Wrc-Bull368 91
Wrc-Bull368 91
Wrc-Bull368 91
developing the solutions to problems in welding and pressure vessel technology. They exchange
knowledge, share perspectives, and execute R and D activities. As needed, the Council organizes
and manages cooperative programs.
MPC A Council of the WRC, the Metal Properties Council is dedicated to providing industry
with the best technology and the best data that can be obtained on the properties of materials to
help meet todays most advanced concepts in design and service, life assessment, fitness-for-
service, and reliability and safety.
PVRC A Council of the WRC, the goal of the Pressure Vessel Research Council is to
encourage, promote and conduct research in the field of pressure vessels and related pressure
equipment technologies, including evaluation of materials, design, fabrication, inspection and
testing.
WRC Bulletins contain final reports from projects sponsored by the Welding Research Council, important
papers presented before engineering societies and other reports of current interest.
No warranty of any kind expressed or implied, respecting of data, analyses, graphs or any other
information provided in this publication is made by the Welding Research Council, and the use of any
such information is at the users sole risk.
All rights are reserved and no part of this publication may be reproduced, downloaded, disseminated, or
otherwise transferred in any form or by any means, including photocopying, without the express written
consent of WRC.
ISSN 0043-2326
Library of Congress Catalog Number: 85-647116
Foreword
In August of 1965 the Welding Research Council published WRC Bulletin No. 107, "Local Stresses in Spherical and
Cylindrical Shells Due to External Loadings," by K. R. Wichman, A. G. Hopper and J. L. Mershon. That document provided
engineers with guidance for the evaluation of localized stresses in pressure vessel shells due to various external loads.
Less than 20 years later, in August of 1984, the Welding Research Council published Bulletin No. 297, "Local Stresses in
Cylindrical Shells Due to External Loadings on Nozzles--Supplement to WRC Bulletin No. 107," by J. L. Mershon, K.
Mokhtarian, G. V. Ranjan and E. C. Rodabaugh. This document provided important improvements to WRC Bulletin No. 107,
accounting for local stresses in the nozzle, as well as, the vessel. The basis for the curves in Bulletin No. 297 was the computer
code developed by Dr. C. R. Steele entitled, FAST2.
The work presented here provides the engineer with guidance for the evaluation of shell and nozzle stresses due to internal
pressure. Eqs. 1 through 4 are based on parametric studies performed with the computer code FAST2. The bulletin also
includes comparisons with other previously developed correlation equations and test data.
It is important that it be recognized that this bulletin does not present any rules for design, but it is rather intended to be an
aid in assessing the local structural integrity of the vessel. No attempt is made to educate or enlighten the individual on stress
categorization rules of Section III or Section VIII, Division 2 of the ASME Boiler and Pressure Vessel Code. It is taken for
granted that the designer understands how, when and where to apply the categorization rules for calculating stresses in
accordance with the methods in this document.
G. E. 0. Widera, PhD
Chairman of Committee on Reinforced
Openings and External Loadings of
the Pressure Vessel
Research Council
i
Stresses in Intersecting Cylinders Subjected to Pressure
Model D T d t Lambda
1 9.92 0.0833 0.47 0.025 0.52
2 99.60 0.4000 3.92 0.080 0.62
3 99.80 0.2000 3.96 0.040 0.89
4 99.00 1. 0000 9.50 0.500 0.95
5 99.00 1.0000 9.80 0.200 0.99
6 99.00 1. 0000 9.90 0.100 1.00
7 9.92 0.0833 0.95 0.050 1. 05
8 9.92 0.0833 0.98 0.020 1.08
9 9.92 0.0833 0.99 0.010 1.09
10 98.67 1.3333 12.66 0.667 1.10
Model D T d t Lambda
...
1------L------L-----~-----L------L-----~----~------L-----~----~------~----~~
..
--:w
. J IDa
e e
cr
0
CD
e L
ID
a:
_j
- ..,.
IT'I
ID El
+
N
m
El -~
N
+ +
.. ..
l.f) e m
-~
X
e
+
e
+
(T)
-. N
+
+
(\J
-
N
+-----.-,----~,----r-1----Tr---~,~--~~k~~,----~,-----T,-----~,----r-,----~~
~ ~ w ~ ~ w ~ m
m
0) ~ m ~ m m
~
o
0
m
~
m ~ m ~
N ~ w 0 0 w ~ N
~ ~ ~ m
'" N N 0
I
-
I
-
I
N
I
N
I I
s~1s.::~~ns1s3A "3JN3~3.:l.::IIO I.
6 WRC Bulletin 368
1------J------~-----J~----~-----J------~-----J~------~-----~----~-~
U)
.. ..
1
e e
El -":
1/)
f)
y
e
El
II
1-r-:~
f)
4 4
Ele
El
} El ~--~
~
CI
D
(I)
~
t.
fO a:
El _j
~"'!
+
El
+4 ..
