P ip i p in i n g - F le l e x b i ty Analysis at
bese besett ttin in
yin st lish lishin in
effo effort rt
impl impl
jff pp oa
rati rati
At the same
o r u la la t o n
prepare
Wa
TilE
na
BL ~I
ILSSur safety safety to ILSSur
agai agains ns
struc-
tura tura
prob proble lem. m. an
lead
Iail Iailur ur
of the piping
overstrain
limiting-stTess
of
types
ri
adequacy of ha Flex Flexib ibil ilit it char charge ge
material
pracit
refo reform rmul ulat atin in
to
hapt hapter er:5 :5 of Sect Sectio io
as torsion.
disc discus ussi sion on
il cent center er (and INTROOUCTION
P re re ss ss ur ur e
P ip ip in in g
significa icant nt at all signif
desirably 8.1110, displacements) lar structural
mitiated in 1951, Task Forc Forc
u bu bu expancion.
2.
on Flex Flexib ibil ilit ity' y'
B31.l
W!l8
locationa in
planes.
tv" on
to to digest
avai availa labl bl flexibility
info inform rmat atio io analysis.
The former
importantly,
its clarity
W!l8
to
clauses
underatandable
readily
u nk nk n w ns ns .
in
and, more
into
task of
thei thei
Ws.B
enti entire rety ty
or
since ra
at
take
respecta,
reactious
aubs aubsta ta
wss
first in nonma nonmanda ndator tor to
selves
with them,
tell
8.
Task Force
to a n in
th
IB r, H. V.
dissenting
AMERICAN
Safety.
ASTM ASTM-A -ASM SM
Y. TH
and
GENE GENERA RA
d eg eg re re e
PROCES OCES-S OF SOLU SOLUTI TION ON
a . . lr lr o
ri
Propert
reac reacti tion on
l, re
[I.
of
Tm:
and
Heat Tran Transfe sfer,
Effect of Temperatur
equi equiva vale lent nt
of
to their
aepar ately
Mech Mecha. a.ri riic ics, s,
tis. tis.il il
to
Report
their
Engineer:Tuoo Turns. h ie ie f e se se ar ar c For ernb ernber erah ahip se aource urce (121). Nu at of th pape paper. r. to the Bibliography Under the cbairm cbairm"ns "nship hip of spectively. as c ha With With S. W.Sp W.Spie ielv lvog ogei ei ha ie ie r e .n .n , n d ..nd members. by Subgroup 'The origi al formul formulati ation on 1; alt.ernate cleuses of th Powe Power, r, Appl Applie ie
system
important:
any
(121)'
pipi piping ng
to apply.
so
However, !.
1953.
(three forces
three introduce
the
tion
will
to
of this chapter
li it
ther ther
l es es se se r n u b e
grou group, p, with with the findings
rn
tern tern
join join
&S
view-
elasticity,
sess sessio io
et ala Eogi-
Rese Resear arch ch
Metals, and
their
4. 19
Paper No. 53-A...s1.
be
rt
no those
ec nn
av
en co er
by
ar te pa
th
ha e x b il il i
hioh hioh tb
stre streng ngth th
as um 1926. It
to
pl it
th
ac
this
proper-ties
po
ul
is ga
ns na
ier-se seri ries es solut solution ion Four ier-
us ll
ul
xe
12h'
nominal
in th abse absenc nc
10
12h'
ol
throughout. posed practice
d e l op op e
gi
tain
of
as
of deta detail iled ed
shella,
where o- le ex bi it e ri ri st st i ch IR/r depends th pipe pipe wall wall thic thickn knes es t, its mean mean adiu adiu r, curvature re radius of curvatu center Orig Origin inal ally ly this this fact factor or was used used only only for correcting the deflection of
Thia
turbine
he ge
mome moment nta, a, or stre strees eses es straints has
to
ap
d.
