ASME Section VIII div 2 2010. ASME Boiler and Pressure Vessel Code. Alternative Rules
Подождите немного. Документ загружается.
2010 SECTION VIII, DIVISION 2
4-65
Table 4.3.2 – Small End Junction
Cylinder Cone
Stress Resultant Calculation
2
s
PSsN
M
Pt M= , see Table 4.3.5
s
XSSsN
M
XtM= , see Table 4.3.6
s
sP sX
M
MM=+
P
SN
QPtQ= , see Table 4.3.5
XSN
QXQ= , see Table 4.3.6
P
X
QQ Q=+
0.25
2
22
3(1 )
cy
SS
Rt
ν
β
⎡⎤
−
=
⎢⎥
⎣⎦
2
S
s
S
PR
NX
=+
()
2
ScySscy
NPR RM Q
θ
ββ
=+ − −
1.0
pc
K =
Stress Calculation
s
sm
S
N
t
σ
=
2
6
s
sb
Spc
M
tK
σ
=
m
S
N
t
θ
θ
σ
=
2
6
s
b
Spc
M
tK
θ
ν
σ
=
Acceptance Criteria
1.5
sm
S
σ
≤
s
msbPS
S
σ
σ
±≤
1.5
m
S
θ
σ
≤
mbPS
S
θθ
σ
σ
±≤
Stress Resultant Calculation
csP sP
M
M
=
csX sX
M
M
=
cs csP csX
MM M
=
+
[
]
[
]
cos sin
α
α
=+
cs
QQ N (1)
[]
cos
α
=
S
C
R
R
0.25
2
22
3(1 )
co
CC
Rt
ν
β
⎡
⎤
−
=
⎢
⎥
⎣
⎦
[
]
[
]
cos sin
α
α
=−
cs s
NN Q
(2)
[]
()
2
cos
S
ccoCcscoc
PR
NRMQ
θ
ββ
α
=+ −+
1.0
cpc
K
=
Stress Calculation
cs
sm
C
N
t
σ
=
2
6
cs
sb
Ccpc
M
tK
σ
=
c
m
C
N
t
θ
θ
σ
=
2
6
cs
b
Ccpc
M
tK
θ
ν
σ
=
Acceptance Criteria
1.5
sm
S
σ
≤
s
msbPS
S
σ
σ
±
≤
1.5
m
S
θ
σ
≤
mbPS
S
θθ
σ
σ
±
≤
Notes:
1. The
Q and
s
N values used to determine the resultant shear force in the cone,
c
Q , are the
same as those defined for the cylinder.
2. The
Q and
s
N values used to determine the resultant meridional membrane force in the
cone,
cs
N , are the same as those defined for the cylinder.
2010 SECTION VIII, DIVISION 2
4-66
Table 4.3.3 – Pressure Applied To Large End Junction
Junction Moment Resultant –
s
N
M
(1)
Equation
Coefficients –
i
C
n
1 1.25 1.5 1.75 2
1 -3.065534 -3.113501 -3.140885 -3.129850 -3.115764
2 3.642747 3.708036 3.720338 3.674582 3.623956
3 0.810048 0.736679 0.623373 0.490738 0.360998
4 -0.221192 -0.239151 -0.241393 -0.224678 -0.209963
5 -0.081824 -0.075734 -0.056744 -0.034581 -0.013613
6 0.035052 0.083171 0.157222 0.240314 0.316184
7 0.025775 0.027432 0.027393 0.025163 0.023508
8 -0.015413 -0.015659 -0.017311 -0.019456 -0.021796
9 0.002102 0.000993 -0.004600 -0.011145 -0.017172
10 -0.005587 -0.013283 -0.025609 -0.039144 -0.050859
Junction Shear Force Resultant –
N
Q (1)
1 -1.983852 -1.911375 -1.893640 -1.852083 -1.816642
2 2.410703 2.292069 2.253430 2.184549 2.126469
3 0.626443 0.478030 0.364794 0.251818 0.152468
4 -0.119151 -0.079165 -0.075123 -0.059024 -0.048876
5 -0.115841 -0.074658 -0.047032 -0.024214 -0.007486
6 0.122993 0.219247 0.282565 0.343492 0.390839
7 0.012160 0.007250 0.007505 0.006116 0.005632
8 -0.016987 -0.021607 -0.024667 -0.027144 -0.029118
9 0.010919 -0.003818 -0.012439 -0.018971 -0.023076
10 -0.016653 -0.033814 -0.043500 -0.052435 -0.058417
Note: (1) The equation to determine
s
N
M
and
N
Q is shown below.
