106
Pa Tangential stress
A) Integral method
f 0.90 Fig. 11.5-4
vi .41 Fig. 11.5-5
3 Fig. 11.5-6
u 21.425
Ie f I0
t I0
e3vi
u I0 g02
I 0.884 ratio2 0.095
Hi M
I g12
Hi 114.433 106
Pa
rI1.333e f I0( ) M
I e2
I0
rI 11.938 106
Pa
Iy M
e2
rIK
21
K2
1
I 16.869 106
Pa
Stress limit B is less than 1000 mm 11.5.4.2
Stress limit Kf 1
fh fd Nominal design stress of hub
fl fd Nominal design stress
Verification for loose hub bed flange method
param1 Kf h param1 8.5 105
Pa 11.5.39( )
param2 Kf r param2 1.018 106
Pa 11.5.40( )
param3 Kf param3 127.109 106
Pa 11.5.41( )
param4 0.5Kf h r( ) param4 9.359 105
Pa 11.5.42( )
param5 0.5Kf h ( ) param5 63.982 106
Pa 11.5.43( )
All parameters are below the stresses limits
fh 120 106
Pa fl 120 106
Pa
Appendix A7
Shell under external pressure 8 Pag 47 EN 13445-3 2002 (E) Top vessel end
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4306, X2CrNi19-11 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Geometrical data: overall length 609mm outer diameter 906mm inner diameter 890mm.
8.5.22 Cylinder thickness
ea 8 mm Selected analysis cylinder thickness
Ri 453mm Inner radius
Rex Ri ea Rex 461mm Outer radius
RavRi Rex
2 Rav 457 mm Mean cylinder radius
Lcyl 609mm
Lc Lcyl Lc 0.609m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts pag 25
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 2.101 106
Pa Py 20.732atm
Lc 609 mm Cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 0.67
Ord1ea
2 Rav Ord1 0.009
0.3 ncy1 6 ncy2 7
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.0017 c2 0.0018 Calculated from formula
c1 0.0017 c2 0.0018
E 200 109
Pa
PmE ea c1
Rav Pm 5.935 10
6 Pa Pm 59.353bar
RatioPm
Py Ratio 2.83
RPr_Py 0.849
Pr RPr_PyPy Pr 1.783 106
Pa Pr 17.835bar
S 1.5 Safety factor
PacPr
S Pac 11.734atm Pac 11.734atm
With the thickness of 8 mm the external pressure can be 11.734 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 2.7mm Selected analysis cylinder thickness
Ri1 450.5mm Inner radius Outer radius
Rex1 Ri1 ea1 Rex1 453.2mm
Rav1Ri1 Rex1
2 Rav1 451.85mm
e 120 106
Pa 8.4.2 8.4.2 for austenitic steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 7.171 105
Pa Py1 7.077atm
Lc 609 mm Cylinder length
Z1 Rav1
Lc Z1 2.331
Asc11Lc
2 Rav1 Asc11 0.67
Ord11ea1
2 Rav1 Ord11 0.003
ncy11 9
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0003
E 200 10
9 Pa
Py1 7.171 105
Pa Py1 7.171bar
Pm1E ea1 c11
Rav1 Pm1 4.019 10
5 Pa Py1 7.171 10
5 Pa
Ratio11Pm1
Py1 Ratio11 0.56
RPr_Py1 0.25
Pr1 RPr_Py1Py1 Pr1 1.793 105
Pa Pr1 1.793bar
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 1.195bar External pressure
The required thickness for only the vacuum can be than 2.7 mm
Using the mi mum thickness 2.7 mm we can evaluate the membrane longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea1 2.7mm
LPext Rav
2 ea1 L 8.463 10
6 Pa
CPext Rav
ea1 C 16.926 10
6 Pa
Appendix A8
Flat top plate
10.5 Un pierced bolted circular Flat ends EN13445-3 (E)
Material X2CRNI18-9 1.4307
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
fd e
Flat gasket with narrow face b) type raised face page 138 EN 13445-3 page. 137