Ma or
i on on s t o
ILCCQuot
forms
ve en
ly
p ro ro xi xi m t io io u o r b o types
n : t io io .
o vg vg a
to
h a . . a been
Kl!.rm rmJi Jin' n' terms in von Kl!. here here the characteristic Ialls
Fourier series fo bend bend prop propor ortio tions ns below 0.3.
genera ra by its gene
of anal analys ysis is
vali validi dity ty
str
1.:5, in
nc ll lt Iimi Iimita tati tion on
pu or upon upon thru thrust sts. s.
in
aus Iyti cal, graphical, comp compar aris ison on with with past past eucc eucces essf sf g re re e im ti
le ds
ca
u fa fa c co id ec of nt p re re s u r o r n d nt The effect of ordin ordinar ar steam. pres pressu sure re on th Be.. Be..x. x.ib ibil ilit ityof yof 6··i 6··in. n.
la ou ta, an ma invo involv lv vari variou ou for approximate solutions included. ed. should be includ e st st a l i e d
clearly
consultation
he
with
d iu iu s
el ow
ge
a me me t
xcrcs
ip ng te o mp mp li li c Jl at.rat.r-e& e&HU HUld ld-s -str trai ai distr distribu ibutio tio in cer i n p i i n be in on of th ct of hi to nd
is
will
relatively
by pe ul ti o mp mp on on e t s u nd nd e t i g z " wi wi t
ordinary beam theory. calc calcul ulat atio ions ns this this is
redu reduct ctio io
no in Bexi Bexibi bili lity ty
90 smalle smalle ares, ares, the ouJd ouJd be expected to be more more pron pronou ounc nced ed by it is igaored
stress stress iatensi iatensifica fica.tio .tion, n,
keep keepin in
calc calcul ulat atio ions ns
reas reason onab ably ly
si ple. ple.
in tb
inte intere rest st
of
to the
to be quite
00.
th
of nominal
multi-
designed to
uc
i bi bi l t y
ct
briefly
tex follo followi wing. ng. Curv Curved ed Elbo Elbows ws or Bend Bends. s.
ar
th
os
i gn gn i
in th
or whic whic
flex flexib ibil ilit it
fact factor or
have have been been deri derive ve
theo theore reti tica call ll
an
h'/' and h'/' be ow to
h'/'"
1.65
and
nt
of providing
in th 1.65
k'
grou grou
be of a.
tangea ta
It
rati rati
to
tend tenden ency cy toward
tangente
IBILIT
th
th
ho
po
stru stru ct rea. rea.
B.8
2J
1.
often
generally curv curved pipe pipe
re
iscu iscussed ssed
known
Jenka' a' prop propos osed ed formula and Jenk paper (17).
Srupman's
Iorrnules
rief riefly ly in
rn
[2b]
for
pp ndix
as originally
3. iv
It.will be no~ t~B.t third third appron appron~at ~atJol Jol th~ d,SCUSSIon of
40
~o
I}
Iar
~. 20
sar
"q
r-,
asyrnp-
'-,
.651t,
-r-,
r",
....
k'=
sponding curved bend
1.65,1h"'"
II.
(114),
'i"'t
I~.
:=
.
'O""'-'..A
0<
ce
b ot h
h'l'
....
Th
i'
11"4'
( lo nq t
-----
tlan~..d
.oa
06
.1
J~
.s
.4
oJ
Flexibilit
CMroctuistic
.6
.8
10
t~
""'~ I.~
'-
i'
O9O/hv,
i_
O.9Q/'hV,
1/(
l' <,
l'
'"'-1
r-
.9-«-
sr TY
ST
-I TE AN
p pe r
lower 1><'10'"
cecv 01 ve
fo
In-p'a.o
T1
WITHOU
tra.D.~veMlo
..nd
,, th
ng,
form flexibilit TO
FO
respectively,
type, attempts
at
whic
Donnell nt ll
will be DOted tha overeetimate
(2
more refine
re
?:r{l
tan
i&lJ
(ab]
is
spacing
fo Widespacing
Equation
ipe-wa
th mitr with inter-
(a arcs
bt in
th flexi-
correlatio
th
factor
firs
pproxi
tion
these variables
from
h.
fa tors
o)
(1
tb
&l".
[2
rese-int ne fica io
tan a),
creased
leNB
1.
Jan of thes specific tests, whil Equation
(1
This
bt e 2 poio\
esrn scur e.
[2
:<
available
FLANGE
c o a ne c ted t . . e : s t 01 ir.ND an kTB,
re "v !.
[or
0.8
assigned
data.
~LJ~
g r- ap b
R.
