The outside diameter of the flange: A 1230 [mm]The bolt pitch circle diameter: C 1160 [mm]Inside diameter of flange: B 991 [mm]

G 1050 [mm]Bolt outside diameter: db 33 [mm]Number of bolts: n 28 []The thickness of hub at small end: g0 12,5 [mm]

g1 18 [mm]The hub length: h 41 [mm]

e 20 [mm]The effective gasket or joint seating width: b 50 [mm]Gasket factor: m 0,25 []

y 0,7 [Mpa]Poisson´s ratio: ν 0,3 []External the calculation pressure: Pe 0,1 [Mpa]External the test pressure: Petest 0,15 [Mpa]

Rp0,2T 295 [Mpa]The minimum tensile strength at 20°C: Rm/20 450 [Mpa]

The minimum yield strength or 0,2% proof strength at calculation temperature:

11.5.5a Narrow face flange - smooth bore (external pressure)

The diameter of gasket load reaction:

The thickness of hub at back of flange:

The minimum flange thickness, measured at the thinnest section:

The minimum required bolt for operating condition:

Bolt material - yield strength: Rp0,2screw 640 [Mpa]Bolt material - strength limit: Rm/20screw 800 [Mpa]Thread: M33x3,5 []Medium diameter: d2 30,727 [mm]Smaller external thread diameter: d3 28,706 [mm]Joint coefficient: z 0,7 []

53,5 yes

The nominal design stress for normal operating cases:

fd 168,8 [Mpa]

The nominal design stress for test cases:

ftest 281,0 [Mpa]The total hydrostatic end force at the compression pressure:

H 8,66E+04 [N]

The total hydrostatic end force at the test pressure:

Htest 1,30E+05 [N]

The compression load on gasket to ensure tight joint for operating condition:

HG 8,25E+03 [N]

The compression load on gasket to ensure tight joint for test condition:

HGtest 1,24E+04 [N]

𝑔 ≤ ℎ + 𝑔

𝑓 = 𝑚𝑖𝑛𝑅 ,

1,5;𝑅 /

2,4

𝑓 = 𝑚𝑖𝑛𝑅 ,

1,5∗ 0,9;

𝑅 /

2,4∗ 0,9 : 𝑧 ≤ 0,7

𝑓 =𝑅 ,

1,05

𝐻 =𝜋

4𝐺 ∗ 𝑃

𝐻 =𝜋

4𝐺 ∗ 𝑃

𝐻 = 2𝜋 ∗ 𝐺 ∗ 𝑏 ∗ 𝑚 ∗ 𝑃

𝐻 = 2𝜋 ∗ 𝐺 ∗ 𝑏 ∗ 𝑚 ∗ 𝑃

The hydrostatic end force applied via shell to flange at the compression pressure:

HD 7,71E+04 [N]The hydrostatic end force applied via shell to flange at the test pressure:

HDtest 1,16E+05 [N]

The hydrostatic end force due to pressure on flange face at the compression pressure:

HT 9,46E+03 [N]

The hydrostatic end force due to pressure on flange face at the test pressure:

HTtest 1,42E+04 [N]The radial distance from bolt circle to circle on which HD:

hD 75,5 [mm]

The radial distance from gasket load reaction to bolt circle:

hG 55 [mm]The radial distance from bolt circle to circle on which HT:

hT 69,75 [mm]The minimum required bolt load for assembly condition:

WA 4,12E+03 [N]

The minimum required bolt load for operating condition at the compression pressure:

Wop 0,0 [N]

𝐻 =𝜋

4𝐵 ∗ 𝑃

𝐻 =𝜋

4𝐵 ∗ 𝑃

𝐻 = 𝐻 − 𝐻

𝐻 = 𝐻 − 𝐻

ℎ = 𝐶 − 𝐵 − 𝑔 /2

ℎ = 𝐶 − 𝐺 /2

ℎ = 2𝐶 − 𝐵 − 𝐺 /4

𝑊 = 𝜋 ∗ 𝑏 ∗ 𝐺 ∗ 𝑦 /n

𝑊 = 0

The minimum required bolt load for operating condition at the test pressure:

Woptest 0,0 [N]The bolt nominal design stress at operating temperature:

fB 200 [Mpa]

The total cross-sectional area of bolts at the section of least bolt diameter at the compression pressure:

AB 20,6 [mm2]

The total cross-sectional area of bolts at the section of least bolt diameter at the test pressure:

ABtest 20,6 [mm2]Nominal area of the bolt:

Asnom 693,6 [mm2]

The design bolt load for assembly condition:

W 7,14E+04 [N]

The total moment acting upon flange for assembly condition:

MA 3,93E+06 [Nmm]

The total moment acting upon flange for operating condition:

Mop 1,72E+06 [Nmm]

The total moment acting upon flange for test condition:

Moptest 2,58E+06 [Nmm]

𝑊 = 0

𝑓 = 𝑚𝑖𝑛𝑅 ,

3;𝑅 /

4

𝐴 > 𝐴 = 𝑚𝑎𝑥𝑊

𝑓;𝑊

𝑓

𝐴 > 𝐴 = 𝑚𝑎𝑥𝑊

𝑓;

𝑊

𝑓 ∗ 1,5

𝐴 =𝜋

4

𝑑 + 𝑑

2

𝑊 = 0,5 𝐴 + 𝐴 ∗ 𝑓

𝑀 = 𝑊 ∗ ℎ

𝑀 = 𝐻 ∗ ℎ − ℎ + 𝐻 ∗ ℎ − ℎ

𝑀 = 𝐻 ∗ ℎ − ℎ + 𝐻 ∗ ℎ − ℎ

Distance between centre lines of adjacent bolts:

δb 129,9 [mm]The bolt pitch correction factor:

CF 1,00 []The ratio of the flange diameters:

K 1,24 []Length parameter given by Equation:

l0 111,30 []Coefficient:

βT 1,82 []Coefficient:

βU 10,01 []Coefficient:

βY 9,11 []

The moment exerted on the flange per unit of length for assembly condition:

MA/B 3,96E+03 [Nmm/mm]The moment exerted on the flange per unit of length for operating condition:

Mop/B 1,74E+03 [Nmm/mm]The moment exerted on the flange per unit of length for test condition:

Moptest/B 2,60E+03 [Nmm/mm]

𝛿 = 𝐶 ∗ sin𝜋

𝑛

𝐶 = 𝑚𝑎𝑥𝛿

2𝑑 +6𝑒

𝑚 + 0,5

; 1

𝐾 = 𝐴/𝐵

𝑙 = 𝐵𝑔

𝛽 =𝐾 1 + 8,55246 log 𝐾 − 1

1,0472 + 1,9448𝐾 𝐾 − 1

𝛽 =𝐾 1 + 8,55246 log 𝐾 − 1

1,36136 𝐾 − 1 𝐾 − 1

𝛽 =1

𝐾 − 10,66845 + 5,7169

𝐾 log 𝐾

𝐾 − 1

𝑀 / = 𝑀𝐶

𝐵

𝑀 / = 𝑀𝐶

𝐵

𝑀 / = 𝑀𝐶

𝐵

Coefficient:

A 0,44 []Coefficient:

C 0,804 []Coefficient:

C1 0,370 []Coefficient:

C2 0,141 []Coefficient:

C3 0,006 []Coefficient:

C4 2,9 []Coefficient:

C5 -3,7 []Coefficient:

C6 1,3 []Coefficient:

C7 22,4 []Coefficient:

C8 2,7 []Coefficient:

C9 2,3 []

𝐴 =𝑔

𝑔− 1

𝐶 = 48 1 − 𝜈ℎ

𝑙

𝐶 =1

3+

𝐴

12

𝐶 =5

42+

17𝐴

336

𝐶 =1

210+

𝐴

360

𝐶 =11

360+

59𝐴

5040+

1 + 3𝐴

𝐶

𝐶 =1

90+

5𝐴

1008−

1 + 𝐴

𝐶

𝐶 =1

120+

17𝐴

5040+

1

𝐶

𝐶 =215

2772+

51𝐴

1232+

120 + 225𝐴 + 150𝐴 + 35𝐴

14

1

𝐶

𝐶 =31

6930+

128𝐴

45045+

66 + 165𝐴 + 132𝐴 + 35𝐴

77

1

𝐶

𝐶 =533

30240+

653𝐴

73920+

42 + 198𝐴 + 117𝐴 + 25𝐴

84

1

𝐶

Coefficient:

C10 -2,7 []Coefficient:

C11 1,2 []Coefficient:

C12 0,7 []Coefficient:

C13 0,2 []Coefficient:

C14 -0,2 []Coefficient:

C15 0,1 []Coefficient:

C16 2,9 []Coefficient:

C17 7,9 []Coefficient:

C18 -10,0 []Coefficient:

C19 3,4 []Coefficient:

C20 0,06 []

𝐶 =29

3780+

3𝐴

704−

42 + 198𝐴 + 243𝐴 + 91𝐴

84

1

𝐶

𝐶 =31

6048+

1763𝐴

665280+

42 + 72𝐴 + 45𝐴 + 10𝐴

84

1

𝐶

𝐶 =1

2925+

71𝐴

300300+

88 + 198𝐴 + 156𝐴 + 42𝐴

385

1

𝐶

𝐶 =761

831600+

937𝐴

1663200+

2 + 12𝐴 + 11𝐴 + 3𝐴

70

1

𝐶

𝐶 =197

415800+

103𝐴

332640−

2 + 12𝐴 + 17𝐴 + 7𝐴

70

1

𝐶

𝐶 =233

831600+

97𝐴

554400+

6 + 18𝐴 + 15𝐴 + 4𝐴

210

1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

Coefficient:

C21 -0,06 []Coefficient:

C22 0,04 []Coefficient:

C23 -0,05 []Coefficient:

C24 0,06 []Coefficient:

C25 -0,03 []Coefficient:

C26 -0,67 []Coefficient:

C27 -13,50 []Coefficient:

C28 -5,68 []Coefficient:

C29 -0,45 []Coefficient:

C30 -0,30 []Coefficient:

C31 3,02 []

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶1

𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶 ∗ 𝐶 + 𝐶 ∗ 𝐶1

𝐶

𝐶 = −𝐶

4

/

𝐶 = 𝐶 − 𝐶 −5

12+ 𝐶 ∗ 𝐶

𝐶 = 𝐶 − 𝐶 −1

12+ 𝐶 ∗ 𝐶

𝐶 = −𝐶

4

/

𝐶 = −𝐶

4

/

𝐶 =3𝐴

2− 𝐶 ∗ 𝐶

Coefficient:

C32 1,51 []Coefficient:

C33 -2,82 []Coefficient:

C34 -16,50 []Coefficient:

C35 2,99 []Coefficient:

C36 1,27 []Coefficient:

C37 -0,27 []Coefficient:

E1 -0,92 []Coefficient:

E2 0,00 []Coefficient:

E3 0,00 []Coefficient:

E4 1,46 []Coefficient:

E5 -0,53 []Coefficient:

E6 -2,38 []

𝐶 =1

2− 𝐶 ∗ 𝐶

𝐶 =𝐶 ∗ 𝐶

2+ 𝐶 ∗ 𝐶 ∗ 𝐶 −

𝐶 ∗ 𝐶

2+ 𝐶 ∗ 𝐶 ∗ 𝐶

𝐶 =1

12+ 𝐶 − 𝐶 − 𝐶 ∗ 𝐶

𝐶 = 𝐶 ∗ 𝐶

𝐶 = 𝐶 ∗ 𝐶 ∗ 𝐶 − 𝐶 ∗ 𝐶 ∗ 𝐶1

𝐶

𝐶 =𝐶 ∗ 𝐶

2+ 𝐶 ∗ 𝐶 ∗ 𝐶 −

𝐶 ∗ 𝐶

2− 𝐶 ∗ 𝐶 ∗ 𝐶

1

𝐶

𝐸 = 𝐶 ∗ 𝐶 + 𝐶 + 𝐶 ∗ 𝐶

𝐸 = 𝐶 ∗ 𝐶 + 𝐶 + 𝐶 ∗ 𝐶

𝐸 = 𝐶 ∗ 𝐶 + 𝐶 + 𝐶 ∗ 𝐶

𝐸 =3 + 𝐶 + 3𝐶

12−

2𝐸 + 15𝐸 + 10𝐸

10

𝐸 = 𝐸3 + 𝐴

6+ 𝐸

21 + 11𝐴

84+𝐸

3 + 2𝐴

210

𝐸 = 𝐸 − 𝐶7

120+

𝐴

36+

3𝐴

𝐶−

1

40−

𝐴

72− 𝐶

1

60+

𝐴

120+

1

𝐶

Coefficient:

βF 0,87 []Coefficient:

βV 0,36 []

The stress correction factor for integral method flange design as given:

ϕ 1,00 []Coefficient:

λ 0,65 []The calculated longitudinal stress in hub for assembly condition:

σHA 18,8 [MPa]The calculated radial stress in flange for assembly condition:

σrA 18,4 [MPa]The calculated tangential stress in flange for assembly condition:

σθA 3,9 [MPa]The calculated longitudinal stress in hub for operating condition:

σHop 8,2 [MPa]The calculated radial stress in flange for operating condition:

σrop 8,1 [MPa]

𝛽 =−𝐸

𝐶3 1 − 𝜈

/ 1 + 𝐴𝐶

𝛽 =𝐸

3 1 − 𝜈𝐶

/

1 + 𝐴

𝜑 = 𝑚𝑎𝑥 1;𝐶

1 + 𝐴

𝜆 =𝑒 ∗ 𝛽 + 𝑙

𝛽 ∗ 𝑙+

𝑒 ∗ 𝛽

𝛽 ∗ 𝑙 𝑔

𝜎 =𝜑𝑀 /

𝜆𝑔

𝜎 =1.333𝑒𝛽 + 𝑙 𝑀 /

𝜆𝑒 𝑙

𝜎 =𝛽 ∗ 𝑀 /

𝑒− 𝜎

𝐾 + 1

𝐾 − 1

𝜎 =𝜑𝑀 /

𝜆𝑔

𝜎 =1.333𝑒𝛽 + 𝑙 𝑀 /

𝜆𝑒 𝑙

The calculated tangential stress in flange for operating condition:

σθop 1,7 [MPa]The calculated longitudinal stress in hub for test condition:

σHoptest 12,3 [MPa]

The calculated radial stress in flange for test condition:

σroptest 12,1 [MPa]The calculated tangential stress in flange for test condition:

σθoptest 2,5 [MPa]Stress factor defined:

k 1,0 []

Stress in flange for assembly condition:18,8 [MPa]18,4 [MPa]

3,9 [MPa]18,6 [MPa]11,3 [MPa]

Stress in flange for operating condition:8,2 [MPa]8,1 [MPa]1,7 [MPa]8,1 [MPa]5,0 [MPa]

𝜎 =𝛽 ∗ 𝑀 /

𝑒− 𝜎

𝐾 + 1

𝐾 − 1

𝜎 =𝜑𝑀 /

𝜆𝑔

𝜎 =1.333𝑒𝛽 + 𝑙 𝑀 /

𝜆𝑒 𝑙

𝜎 =𝛽 ∗ 𝑀 /

𝑒− 𝜎

𝐾 + 1

𝐾 − 1

𝐵 ≤ 1000𝑚𝑚 → 𝑘 = 1

𝐵 ≥ 2000𝑚𝑚 → 𝑘 = 1,333

1000𝑚𝑚 < 𝐵 > 2000𝑚𝑚 → 𝑘 =2

31 +

𝐵

2000

𝑘 ∗ 𝜎 ≤ 1,5𝑓

𝑘 ∗ 𝜎 ≤ 𝑓

𝑘 ∗ 𝜎 ≤ 𝑓

0,5𝑘 𝜎 + 𝜎 ≤ 𝑓

0,5𝑘 𝜎 + 𝜎 ≤ 𝑓

𝑘 ∗ 𝜎 ≤ 1,5𝑓

𝑘 ∗ 𝜎 ≤ 𝑓

𝑘 ∗ 𝜎 ≤ 𝑓

0,5𝑘 𝜎 + 𝜎 ≤ 𝑓

0,5𝑘 𝜎 + 𝜎 ≤ 𝑓

Stress in flange for test condition:12,3 [MPa]12,1 [MPa]

2,5 [MPa]12,2 [MPa]

7,4 [MPa]

𝑘 ∗ 𝜎 ≤ 1,5𝑓

𝑘 ∗ 𝜎 ≤ 𝑓

𝑘 ∗ 𝜎 ≤ 𝑓

0,5𝑘 𝜎 + 𝜎 ≤ 𝑓

0,5𝑘 𝜎 + 𝜎 ≤ 𝑓