C 1544mm Bolt pitch circle
G 1518mm Gasket circle (mean contact surface for our case
fa fd Bolt Material nominal design stress at ambient temperature
pset 200N
mm Presetting pressure sealing gasket
pavg G Average perimeter
TpreF pavg pset TpreF 9.538 105
N TpreF 107.21tonf
f fd Nominal design stress
nb 52 Number of bolts
boltloadTpreF
nb boltload 18.342 10
3 N
boltps 20000newton Pre loading of each bolt
W nb boltps Total pre loading force M12 A4 property class 70
b 10 mm
P 0.1106
Pa
W 1040000N W 116.901tonf Total pre loading force
ypset
b
Wa b G y Presetting assembly condition
Wa 9.538 105
newton Wa 107.21tonf
Thickness of the plate without holes
The minimum thickness within the Gasket
0.3 m 1
ep 33
32 G
2 3
G
42 b m
C G( )
P
f ep 24.901mm
ea3 C G( )
G
W
fa
ea 11.906mm
e maxea ep( )
e 24.901mm
10.5.2.2 The minimum thickness for the flange extension Peg 137
ep1 3G
42 b m
C G( )P
f
e1 maxea ep1( )
e1 11.906mm
For a single opening central hole 890mm dia
d1 890mm j1 2 800 mm
Y21j1
j1 d1 e1r Y21e e1r 37.38mm
ASME verification solid plate
adm fd
Thick1 C0.3P
adm Thick1 24.413mm
hgC G
2 hg 13mm Distance between the bolt and the gasket reaction
Thick2 C0.3P
adm1.9
W hg
adm C3
Thick2 27.104mm
_____________________________________________________________________________________
Analytical calculation Roark page 393 sixth Edition
Note: The formulas in this table are only valid if the equations in Table 24 yielded deflections greater than one-half the plate thickness, i.e. ymax>t/2.
Provides a description of Table 24a and the notation used.
Plate dimensions:
Notation file
Enter dimensions, properties
and loading
Thickness:
tp 45mm Average radius of contact radius:
ra 772mm Applied uniform pressure:
pd 0.1106
Pa
Modulus of elasticity: Em 200 10
9 Pa
Poisson's ratio:
m 0.3
Calculation procedure The maximum deflection, ymax, and stress, max are solved for by the following expressions:
DplEm tp
3
12 1 m2
Plate constant
Dpl 1.669 106
J pd 1 105
Pa
dmaxpd ra
4
64 Dpl
5 m
1 m Max deflection
dmax 1.356 mm
Mmaxpd ra
2
163 m( )
Mmax 1.229 104
N
max6 Mmax
tp2
max 36.421 106
Pa Maximum stress
Shell under external pressure 8 Pag 47 EN 13445-3 2002 (E)
Appendix A9
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4306, X2CrNi19-11 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Geometrical data: overall length 1805mm outer diameter 870mm inner diameter 860mm.
8.5.22 Cylinder thickness
ea 10 mm Selected analysis cylinder thickness
Ri 740mm Inner radius
Rex Ri ea Rex 750mm Outer radius
RavRi Rex
2 Rav 745 mm Mean cylinder radius
Lcyl 2109mm h1 296mm h11 296mm
Lc Lcyl 0.4h1 0.4h11 Lc 2.346m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts pag 25
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 1.611 106
Pa Py 15.897atm
Lc 2.346 103
mm Cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 1.57
Ord1ea
2 Rav Ord1 0.007
0.3 ncy1 4 ncy2 5
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.0005 c2 0.0005
c1 0.0005 c2 0.0005
E 200 109
Pa
PmE ea c1
Rav Pm 1.326 10
6 Pa Pm 13.255bar
RatioPm
Py Ratio 0.82
RPr_Py 0.4
Pr RPr_PyPy Pr 6.443 105
