JGW-T1301483-TowerB1 B2 vacuum v3 - University of Tokyogwdoc.icrr.u-tokyo.ac.jp/DocDB/0014/T1301483/001/appendices JGW... · Appendix A2 Shell under external pressure 8 Pag 47 EN

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



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


Pye ea


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


Pa Pr 12.341bar

S 1.5 Safety factor

PacPr




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

_________________________________________________________________________________


Rp01 180 106

Pa Normal operational load cases

eRp01

1.5 e 120 10


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


Rp01 180 106

Pa

eRp01

1.5 e 120 10







RavRi Rex


Lcyl 440mm

Lc Lcyl Lc 0.44m


Pye ea


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


Pa Pr 11.582bar

S 1.5 Safety factor

PacPr





ea1 3 mm Selected analysis cylinder thickness


Rex1 Ri1 ea1 Rex1 750mm Outer radius

Rav1Ri1 Rex1

2 Rav1 748.5mm

e 120 106


Py1e ea1


Py1 4.81 105

Pa Py1 4.747atm


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


Pac1Pr1


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


Rp01 180 106

Pa

eRp01

1.5 e 120 10


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


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



Rp02t 175 106


Rm26 600 106


0.29 Poisson ratio

Al% 35 Elongation to the Breaking point _________________________________________________________________________________


Normal operational load cases Rp01 180 10

6 Pa

eRp01

1.5 e 120 10


fd e


A 983 mm B 890mm e 35mm g1 16mm

C 950mm g0 8 mm G 924mm h 8 mm



bow





G 0.924m Mean diameter of the gasket contact area of gasket

P 0.1106


H

44 G


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


ycalpc

b ycal 40 10


y 54 106


Wa b G y

nbHg

42

Wa 88.099tonf

C 950mm Bolt pitch circle diameter

Operating condition


Possible Prealoaging during the assembly condition


Rpbolt 700 106

Pa

fbRpbolt

4 fb 175 10

6 Pa 11.4.3 Bolting page 151


Ab_min maxWa

fba

Wop

fb


Ab_min 4.479 103

mm2


Adbe12

4dbe

2 Adbe12 105.683mm

2

n12regAb_min


nbused 42


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




hgC G



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


N m


Flange Stresses and limits 11.5.4.1



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


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


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


r1.333e fl I0( ) M

e2

I0

r 1.018 106

Pa Radial stress

y M

e2

rK

21

K2

1

127.109 106


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



Verification for loose hub bed flange method


Pa 11.5.39( )


Pa 11.5.40( )


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







RavRi Rex


Lcyl 609mm

Lc Lcyl Lc 0.609m


Rp01 180 106

Pa

eRp01

1.5 e 120 10


Pye ea


Py 2.101 106

Pa Py 20.732atm


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

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


Pa Pr 17.835bar

S 1.5 Safety factor

PacPr





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


Py1e ea1


Py1 7.171 105

Pa Py1 7.077atm


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


Pac1Pr1


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




Rp01 180 106

Pa

eRp01

1.5 e 120 10


fd e





pset 200N

mm Presetting pressure sealing gasket



N TpreF 107.21tonf

f fd Nominal design stress

nb 52 Number of bolts

boltloadTpreF


3 N

boltps 20000newton Pre loading of each bolt


b 10 mm

P 0.1106

Pa


ypset

b

Wa b G y Presetting assembly condition

Wa 9.538 105




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


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



Plate dimensions:

Notation file

Enter dimensions, properties

and loading

Thickness:

tp 45mm Average radius of contact radius:


pd 0.1106

Pa


9 Pa

Poisson's ratio:

m 0.3


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







RavRi Rex


Lcyl 2109mm h1 296mm h11 296mm

Lc Lcyl 0.4h1 0.4h11 Lc 2.346m


Rp01 180 106

Pa

eRp01

1.5 e 120 10


Pye ea


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


Pa Pr 6.443bar

S 1.5 Safety factor

PacPr








Rav1Ri1 Rex1

2 Rav1 747.5mm

e 120 106

Pa 8.4.2 8.4.2 for austenich steel

Py1e ea1


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


Pac1Pr1



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


Rp01 180 106

Pa

eRp01

1.5 e 120 10







RavRi Rex


Lcyl 623mm

Lc Lcyl Lc 0.623m


Pye ea


Py 1.589 106

Pa Py 15.686atm


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


Pa Pr 12.715bar

S 1.5 Safety factor

PacPr






Ri1 605.0mm Inner radius


Rav1Ri1 Rex1

2 Rav1 606.5mm

e 120 106


Py1e ea1


Py1 5.936 105

Pa Py1 5.858atm


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


Pac1Pr1

S Pac1 1.108bar


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



Rp02t 175 106


Rm26 600 106


0.29 Poisson ratio

Al% 35 Elongation to the Breaking point _________________________________________________________________________________