[] [] []
()
[]
()
[][]
[]
()
[]
()
[] []
()
[]
()
[]
22
12 3 4 5 6
33 2 2
789 10
+ ln + ln + ln + ln + ln ln +
=exp
ln + ln + ln ln + ln ln
sN N
CC H C B C H C B C H B
M,Q
CHCBCHBC H B
⎡⎤
⎢⎥
−
⎢⎥
⎣⎦
标准分享网 www.bzfxw.com 免费下载
2010 SECTION VIII, DIVISION 2
4-67
Table 4.3.4 – Equivalent Line Load Applied To Large End Junction
Junction Moment Resultant –
s
N
M
(1)
Equation
Coefficients –
i
C
n
1 1.25 1.5 1.75 2
1 -5.697151 -5.727483 -5.893323 -6.159334 -6.532748
2 0.003838 0.006762 0.012440 0.019888 0.029927
3 0.476317 0.471833 0.466370 0.461308 0.454550
4 -0.213157 -0.213004 -0.211065 -0.207037 -0.200411
5 2.233703 2.258541 2.335015 2.449057 2.606550
6 0.000032 0.000010 -0.000006 -0.000008 -0.000004
7 0.002506 0.003358 0.004949 0.007005 0.009792
8 -0.001663 -0.002079 -0.003105 -0.004687 -0.007017
9 -0.212965 -0.216613 -0.224714 -0.235979 -0.251220
10 0.000138 -0.000108 -0.000721 -0.001597 -0.002797
11 -0.106203 -0.106269 -0.107142 -0.108733 -0.110901
Junction Shear Force Resultant –
N
Q (1)
1 -4.774616 -5.125169 -5.556823 -6.113380 -6.858200
2 0.000461 0.021875 0.049082 0.084130 0.131374
3 -0.002831 -0.055928 -0.127941 -0.225294 -0.361885
4 -0.197117 -0.196848 -0.196204 -0.194732 -0.193588
5 1.982132 2.156708 2.378102 2.668633 3.069269
6 0.000069 -0.000450 -0.001077 -0.001821 -0.002760
7 -0.000234 0.000188 0.000821 0.001694 0.002958
8 -0.003536 -0.005341 -0.007738 -0.010934 -0.015089
9 -0.202493 -0.223872 -0.251223 -0.287283 -0.337767
10 -0.000088 -0.002426 -0.005428 -0.009440 -0.015045
11 0.001365 0.012698 0.027686 0.047652 0.075289
Notes: (1) The equation to determine
s
N
M
and
N
Q is shown below.
[]
(
)
[]
()
[]
[]
()
[]
()
[]
2
2
22 2
13 5 7 9 11
2
2
22 2
246 8 10
+ ln + ln + ln + ln + ln ln
,=exp
1+ ln + ln + ln + ln + ln ln
sN N
CC H C C H C C H
MQ
CHC C H C C H
α
αα
ααα
⎡⎤
⎡⎤ ⎡⎤ ⎡⎤
⎣⎦ ⎣⎦ ⎣⎦
⎢⎥
−
⎢⎥
⎡⎤ ⎡⎤ ⎡⎤
⎢⎥
⎣⎦ ⎣⎦ ⎣⎦
⎣⎦
2010 SECTION VIII, DIVISION 2
4-68
Table 4.3.5 – Pressure Applied To Small End Junction
Junction Moment Resultant –
s
N
M
(1)
Equation
Coefficients –
i
C
n
1 1.25 1.5 1.75 2
1 -9.615764 -10.115298 -11.531005 -14.040332 -18.457734
2 1.755095 1.858053 2.170806 2.762452 3.859890
3 3.937841 4.222547 4.872664 5.973215 7.923210
4 -0.043572 -0.053476 -0.080011 -0.131830 -0.228146
5 -1.035596 -1.100505 -1.213287 -1.388782 -1.685101
6 -0.008908 -0.033941 -0.121942 -0.288589 -0.612009
7 0.003984 0.004388 0.005287 0.006975 0.010041
8 0.115270 0.121595 0.129218 0.139465 0.154368
9 0.013712 0.015269 0.022097 0.034632 0.059879
10 -0.007031 -0.006067 -0.002848 0.003867 0.017109
Junction Shear Force Resultant –
N
Q (2)
1 0.028350 0.207327 0.376538 0.532382 0.682418
2 0.000020 0.000007 -0.000008 -0.000023 -0.000040
3 0.001668 0.003856 0.005918 0.007947 0.009881
4 0.002987 0.002885 0.002781 0.002709 0.002632
5 0.001125 -0.000330 -0.001848 -0.002664 -0.003542
6 0.000000 0.000000 0.000000 0.000000 0.000000
7 0.000001 -0.000001 -0.000003 -0.000005 -0.000006
8 -0.000122 -0.000120 -0.000118 -0.000117 -0.000116
9 -0.000181 -0.000139 -0.000106 -0.000090 -0.000079
10 0.000001 0.000001 0.000001 0.000001 0.000001
11 -0.004724 -0.004417 -0.004128 -0.003847 -0.003570
Notes:
1. The equation to determine
s
N
M
is shown below.