Pa Pr 6.443bar
S 1.5 Safety factor
PacPr
S Pac 4.239atm Pac 4.239atm
With the thickness of 10 mm the external pressure can be 4.237 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 5 mm Selected analysis cylinder thickness
Ri1 745mm Inner radius
Rex1 Ri1 ea1 Rex1 750mm Outer radius
Rav1Ri1 Rex1
2 Rav1 747.5mm
e 120 106
Pa 8.4.2 8.4.2 for austenich steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 8.027 105
Pa Py1 7.922atm
Lc 2345.8mm Cylinder length
Z1 Rav1
Lc Z1 1.001
Asc11Lc
2 Rav1 Asc11 1.57
Ord11ea1
2 Rav1 Ord11 0.003
ncy11 6
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0002 E 200 109
Pa
Py1 8.027 105
Pa Py1 8.027bar
Pm1E ea1 c11
Rav1 Pm1 2.278 10
5 Pa Py1 8.027 10
5 Pa
Ratio1Pm1
Py1 Ratio1 0.28
RPr_Py1 0.19
Pr1 RPr_Py1Py1 Pr1 1.525 105
Pa
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 1.017bar External pressure
The required thickness for only the vacuum can be 5mm
Using the mime thickness 10 mm we can evaluate the menbranal longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea 10mm
LPext Rav
2 ea L 3.725 10
6 Pa
CPext Rav
ea C 7.45 10
6 Pa
Appendix A10
Shell under external pressure 8 Pag 47 EN 13445-3 2002 (E) Top vessel
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Geometrical data: overall length 440mm outer diameter 1500mm inner diameter 1484mm.
8.5.22 Cylinder thickness
ea 8 mm Selected analysis cylinder thickness
Ri 600mm Inner radius
Rex Ri ea Rex 608mm Outer radius
RavRi Rex
2 Rav 604 mm Mean cylinder radius
Lcyl 623mm
Lc Lcyl Lc 0.623m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts page 25
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 1.589 106
Pa Py 15.686atm
Lc 623 mm Cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 0.52
Ord1ea
2 Rav Ord1 0.007
0.3 ncy1 8 ncy2 8
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.0015 c2 0.0015
c1 0.0015 c2 0.0015
E 200 109
Pa
PmE ea c1
Rav Pm 3.914 10
6 Pa Pm 39.145bar
RatioPm
Py Ratio 2.46
RPr_Py 0.8
Pr RPr_PyPy Pr 1.272 106
Pa Pr 12.715bar
S 1.5 Safety factor
PacPr
S Pac 8.366atm Pac 8.366atm
With the thickness of 8 mm the external pressure can be 8.3 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 3 mm Selected analysis cylinder thickness
Ri1 605.0mm Inner radius
Rex1 Ri1 ea1 Rex1 608mm Outer radius
Rav1Ri1 Rex1
2 Rav1 606.5mm
e 120 106
Pa 8.4.2 8.4.2 for austenitic steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 5.936 105
Pa Py1 5.858atm
Lc 623 mm Cylinder length
Z1 Rav1
Lc Z1 3.058
Asc11Lc
2 Rav1 Asc11 0.51
Ord11ea1
2 Rav1 Ord11 0.002
ncy11 11
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0003
E 200 109
Pa
Py1 5.936 105
Pa Py1 5.936bar
Pm1E ea1 c11
Rav1 Pm1 3.383 10
5 Pa Py1 5.936 10
5 Pa
Ratio1Pm1
Py1 Ratio1 0.57
RPr_Py1 0.28
Pr1 RPr_Py1Py1 Pr1 1.662 105
Pa
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 1.108bar
The required thickness for only the vacuum can be 3mm
Using the mi mum thickness 2.5 mm we can evaluate the membrane longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea1 3 mm
LPext Rav
2 ea1 L 10.067 10
6 Pa
CPext Rav
ea1 C 20.133 10
6 Pa
Appendix A11