.. 9
'"
N
CD f) e
~r
e
IK
r-- -~
N
+
E)
a
.r
co + El
+ e 0
EJ
1t
~
IJ')
.. .. 9 i-":
e
f)
X
::J' +
. .
f
+ e El
~
::J
e N Ul
~--~
(T)
. I(
+
~
C\J
'-+ I-
C\1
++ +
N
(/)
Lt.;
>
C'l
e N
&
LU
... In
I
I I r I
0
I
0
I
0
I
0
I
0
0
Ul
Q)
(.)
0 0 0 c
- -
0 0 0 0 0 0 0 0
0 0 0 ~
c:i &0 c:i
0 0 0
c:i .,; c:i .,; c:i Q)
:;::
N 1/) 0 10 C\1 C\1 Cll
I I I I I I iS
~
c,
"SHlS"9W~W"lZON ~JN)H]~~ro I. u:::
.
--:
U)
-~It)
e
e
e El
8 I-":
::!1'
El
'II
.. El
..
8
0
El
j. ~~
::!1'
CI
0
(D
0 ~
EJ CI
EJ a
a El
_J
19 ~-~
e
. .
en
N
0
ee
+
El
+ .
OJ fl,
El a 8
0 e a
.c e
r--
El
-"!
N
e
...
El
(0
e
+
El II . 8
...
..
E>
Ln
El
. . e
0
. ~'"!
El
e
a
X El
:::l' +
+ e
.. . . a
e
jg
::I
N X rh
en 0 I-"! ~
~ + .+ C\1
tn
C\1 N
+ + + <(
u.
u;
>
'
E)
&
N
T I T l I
tl
I I
c
I
Ill
0 !
Ql
C)
0 c 0 0 0
c
0 0 c
0 0 c 0 0 c 0 0 0 0
~
0
en
&0
N
0
N
&0 ...0 0
II)
0
0
0
Ul
I -0 I -
&0
I
0
N
I
(I)
!E
0
"0
I
sldlS . .:lldnslzoN "3JN3ld3.:l.:IIO l. dl
u:::
" "
f-. -
CD
e
-~
Ill
El
e
e
e
ee
e
e
El
e
El a:
0
(IJ
:L:
a:
_j
-"!
en
+
N
CD
-~
N
..
co
+
Ln
X
:3'
+ e.
N
. N
+
c-
w
C\1
0
N
K ~
+-----~,----~,r-----,~----~~L-r-,----r-,----r-,----~,----~,----+-0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0
~ 0 0 0 0 0 ~ 0 ~ 0
(\1 ~ 0 ~I -I -I N
I
N
l
Cl')
I
"SH1S"8W3W"XtJW 3JN3~3.:1.:1IO I.
1--:
co
8
El
El
E)
El
!-"':
-J..
9
El :::JI'
El
El e
E)
E)
t El
E) ~--~
:::JI'
a:
0
OJ
::E
a:
El _j
e El
E)
El
i-"! ('l
E)
N
E) +
4
+El 4
(0 fS
aa
e e Ele
t< El
r-
e ~--~
N
. f)
e
El
(0
e
~ +
E) ..
..
e
& e El
ll) e 4 i-11!
E)
e
X
0 ~
e :::1
rn
::::f' + ~
(\J
e 1-
(/)
+
N
e
4
X
4
9 <(
u..
El
~--~ ui
(1")
~ +
.+
>
'<!"
ciS
N
N
+ + + (\J
&
L.U
0
e> N
~
E
_... ... II)
~
I 1 I I I I I 1 c:i Q)
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 c:
0
~
ci
co
ci
II)
0
:::JI'
c:i
('l
ci
N
ci
0
ci - ci
I
ci
N
'
ci
('l
I
ci
:::JI'
I
~
0
l
~
cil
s~3 stHS dHns xuw 3JN3H3d.:liO I. [[
.. ..
e ~"':
e
"'
e
e
i ffJ
. a
e
8
e
..
r-"":
~
.1
0
1--
~
cr:
0
fD
IE)
::E
IE)
E) a a:
__.J
IE)
a
a El ~
(I')
..,
e
N
E)
a
.. 11 +
to f) e
f) El
e e&e
t(
a
,.... t-"!
e N
w
.. e
e
E)
e
lEI
e
El
.. I" +
lEI a
lEI
Ul lEI . 4 4
r-~
X
"::1'
e ' 1 f)
+
e
. .. :If!:::1
+ El
. El
X N
~
(T) lEI
.. +
. + K
r-~
C\1
1-
+ U)
~
~ + Li:
N ui
N
>
Lt>
cT
E) N UJ
1/) I
I l I "" I I I I I I I 0
rn
Q)
0
g g g g g 0 0 0 0 0 0 0 c
0 0 0 0 0 0 0 0 0 0 0 0 0 ~
c:i 0 c:i c:i
0
c:i c:i c:i 0 0 0CQ ,...c:i a ==
Q)
c:i ~ OJ
~ Cl) N N
I
(I')
I I "' I I I I i5
~
C\1
0,
s- C:J3 stJlS"..:ItJnsxt:Jw "3JN3H3..:1.:1IO I. u:::
1--:w
lEI
e i-"':
e ..,
9
El
El
9
eEl
lEI I-":
;3'
El
c
ee
4
e
lEI ) ~--~
El ;3'
9 a:
D
CD
~
ee a::
Ele
a 9
_j
N
El
e
e
e
..
e
...
e
+ +
~--~
(f)
Q) e e
e e E>a
e f)
K e
....... ..... ~
N
,
f)
w eEl
... e
.. + +
l
E)
IJ)
E)
.
a
..... ~---~
E)
e
8
X
"3 +
e
+ e 4
.l!l
"S
(Y) El
' + ..