Normal operational load cases Rp01 180 10

6 Pa

eRp01

1.5 e 120 10


fd e


A 1310mm B 1190mm e 35mm g1 16mm

C 1260mm g0 8 mm G 1234mm h 8 mm



bow





G 1.234 103

mm Mean diameter of the gasket contact area of gasket

P 0.1106


H

44 G


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


ycalpc

b ycal 40 10


y 54 106


Wa b G ycal

nbHg

42

Wa 87.152tonf nb 1882.457kgf

C 1.26 103

mm Bolt pitch circle diameter

Operating condition


Possible Preloading during the assembly condition


Rpbolt 700 106

Pa

fbRpbolt

4 fb 175 10

6 Pa 11.4.3 Bolting page 151


Ab_min maxWa

fba

Wop

fb


Ab_min 4.431 103

mm2


Adbe12

4dbe

2 Adbe12 105.683mm

2

n12regAb_min


nbused 42


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




hgC G



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


N m


Flange Stresses and limits 11.5.4.1



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


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


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


r1.333e fl I0( ) M

e2

I0

r 8.346 105

Pa Radial stress

y M

e2

rK

21

K2

1

112.199 106


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



Verification for loose hubbed flange method


Pa 11.5.39( )


Pa 11.5.40( )


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







RavRi Rex


Lcyl 2333mm h1 295mm h11 0 mm

Lc Lcyl 0.4h1 0.4h11 Lc 2.451m


Rp01 180 106

Pa

eRp01

1.5 e 120 10


Pye ea


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


Pa Pr 6.121bar

S 1.5 Safety factor

PacPr








Rav1Ri1 Rex1

2 Rav1 747mm

e 120 106


Py1e ea1


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


Pac1Pr1

S Pac1 1.157bar



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







RavRi Rex


Lcyl 450mm

Lc Lcyl Lc 0.45m


Rp01 180 106

Pa

eRp01

1.5 e 120 10


Pye ea


Py 1.916 106

Pa Py 18.911atm


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


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


Pa Pr 16.862bar

S 1.5 Safety factor

PacPr





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


Py1e ea1


Py1 5.955 105

Pa Py1 5.877atm


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


Pac1Pr1


The required thickness for only the vacuum can be than 3 mm


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




Rp01 180 106

Pa

eRp01

1.5 e 120 10

6 Pa 8.4.2 for austenich steel

fd e





pset 200N




N TpreF 60.597tonf



boltloadTpreF


3 N



b 10 mm

P 0.1106

Pa


ypset

b

Wa b G y Presetting assembly conduction

Wa 5.391 105




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


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

_____________________________________________________________________________________




Plate dimensions:

Notation file

Enter dimensions,

properties and loading

Thickness:



pd 0.1106

Pa


9 Pa

Poisson's ratio: m 0.3


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




Rp01 180 106

Pa

eRp01

1.5 e 120 10


fd e





pset 200N




N TpreF 74.722tonf



boltloadTpreF


3 N



b 10 mm

P 0.1106

Pa


ypset

b


Wa 6.648 105




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


ep1 3G

42 b m

C G( )P

f

e1 maxea ep1( )

e1 0 mm


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 _____________________________________________________________________________________




Plate dimensions:

Notation file

Enter dimensions,


Thickness:



pd 0.1106

Pa


9 Pa



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




Rp01 180 106

Pa

eRp01

1.5 e 120 10


fd e





pset 200N




N TpreF 87.152tonf



boltloadTpreF

nb boltload 18460.6N



b 10 mm

P 0.1106

Pa


ypset

b


Wa 7.753 105




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


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


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

_____________________________________________________________________________________




Plate dimensions:

Notation file

Enter dimensions,


Thickness:



pd 0.1106

Pa


9 Pa



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

Documents

JGW-T1301483-TowerB1 B2 vacuum v3 - University of Tokyogwdoc.icrr.u-tokyo.ac.jp/DocDB/0014/T1301483/001/appendices JGW... · Appendix A2 Shell under external pressure 8 Pag 47 EN