11.1 Flanges EN13445-3 (E) TOP VESSEL END
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45 )
Rp02t 175 106
Pa Minimum 0.2 % proof strength at the working temp
Rm26 600 106
Pa Minimum tensile strength at the working temp
0.29 Poisson ratio
Al% 35 Elongation to the Breaking point _________________________________________________________________________________
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts page 25
Normal operational load cases Rp01 180 10
6 Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
fd e
11 Flanges page 155 EN 13445-3
A 1310mm B 1190mm e 35mm g1 16mm
C 1260mm g0 8 mm G 1234mm h 8 mm
11.5.2 Bolts loads and areas
w 10mm Contact width of gasket
bow
2 Basic effective gasket or joint seating width
bo 5 mm bo is less than 6.3 mm b=bo
b bo b is the effective gasket or joint width
When bo is less that 6.3 mm G is the mean diameter of the gasket contact area
G 1.234 103
mm Mean diameter of the gasket contact area of gasket
P 0.1106
Pa External pressure
H
44 G
2 P Total hydrostatic Force
H 53.773tonf Total force in ton
m1 0.04m
Hg 2 G m1 P Compression load on the gasket to assure the tightness
Hg 3.486tonf
pc 200newton
mm Compression force for sealing 200N/mm
Hg G pc Hg 87.152tonf Presetting force
Assembly condition minimum bolt load
ycalpc
b ycal 40 10
6 Pa Pressure contact on sealing
y 54 106
Pa y is the minimum gasket or joint seating pressure
Wa b G ycal
nbHg
42
Wa 87.152tonf nb 1882.457kgf
C 1.26 103
mm Bolt pitch circle diameter
Operating condition
Wop H Hg Wop 33.379tonf
Possible Preloading during the assembly condition
fa fd Bolt Material nominal design stress at ambient temperature
Rpbolt 700 106
Pa
fbRpbolt
4 fb 175 10
6 Pa 11.4.3 Bolting page 151
fba fb Normal design stress for assembly temperature
Ab_min maxWa
fba
Wop
fb
Minimum Bolt stress area
Ab_min 4.431 103
mm2
dbe 11.6mm Effective diameter for M12
Adbe12
4dbe
2 Adbe12 105.683mm
2
n12regAb_min
Adbe12 n12reg 41.923
nbused 42
Fpre24 Adbe12 fb Fpre24 18494.556N Fpre24 2.079tonf
Pre-loading Austenitic steel A1-A2-A4 M12 calss 70 19100 -29200 Newton torque between 50-88 NewtonXm
The flange has 42 bolts M12. Allowing during the assembly condition to make in contact the other flange. However we limit the preloads at about to 19000 Newton using a torque of 60 NewtonXm
wused 16013newton wused 1.8tonf
Wu nbused wused The total bolts loads
Wu 75.597tonf Total pre loading force
hgC G
2 hg 13mm Arm of the moment during to the pre-loading
Ma Wu hg Max flange momentum during the bolt pre loading
Ma 8.743 103
N m
Hd
4B
2 P hd
C B( )
2 hd 35 mm
HT Hd H
ht2C G B( )
4 ht 24 mm
11.8.2 External pressure
Mop Hd hd( ) HT ht( ) Hg hg Mop 5.16 103
N m
For pair of flange that traps a tube sheet, bolts loads should be calculated at assembly and operating condition for each flange/gasket combination separately. Whop and WA shall be taken the greater of the two calculated values
Flange Stresses and limits 11.5.4.1
b 0 mm Nominal gap between the sheet and the loose flange in the lap joint
e 35 mm Minimum flange thickness
db 12mm Are bolts outside diameter?
