en 13445-3 11.5.5a - met-calc - homemet-calc.com/soubory/content/narrow face flange - smooth... ·...
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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
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