[]
(
)
[]
()
[]
()
[]
()
[]
()
()
[]
2
2
22 2
12 3 4 5 6
3 2
32
222
789 10
+ ln + ln + ln + ln + ln ln
=exp
ln + ln + ln ln + ln ln
sN
CC H C C H C C H
M
CH C CH C H
ααα
αα α
⎡⎤
⎡⎤ ⎡⎤ ⎡⎤
+
⎣⎦ ⎣⎦ ⎣⎦
⎢⎥
⎢⎥
⎡⎤ ⎡⎤ ⎡⎤
⎢⎥
⎣⎦ ⎣⎦ ⎣⎦
⎣⎦
2. The equation to determine
N
Q is shown below.
24 2
13 5 7 9 11
24 2
246810
1
2
N
2
C+CH C +CH +C +C H
Q=
+C H +C +C H +C +C H
α
αα
α
αα
⎛⎞
+
⎜⎟
⎝⎠
标准分享网 www.bzfxw.com 免费下载
2010 SECTION VIII, DIVISION 2
4-69
Table 4.3.6 – Equivalent Line Load Applied To Small End Junction
Junction Moment Resultant –
s
N
M
(1)
Equation
Coefficients –
i
C
n
1 1.25 1.5 1.75 2
1 -0.000792 0.000042 0.002412 0.005766 0.009868
2 -0.000627 -0.000327 -0.000033 0.000236 0.000453
3 -0.001222 -0.001188 -0.001079 -0.000951 -0.000860
4 0.142039 0.132463 0.125812 0.121877 0.120814
5 0.010704 0.009735 0.009802 0.010465 0.010928
6 0.000013 0.000006 -0.000002 -0.000009 -0.000015
7 -0.000006 -0.000001 -0.000006 -0.000008 -0.000008
8 0.009674 0.008839 0.007580 0.006261 0.005044
9 0.006254 0.005493 0.003701 0.001619 0.000381
10 -0.000046 0.000011 0.000088 0.000171 0.000230
11 0.202195 0.208304 0.205169 0.197061 0.186547
Junction Shear Force Resultant –
N
Q (2)
1 -0.460579 -0.444768 -0.428659 -0.412043 -0.396046
2 -0.002381 0.006711 0.013388 0.019509 0.026272
3 -0.400925 -0.376106 -0.353464 -0.331009 -0.309046
4 0.001550 -0.000672 -0.002169 -0.003562 -0.005266
5 -0.140077 -0.129459 -0.121074 -0.113195 -0.105461
6 0.000793 0.001950 0.002212 0.002168 0.002310
7 -0.000219 -0.000023 0.000098 0.000215 0.000374
8 -0.019081 -0.017115 -0.015814 -0.014699 -0.013625
9 0.000384 0.000618 0.000739 0.000806 0.000860
10 0.000103 0.000006 0.000038 0.000102 0.000117
Notes:
1. The equation to determine
s
N
M
is shown below.
2
13 5 7 9 11
2
246 8 10
1
2
sN
2
C+CH+CB+CH +CB +C HB
M=
+C H +C B+C H +C B +C HB
⎛⎞
⎜⎟
⎝⎠
2. The equation to determine
N
Q is shown below.