m 1
Cf maxb
2 db6 e
m 0.5
1
Cf 1
A 1.31m B 1.19m
KA
B K 1.101
M MaCf
B M 7.347 10
3 N
m
m For assembly condition
c) Loose hubbed flange method
g1 16mm g0 8 mm
ratiog1
g0 ratio 2
tttB
g0 ttt 148.75
I0 B g0 I0 0.1m
h 8 103
m
ratio2h
I0 ratio2 0.08 ratio 2
tK
21 8.555246log K( )( ) 1
1.0472 1.9448K2
K 1( )
t 1.877
uK
21 8.55246log K( )( ) 1
1.36136 K2
1 K 1( )
u 22.154
y1
K 10.66845 5.7169
K2
log K( )
K2
1
y 20.16
fl 7.5 vl 100 From diagram 11.5.7 and 11.5.8
e fl I0
t I0
e3vl
u I0 g02
32.958
hM
g12
h 8.708 105
Pa Longitudinal hub stress
r1.333e fl I0( ) M
e2
I0
r 8.346 105
Pa Radial stress
y M
e2
rK
21
K2
1
112.199 106
Pa Tangential stress
A) Integral method
f 0.895 Fig. 11.5-4
vi .42 Fig. 11.5-5
3.2 Fig. 11.5-6
u 22.154
Ie f I0
t I0
e3vi
u I0 g02
I 0.834 ratio2 0.082
Hi M
I g12
Hi 110.141 106
Pa
rI1.333e f I0( ) M
I e2
I0
rI 10.271 106
Pa
Iy M
e2
rIK
21
K2
1
I 13.675 106
Pa
Stress limit B is less than 1000 mm 11.5.4.2
Stress limit Kf 1
fh fd Nominal design stress of hub
fl fd Nominal design stress
Verification for loose hubbed flange method
param1 Kf h param1 8.7 105
Pa 11.5.39( )
param2 Kf r param2 8.346 105
Pa 11.5.40( )
param3 Kf param3 112.199 106
Pa 11.5.41( )
param4 0.5Kf h r( ) param4 8.527 105
Pa 11.5.42( )
param5 0.5Kf h ( ) param5 56.535 106
Pa 11.5.43( )
All parameters are below the stresses limits
fh 120 106
Pa fl 120 106
Pa
Appendix A12
Shell under external pressure 8 Page 47 EN 13445-3 2002 (E) Top vessel end
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4306, X2CrNi19-11 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Geometrical data: overall length 2631mm outer diameter 1500mm inner diameter 1480mm.
8.5.22 Cylinder thickness
ea 10 mm Selected analysis cylinder thickness
Ri 740mm Inner radius
Rex Ri ea Rex 750mm Outer radius
RavRi Rex
2 Rav 745 mm Mean cylinder radius
Lcyl 2333mm h1 295mm h11 0 mm
Lc Lcyl 0.4h1 0.4h11 Lc 2.451m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts page 25
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 1.611 106
Pa Py 15.897atm
Lc 2.451 103
mm Cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 1.64
Ord1ea
2 Rav Ord1 0.007
0.3 ncy1 5 ncy2 5
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.0005 c2 0.0005
c1 0.0005 c2 0.0005
E 200 109
Pa
PmE ea c1
Rav Pm 1.26 10
6 Pa Pm 12.599bar
RatioPm
Py Ratio 0.78
RPr_Py 0.38
Pr RPr_PyPy Pr 6.121 105
Pa Pr 6.121bar
S 1.5 Safety factor
PacPr
S Pac 4.027atm Pac 4.027atm
With the thickness of 8 mm the external pressure can be 4.027 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 6 mm Selected analysis cylinder thickness
Ri1 744mm Inner radius
Rex1 Ri1 ea1 Rex1 750mm Outer radius
Rav1Ri1 Rex1
2 Rav1 747mm
e 120 106
Pa 8.4.2 8.4.2 for austenitic steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 9.639 105
Pa Py1 9.513atm
Lc 2.451 103
mm Cylinder length
Z1 Rav1
Lc Z1 0.957
Asc11Lc
2 Rav1 Asc11 1.64
Ord11ea1
2 Rav1 Ord11 0.004
ncy11 6
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0002
Py1 9.639 105
Pa Py1 9.639bar
Pm1E ea1 c11
Rav1 Pm1 3.732 10
5 Pa Py1 9.639 10
5 Pa
Ratio1Pm1
Py1 Ratio1 0.39
RPr_Py1 0.18
Pr1 RPr_Py1Py1 Pr1 1.735 105
Pa
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 1.157bar
The required thickness for only the vacuum can be 6mm
Using the mi mum thickness 6 mm we can evaluate the membrane longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea1 6 mm
LPext Rav
2 ea1 L 6.208 10
6 Pa
CPext Rav
ea1 C 12.417 10
6 Pa
Appendix A13
Shell under external pressure 8 Peg 47 EN 13445-3 2002 (E) Top vessel end
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4306, X2CrNi19-11 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Geometrical data: overall length 450mm outer diameter 1010mm inner diameter 994mm.