. +
X
I(
N
!-"'! ~
~
(J)
.. +
+
+ +
en
<(
LL.
N N u;
>
CD
&
w
E)
.,.
N
.., I
(J)
I I I I I I I I I I 0 2l<::
0 0 0 0 0 0 0 0 0 0 0 0
~ ~
0 0
0
~
0 0 0 Cl
~
Cl
~ 0
0
~
0
I')
c:i
N
c:i
0
c:i
c:i
....
I
0
"'
I
c:i
I')
I
0
~
I
..,
0
I
c:i
II)
I
ci
,....
I
0
CD
I
.m
0
I
.0
C\1
e e
E) -~
11'1
E)
EJ
EJ
e
E) e f.-"':
E)
~
e
4
e
...
e
EJ
E)
f-~ ,
e
E) a:
D
OJ
EJ
::
a El a:
E)
a E) ...J
a El
I-"!
..,
N
e
e e
.. .. + . +
<D EJ
a
El
E)
e e EJ
r
K
r- -. U)
w
. e
e
.... E)
e e
.. + . +
J
FP
0
1./)
E)
e
. 4
f-~
e E)
EJ
X
::l' +
B
+ .. ee
X N
.!!l
"5
en
In
...
- . N
2!
I
+ +
I(
~
. +
+ i+
N
en
<(
u..
N ui
>
e N
"'&
LlJ
II( 11'1
en
I
I r I I I I T T 0 Q)
()
0 0 0 0 0 0 0 0 0 0 c
0 0 0 0 0 0 0 0
0 0 0 ~
.
c
N
c 0
0
-
c
I
c:i
N
I
c:i
trl
I
c:i
~
I
c:i
111
I
c:i
(D
I
c:i
,....
I
c:i
CD
I
Q)
ll=
i5
~
C\1
cil
L"l'J3 st~lS".:Itlnsxttw .3JN3ti3.:1.:HO I. u::
8 8
~"':
It)
El
El
E) ,...
El
El
El
E)
r- . ,.
. El
e
El
e
0
E) El r- .
El ~
El cr:
0
[I)
~
El
El
El
E) cr:
El _j
a IT)
El
El ...,
t-
N
0
eEl
..
E)
.. + .. +
El
tO e
e 9 B
El
EJ G
t< El
...... t-
CD
e N
e
+
w a
El
....
e e
.. +
afJ
. +
J . ..
El e
(JJ
IJ) r-.
II
El
El
X
:::r +
e
+ .. Elf) 1!l:J
(1') "e X N
t- .
N
"'
~
. + + JJC . C\1
. +
+ ++
N
t-
CJ)
<(
u..
N ui
>
co
E) N
o-
LU
"'I
1,() I
I I I I I I I 0 "'
(])
0
0 0 0 0 0 0 0 0 0 CJ c
0 0 0 CJ CJ 0 0 0 0 CJ CJ ~
C>
0 0 0 0(I') ci ci ci 0
.....
ci ci (])
!!::
0 N ~ Ill ID II) (J)
I I I I I I I I Cl
I
"'C
C\1
Model Lambda Eq. ( 1) Eq. ( 2) Eq. ( 3) Eq. ( 4) Eq. ( 1/3) Eq. ( 2/4)
0
r-
C\J
I
I
Ln i i
C\J i i
----------1------------j----------
C\J i i
i I
:L i
i
i
i
::J I i
i
u I i
I
a:::
~--<o
. I
i
i
i
i
i
i I i !
Uco ------------L--- ------j------------L-----------..1.----------
i i i i
i i i i
(f) i i ! i
i I i
w i
i
I
i
i
i
w i i
i
i
a::: i
i i
i
i
<...:)' i I i
wzg I i
i i
------------~ ----------;------------j----------
I
o.-. I i
i
i
i
_.J _.J _.J
ww w
U1 U1 U1
U1 U1 U1
ww w
>> >
0
(])
EJX(J
w~ I J
--------r-------------1------
. I
----~-----------~------------!
0---< i I i i i
I . I I I
I I I I
l I I I
1 I l _j_j _j :
:
I i
!
I
! ~~ ~
I WW W
!
I
I I I 1 >> > I
0 ----L-----------.1------------L-----------J._ ----1
m :I :i :
I
I
I
I
a:t-- I
lI
i i 1 i 1 za: t- 1
i . I I I Z Z 1
I I I I I I
I i i i i i
I I I i I
I
I
i
I
i i
I
i
1
E)(> +
i I I ; I
Ln i I I I I 1
------------;--- -------;-------------;------ ----r-------------;- -----------1
::r I I I I I I
I I . I
I I
i !
I
I
i
I
I
I
0 I