[] [] []
()
[]
()
[][]
[]
()
[]
()
[] []
()
[]
()
[]
22
12 3 4 5 6
33 2 2
789 10
+ln +ln + ln + ln +ln ln
=
ln + ln + ln ln + ln ln
N
CC H C B C H C B C H B
Q
CHCBCHBC H B
⎛⎞
+
⎜⎟
⎜⎟
⎝⎠
2010 SECTION VIII, DIVISION 2
4-70
Table 4.3.7 – Stress Calculations – Knuckle – Large End Cylinder
Compact Knuckle:
[]
()
{
}
()
0.5
0.5
1
2tan 0.7
kmk kk m
rKR rt whereK
ααα
−
<⋅+ =
Stress Calculation
()
()
()
2
11
0.5
mL LL k kC kk ek
m
mL LL C kC kk
PK R R t L L t PL r P L
Kt Rt t Lt tr
θ
α
σ
α
++−
=
++
1
2
ek
sm
k
PL
t
σ
=
22 33
11
2
cos cos
22
α
α
ππ
=+ ±
⎡⎤ ⎡⎤
⎢⎥ ⎢⎥
⎣⎦ ⎣⎦
LL
e
kk
FM
PP
LL
[]
cos
k
kk
R
Lr
α
=+
[]
()
0.5
1
1
tan
αα
−
=⋅ +
kk k
LR r
Acceptance Criteria
m
S
θ
σ
≤
sm
S
σ
≤
Non-Compact Knuckle:
[]
()
{
}
()
0.5
0.5
1
2tan 0.7
kmk kk m
rKR rt whereK
ααα
−
≥⋅+ =
Stress Calculation At TL-1
()
()
2
11
1
0.5
Lm LL k kk ek
m
mL LL k kk
PR K R t PL r P L
Kt Rt t Lt
θ
β
σ
+−
=
+
1
2
ek
sm
k
PL
t
σ
=
22 33
11
2
cos cos
22
β
β
ππ
=+ ±
⎡⎤ ⎡⎤
⎢⎥ ⎢⎥
⎣⎦ ⎣⎦
LL
e
kk
kk
FM
PP
LL
[]
()
0.5
1
1
tan
ββ
−
=⋅ +
kkk k k
LR r
m
kLk
k
K
R
t
r
β
⎛⎞
=
⎜⎟
⎝⎠
Stress Calculation At TL-2
(
)
()
()
2
11
1
0.5
θ
αβ
σ
+− −
=
+
km kC k kk ek
m
mC kC k kk
PL K L t PL r P L
Kt Lt tLt
1
2
σ
=
ek
sm
k
PL
t
[] []
22 33
11
2
cos cos
π
φπ φ
=+ ±
LL
e
kkkk
FM
PP
LL
[]
cos
k
kk
R
Lr
α
=
+
[] [ ]
{}
{}
(
)
0.5
1
1
tan tan
kk k k k
LR r
αβαβ
−
=
−−+
m
kkk
k
K
Lt
r
βα
⎛⎞
=−
⎜⎟
⎝⎠
(
)
2
k
k
α
β
φ
+
=
标准分享网 www.bzfxw.com 免费下载
2010 SECTION VIII, DIVISION 2
4-71
Table 4.3.7 – Stress Calculations – Knuckle – Large End Cylinder
Stress Calculation In The Non-Compact Knuckle Region
Note: The number of locations around the knuckle that shall be evaluated is given by the following equation.
[]
()
() ()
12
12
1
2
2
1
1
0
1
23
23
11
1
2int 1 1
cos
1,..., ,
2
2
2
cos cos
kk
k
kk
m
kLk
k
m
kkk
k
k
kk
k
jj
j
ek
j
k
m
kkk
jj
j
ek
sm
k
j
LL
e
jjjj
kkkk
j
k
j
where
K
Rt
r
K
Lt
r
R
Lr
For j j compute
PL
PL
trt
PL
t
where
FM
PP
LL
L
αβ β
ββ
β
β
α
σ
σ
π
φπ φ
⎛⎞
⎡⎤
−−
=++
⎜⎟
⎢⎥
⎜⎟
+
⎣⎦
⎝⎠
=
=
=+
=
=−
=
=+ ±
⎡⎤ ⎡⎤
⎣⎦ ⎣⎦
=
()
1
2
cos
1
1
k
k
j
k
es
js
kk
kk
k
s
kk
e
kk
R
r
j
j
φ
φφ
φφ
φβ
φαβ
+
⎡⎤
⎣⎦
⎛⎞
−
=+−
⎜⎟
−
⎝⎠
=
=−
Acceptance Criteria
m
S
θ
σ
≤
sm
S
σ
≤
j
m
S
θ
σ
≤
j
sm
S
σ
≤