8.5.22 Cylinder thickness
ea 8 mm Selected analysis cylinder thickness
Ri 497mm Inner radius
Rex Ri ea Rex 505mm Outer radius
RavRi Rex
2 Rav 501 mm Mean cylinder radius
Lcyl 450mm
Lc Lcyl Lc 0.45m
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than bolts page 25
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenitic steel
Pye ea
Rav Pressure at the mean circumferential stress reaches the yield point
Py 1.916 106
Pa Py 18.911atm
Lc 450 mm Cylinder length
Z Rav
Lc
Asc1Lc
2 Rav Asc1 0.45
Ord1ea
2 Rav Ord1 0.008
0.3 ncy1 8 ncy2 8
c11
ncy12
1Z
2
2
1
ncy12
Z2
1
2
ea2
12 Rav2
1 2
ncy1
21 Z
2
2
c21
ncy22
1Z
2
2
1
ncy22
Z2
1
2
ea2
12 Rav2
1 2
ncy2
21 Z
2
2
c1 0.0023 c2 0.0023 Calculated from formula
E 200 109
Pa
PmE ea c1
Rav Pm 7.297 10
6 Pa Pm 72.965bar
RatioPm
Py Ratio 3.81
RPr_Py 0.88
Pr RPr_PyPy Pr 1.686 106
Pa Pr 16.862bar
S 1.5 Safety factor
PacPr
S Pac 11.095atm Pac 11.095atm
With the thickness of 8 mm the external pressure can be 11.095 bar
We can search for the minimum thickness to have a pressure of 1 bar.
8.5.22 Minimum Cylinder thickness
ea1 2.5mm Selected analysis cylinder thickness
Ri1 502.5mm Inner radius Outer radius
Rex1 Ri1 ea1 Rex1 505mm
Rav1Ri1 Rex1
2 Rav1 503.75mm
e 120 106
Pa 8.4.2 8.4.2 for austenitic steel
Py1e ea1
Rav1 Pressure at the mean circumferential stress reaches the yield point
Py1 5.955 105
Pa Py1 5.877atm
Lc 450 mm Cylinder length
Z1 Rav1
Lc Z1 3.517
Asc11Lc
2 Rav1 Asc11 0.45
Ord11ea1
2 Rav1 Ord11 0.002
ncy11 12
0.3
c111
ncy112
1Z1
2
2
1
ncy112
Z12
1
2
ea12
12 Rav12
1 2
ncy11
21 Z1
2
2
c11 0.0004 E 200 10
9 Pa
Py1 5.955 105
Pa Py1 5.955bar
Pm1E ea1 c11
Rav1 Pm1 4.039 10
5 Pa Py1 5.955 10
5 Pa
Ratio11Pm1
Py1 Ratio11 0.68
RPr_Py1 0.28
Pr1 RPr_Py1Py1 Pr1 1.667 105
Pa Pr1 1.667bar
S 1.5 Safety factor for design condition
Pac1Pr1
S Pac1 1.112bar External pressure
The required thickness for only the vacuum can be than 3 mm
Using the mi mum thickness 3 mm we can evaluate the membrane longitudinal and circular stress
Pext 0.1106
Pa Pext 1 bar
ea1 2.5mm
LPext Rav
2 ea1 L 10.02 10
6 Pa
CPext Rav
ea1 C 20.04 10
6 Pa
Appendix A14
Flat top plate
10.5 Un pierced bolted circular Flat ends EN13445-3 (E)
Material X2CRNI18-9 1.4307
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenich steel
fd e
Flat gasket with narrow face b) type raised face page 138 EN 13445-3 page. 137
C 858mm Bolt pitch circle
G 858mm Gasket circle (mean contact surface for our case
fa fd Bolt Material nominal design stress at ambient temperature
pset 200N
mm Presetting pressure sealing gasket
pavg G Average perimeter
TpreF pavg pset TpreF 5.391 105
N TpreF 60.597tonf
f fd Nominal design stress
nb 52 Number of bolts
boltloadTpreF
nb boltload 10.367 10
3 N
boltps 20000newton Pre loading of each bolt
W nb boltps Total pre loading force M12 A4 property class 70
b 10 mm
P 0.1106
Pa
W 1040000N W 116.901tonf Total pre loading force
ypset
b
Wa b G y Presetting assembly conduction
Wa 5.391 105
newton Wa 60.597tonf
Thickness of the plate without holes