It should be note-dtha bend is vening tange ts, Corruqaied Pipe
1'-.
u pp e
cot
[1 I,
R.
and 2.D
9Qlh'!>
1"'1
(Co.
as
where!' ia th mitr radius an
b..
..ad cT9;
characteristic
R.
r........
ro
va la
have been eVll.luo.ted conservatively
<,
IH
~lII..I...L'
fFS
tn
he sp rs
1.52
~~
'.0.
0lh ..-.d.
de lopm t,
.......
ii:
0.-...
he re ic
'(ol.~'"
',
?:
T C f 'l o9 r nt l
of fb.nge
effect
pliCJl.-
nnis
(45),
workin
wi
6-in st nd rd we gh
between 6.4 and 7,2
ta ge ts an bends. Otlw Components, na.y xhibit
cr as
or
cr as
le ibil ty
as
pa ed
wi
appear unwarranted
a.t
80
doin
wi ne
om part of
th line spec to stress calculations are Bends. tacit adrniesion
re se
lexi ilit
pr
hing
th
urve
nds, part cula ly 80
STRESs-INTENSIFlCATION
lezigtha
in
discussion of Pa du
nd Vignesa'
In discus in
stre.ss-in ens- fi il io
FACTOR-'!
Ia tora
or
ip ng
ompo
.5
to
st ain-gage
test
such obtained
and
a u h or '
It seemed
o bs er va t o n
ul
ideal n.
in],
0.9
results
(5]
1.
t.
where h.
(LJlJr2l
sionless) less)
an I,
will
-i
influences)
effectiv
thickness,
fittin
in.
tees' ll thickness
to that unde consideration.
part stress versus
straight
-h
branch, saddle, for reinforced fabricated intersectioue bends, or unreio-
:1.
thickness
pipe
equal
to
cornponents,
matching ;SN°·'
I~
C"
where
th
R.
nominn
r, a te ri a
tees,'
fo weldin
where
--
Ie
constant.
sr.
cot a)
re
(114),
t.e;rt.s
245,000
was
files,
r'
deg 11
(ll4).
347, at 1050 F.
pertinent
to
itself
a.t 20 as at 2,000,000
author
ha
S-N curve a.t some
CASe
trend
account
'I. and .h 'I,
evi-
Corrugated Pipe 8.
atress-inteneification
the Pr
to
recommends8.
of .B
bars.
suggeste itself S-N
h e a tr ee s- in t n e i ce t. io n
Boon
to
lU
ib
that
"noneyclic" service is 8. atrees-reduction
th
I ac to r
The
settin of
published
in th
stress sources data
selected is definitely cyclic
value
important influence the pipe, 8.8 also the shape, the corrugation
thickness
type,
Proposed
Rules
1939; th
th
assignment
a.
oversimplification. mental
Boiled Flange
gTOUP
Connections.
from the
is necessary
tests li
rm
the
th
-d pr ac icc.
test
th
yield
to con-
or R.
1.35
and I,
onf
n.
to
(97)
of this
to
o.bout
40,000
lished
data
The
paper,
evnluat
t.he i n i t i a l author
isolated
test
ub
runs
ri p e J o n ts ,
ILt the
0.
ar
1.
r ol l n g
Se
s tr es s
are given
same values
Tape-re
Tran.siti0n8
iF,
Components
nect.ing
the following
approxirnate
stresstests
rue
iF
Se.
!6b]
where a pe r
1.1
3O-deg taper,
1 5- de g
1.2
5 -d e
a pe r
spring
wa based;
perature;
1.3
E, is
L:.t
and '[Lnd
including
0.
Oihtr Components
1Gb]
{I
F'
and
.,
computation
piping
Il.
to
L3
to call attentio
is
flexibility
to
to
i'v
industry
(38). PRIMAR
L).
ANALYSIS
to s in gl e- p a n
p ro bl e
(61).
to
100 thAt
to
it b e a ss u e d
following section is
L-------------R~~·I
I)
I.
Ii
FOR COLo-SPRINGING
d er iv e acquaint,
." lO
(. -.1)
validit.y of
h e c on c u s o n
eL-1
a.
\V R. Burrows
ts a.nd
tw
companie
(121).
which a. SE l'"-SPfUNG
elbows
.N
-SP
NG
"F
TS
an th
foregoin
to
ha conditions.
square-corner
th
will
investigation
0.
actual
practice.
flexibility
resulta
eeL
as
approach.
and
[50]
more Introduction
[6a]
of
and
[6b]
1.