2010 SECTION VIII, DIVISION 2
4-72
Table 4.3.8 – Stress Calculations – Flare – Small End Cylinder
Compact Flare:
[]
()
{
}
()
0.5
0.5
1
2 tan 0.7
fmf ff m
r K R r t where K
ααα
−
<⋅− =
Stress Calculation
()
()
()
2
11
0.5
mS SS f fC ff ef
m
mS SS C fC ff
PK R R t L L t PL r P L
Kt Rt t Lt tr
θ
α
σ
α
+++
=
++
1
2
ef
sm
f
PL
t
σ
=
22 33
11
2
cos cos
22
α
α
ππ
=+ ±
⎡⎤ ⎡⎤
⎢⎥ ⎢⎥
⎣⎦ ⎣⎦
SS
e
ff
FM
PP
LL
[]
cos
f
f
f
R
Lr
α
=−
[]
()
0.5
1
1
tan
f
ff
LR r
αα
−
=⋅ −
Acceptance Criteria
m
S
θ
σ
≤
sm
S
σ
≤
Non-Compact Flare:
[]
()
{
}
()
0.5
0.5
1
2tan 0.7
ααα
−
≥⋅− =
fmf ff m
r K R r t where K
Stress Calculation At TL-3
()
(
()
1
1
0.5
f
mfC f ff e
m
mC fC f ff
PL K L t PL r P
L
Kt Lt t Lt
θ
αβ
σ
+− +
=
+
1
2
ef
sm
f
PL
t
σ
=
22 33
11
2
cos cos
π
φπ φ
=+ ±
⎡⎤ ⎡⎤
⎣⎦ ⎣⎦
SS
e
f
fff
FM
PP
LL
[]
cos
f
f
f
R
Lr
α
=−
[]
{}
{}
(
)
0.5
1
1
tan tan
αβαβ
−
⎡⎤
=− −−
⎣⎦
f
fff
f
LR
r
m
f
ff
f
K
Lt
r
βα
⎛⎞
=−
⎜⎟
⎜⎟
⎝⎠
()
2
f
f
α
β
φ
+
=
Stress Calculation At TL-4
(
)
()
2
11
1
0.5
Sm SS f ff e f
m
mS SS f ff
PR K R t PL r P L
Kt Rt t Lt
θ
β
σ
++
=
+
1
2
ef
sm
f
PL
t
σ
=
22 33
11
2
cos cos
22
β
β
ππ
=+ ±
⎡
⎤⎡⎤
⎢
⎥⎢⎥
⎣
⎦⎣⎦
SS
e
ff
ff
FM
PP
LL
(
)
0.5
1
1
tan
ββ
−
⎡⎤
=
⋅−
⎣⎦
f
ff f f
LR r
m
f
Sf
f
K
R
t
r
β
⎛⎞
=
⎜⎟
⎜⎟
⎝⎠
标准分享网 www.bzfxw.com 免费下载
2010 SECTION VIII, DIVISION 2
4-73
Table 4.3.8 – Stress Calculations – Flare – Small End Cylinder
Stress Calculation In The Non-Compact Flare Region
Note: The number of locations around the flare that shall be evaluated is given by the following equation.
[]
()
() ()
12
12
1
2
2
1
1
1
23
23
11
1
2int 1 1
cos
1,..., ,
2
2
2
cos cos
ff
f
ff
m
fff
f
m
fsf
f
f
ff
f
jj
j
ef
f
j
m
fff
jj
ef
j
sm
f
j
SS
e
jjjj
f
ff f
f
j
where
K
Lt
r
K
Rt
r
R
Lr
For j j compute
PL
PL
trt
PL
t
where
FM
PP
LL
L
θ
αβ β
ββ
β
β
α
σ
σ
π
φπ φ
⎛⎞
⎡⎤
−−
=++
⎜⎟
⎢⎥
⎜⎟
+
⎢⎥
⎣⎦
⎝⎠
=
=
=−
=
=+
=
=+ ±
⎡⎤ ⎡⎤
⎣⎦ ⎣⎦
()
1
2
cos
1
1
f
j
f
j
f
se
ff
js
ff
f
s
ff
e
ff
R
r
j
j
φ
φφ
φφ
φαβ
φβ
=−
⎡⎤
⎣⎦
⎛⎞
−
=−−
⎜⎟
⎜⎟
−
⎝⎠
=−
=
Acceptance Criteria
m
S
θ
σ
≤
sm
S
σ
≤
j
m
S
θ
σ
≤
j
sm
S
σ
≤
2010 SECTION VIII, DIVISION 2
4-74
4.3.15 Figures
Conical
D
t
α
Figure 4.3.1 – Conical Shell
α
1
α
2
Figure 4.3.2 – Offset Transition Detail
标准分享网 www.bzfxw.com 免费下载