The minimum thickness within the Gasket
0.3 m 1
ep 33
32 G
2 3
G
42 b m
C G( )
P
f
ep 14mm
ea3 C G( )
G
W
fa
ea 0 mm
e maxea ep( )
e 14 mm
10.5.2.2 The minimum thickness for the flange extension Peg 137
ep1 3G
42 b m
C G( )P
f
e1 maxea ep1( )
e1 0 mm
adm fd
Thick1 C0.3P
adm Thick1 13.566mm
hgC G
2 hg 0 mm Distance between the bolt and the gasket reaction
Thick2 C0.3P
adm1.9
W hg
adm C3
Thick2 13.566mm
_____________________________________________________________________________________
Analytical calculation Roark page 393 sixth Edition
Note: The formulas in this table are only valid if the equations in Table 24 yielded deflections greater than one-half the plate thickness, i.e. ymax>t/2.
Provides a description of Table 24a and the notation used.
Plate dimensions:
Notation file
Enter dimensions,
properties and loading
Thickness:
tp 30mm Average radius of contact radius:
ra 435mm Applied uniform pressure:
pd 0.1106
Pa
Modulus of elasticity: Em 200 10
9 Pa
Poisson's ratio: m 0.3
Calculation procedure The maximum deflection, ymax, and stress, max are solved for by the following expressions:
DplEm tp
3
12 1 m2
Plate constant
Dpl 4.945 105
J pd 1 105
Pa
dmaxpd ra
4
64 Dpl
5 m
1 m Max deflection
dmax 0.461 mm
Mmaxpd ra
2
163 m( )
Mmax 3.903 103
N
max6 Mmax
tp2
max 26.018 106
Pa Maximum stress
Appendix A15
Flat top plate
10.5 Un pierced bolted circular Flat ends EN13445-3 (E)
Material X2CRNI18-9 1.4307
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenich steel
fd e
Flat gasket with narrow face b) type raised face page 138 EN 13445-3 page. 137
C 1058mm Bolt pitch circle
G 1058mm Gasket circle (mean contact surface for our case
fa fd Bolt Material nominal design stress at ambient temperature
pset 200N
mm Presetting pressure sealing gasket
pavg G Average perimeter
TpreF pavg pset TpreF 6.648 105
N TpreF 74.722tonf
f fd Nominal design stress
nb 52 Number of bolts
boltloadTpreF
nb boltload 12.784 10
3 N
boltps 20000newton Pre loading of each bolt
W nb boltps Total pre loading force M12 A4 property class 70
b 10 mm
P 0.1106
Pa
W 1040000N W 116.901tonf Total pre loading force
ypset
b
Wa b G y Presetting assembly conduction
Wa 6.648 105
newton Wa 74.722tonf
Thickness of the plate without holes
The minimum thickness within the Gasket
0.3 m 1
ep 33
32 G
2 3
G
42 b m
C G( )
P
f ep 16.988mm
ea3 C G( )
G
W
fa
ea 0 mm
e maxea ep( )
e 16.988mm
10.5.2.2 The minimum thickness for the flange extension Peg 137
ep1 3G
42 b m
C G( )P
f
e1 maxea ep1( )
e1 0 mm
ASME verification solid plate
adm fd
Thick1 C0.3P
adm Thick1 16.728mm
hgC G
2 hg 0 mm Distance between the bolt and the gasket reaction
Thick2 C0.3P
adm1.9
W hg
adm C3
Thick2 16.728mm _____________________________________________________________________________________
Analytical calculation Roark page 393 sixth Edition
Note: The formulas in this table are only valid if the equations in Table 24 yielded deflections greater than one-half the plate thickness, i.e. ymax>t/2.
Provides a description of Table 24a and the notation used.
Plate dimensions:
Notation file
Enter dimensions,
properties and loading
Thickness:
tp 30mm Average radius of contact radius:
ra 520mm Applied uniform pressure:
pd 0.1106
Pa
Modulus of elasticity: Em 200 10
9 Pa
Poisson's ratio: m 0.3
Calculation procedure The maximum deflection, ymax, and stress, max are solved for by the following expressions:
DplEm tp
3
12 1 m2
Plate constant
Dpl 4.945 105
J pd 1 105
Pa
dmaxpd ra
4
64 Dpl
5 m
1 m Max deflection
dmax 0.942 mm
Mmaxpd ra
2
163 m( )
Mmax 5.577 103
N
max6 Mmax
tp2
max 37.18 106
Pa Maximum stress
Appendix A15
Flat top plate
10.5 Un pierced bolted circular Flat ends EN13445-3 (E)
Material X2CRNI18-9 1.4307
Material AISI304L that correspond to EN 10028-2 1993 Number 1.4307, X2CrNi18-9 Mechanical data R1%min=180 Mpa R2%min=145Mpa Rul=450-650 Mpa Al%=35-45
Rp01 180 106
Pa
eRp01
1.5 e 120 10
6 Pa 8.4.2 for austenich steel
fd e
Flat gasket with narrow face b) type raised face page 138 EN 13445-3 page. 137
C 1260mm Bolt pitch circle
G 1234mm Gasket circle (mean contact surface for our case
fa fd Bolt Material nominal design stress at ambient temperature
pset 200N
mm Presetting pressure sealing gasket
pavg G Average perimeter
TpreF pavg pset TpreF 7.753 105
N TpreF 87.152tonf
f fd Nominal design stress
nb 42 Number of bolts
boltloadTpreF
nb boltload 18460.6N
boltps 20000newton Pre loading of each bolt
W nb boltps Total pre loading force M12 A4 property class 70
b 10 mm
P 0.1106
Pa
W 840000N W 94.42tonf Total pre loading force
ypset
b
Wa b G y Presetting assembly conduction
Wa 7.753 105
newton Wa 87.152tonf
Thickness of the plate without holes
The minimum thickness within the Gasket
0.3 m 1
ep 33
32 G
2 3
G
42 b m
C G( )
P
f ep 20.345mm
ea3 C G( )
G
W
fa
ea 11.868mm
e maxea ep( )
e 20.345mm
10.5.2.2 The minimum thickness for the flange extension Peg 137
ep1 3G
42 b m
C G( )P
f
e1 maxea ep1( )
e1 11.868mm
For a single hole
d2 125mm Di 1310mm
J2 Di J2 1.31m
Y22J2
J2 d2
e2r Y22e e2r 21.392mm
ASME verification solid plate
adm fd
Thick1 C0.3P
adm Thick1 19.922mm
hgC G
2 hg 13mm Distance between the bolt and the gasket reaction
Thick2 C0.3P
adm1.9
W hg
adm C3
Thick2 23.111mm
_____________________________________________________________________________________
Analytical calculation Roark page 393 sixth Edition
Note: The formulas in this table are only valid if the equations in Table 24 yielded deflections greater than one-half the plate thickness, i.e. ymax>t/2.
Provides a description of Table 24a and the notation used.
Plate dimensions:
Notation file
Enter dimensions,
properties and loading
Thickness:
tp 35mm Average radius of contact radius:
ra 655mm Applied uniform pressure:
pd 0.1106
Pa
Modulus of elasticity: Em 200 10
9 Pa
Poisson's ratio: m 0.3
Calculation procedure The maximum deflection, ymax, and stress, max are solved for by the following expressions:
DplEm tp
3
12 1 m2
Plate constant
Dpl 7.853 105
J pd 1 105
Pa
dmaxpd ra
4
64 Dpl
5 m
1 m Max deflection
dmax 1.493 mm
Mmaxpd ra
2
163 m( )
Mmax 8.849 103
N
max6 Mmax
tp2
max 43.34 106
Pa Maximum stress
top related