C8.8e
square-comer
a. factor
solu-
c.
a.
he initial
cold
stress is
Cil.SCS,
"./7] per (1
cal (30)
ta in
e,
elasticity
S.
conservative
c)ere-
where
(1
c)
E~
}!
(8)
E.
temperature.
ut
and
during
successive
(to
which
grsphoanalytical methods
(76)
creep,
range
a.re
creeo limit. es
c o p le t
relax
precalculatlons
and displacemen (33 37,105); to simple configurations
in which
with
W!l.S
atmospheric
dropped
temperature.
tbe
few
( ) f f to
If the stress
be
S" comes displacements
either springs
(52,56,
S,
="
S,.,
gages
at least
expressions
re
shown
lI.3
a bs o u t
v al u s .
~"COld5P~
As on limit, applicable E,; then set E.
Upon
stress become S:
[101
Sg
It.
subject
to
to
S:
s~'
S/
S.'
te As se nd ppro tion limi S, is small, se E.
,,,,,,.
,.,.
' . , , .
, . , . , . [I2a)
'hE,,; then
system,
-3
LIbJ
relaxation or not.
+S.'
(l2bl E;
to
Sf!
i.e. is constant
to
8.S
to [101 by RISe
R: R/ to
I-
S, SI
,."
. " ,1131
c)
.'
R .
S!
[16J
R""",.",.,
that
Deta le
Iollowa.
discussi
[14J
he el xa io
im
S, ba be
defe re
[S to
cSs,,""·"
[I
be
to control a.,;
d0€9
occur, it
8.3
or cree somewher in th system Th relaxation limi S, ca de in
8.S
it
BL
result
yi ldin
ee
is no possible
Bow
.6 S., where S. is
suitable
ondi io fo Bo thes tw limiting stresses
Bum of
or
••
S., where S. is
1.6 (S
[(9)
Bo
Piping Sectio 25
equals
stresses by lows
62 ce
60
..
of
uc S,
more conservative
S!.
thirds
Herein varying fromj
0.50S
(1.25S.
7000 cycles to 0. fo N ' : 2 2 5 0, 00 0 5. Th variatio rcughlyIollows the la
since
ignored,
24 cycles pe day 20 yecr life
followin equationa: ho re tion
ra le in
qu tion
R . - 1 -~ e
·120)
• .• •• •. .. .. .
conditions,
fo
computatioo
th
is, of course
tr
•• to which th
limit.
of
st engt
1.63
inatalla
producing 1.6
NG
S,
S,
it
to S,
STR SS
to assign an accurate
(14J
- I " "
.~.8
E,
:::J
~.71---+---+---~
\13J and [16J after subatitut.ing
S.
with th
urth
a:::
ro so
E.6~--~--~---+--~~
in
.5
.2
wlur
0~
"jJ..J
0:::
I~
0::
s:
PflOPOBED
IT
hi
uY\W' .~
::
-=--
\4].
th
para le
he orrela io
he iv fo se ec in ppli at on of ac or
::
system 0"
IO
BY
COIo{PlrI'ED
TO THEORETf
a O O Sl :
U:
Spw
EA TION
tigu -t st da in 1946; 7000 cycles
ar
greater R. which
Ii.S
eR or Fig. hy th
gives Proposed Rules
servicea
E,
of relaxation.
tication
on
th
S-valucs
. .
0.75 S. se
prefer basing the in thi section.
t.
se
fo
this
ha.t
Spw
1.25 (S.
[22J
SA)·····
it
il bl ct review.
result of relaxation io
assu tion conditions
is
pressure an
SJ
while !L~
years, which
(8)
comparison of th reaction computed he vy so id lines) .m th corresponding
absence illustrate
(reactlon
nl\\'ay~ is higher
8.8
period subjecte to
[20J;
that (S!/SI<)(EJE!) otherwis woul obtain
piping comalso Equation
this
];
FlO.
RULES
.J::
0::
~Iu)
toto nuTlber at cycles
ll
stress ra ge he
gh
••
aide of th
in
equation
is
discussion
and
250,000
10
oeat
tc
ec
in
Room
'
r m u l
-
ev p,i
2C/7oo0'·'
1.
yc
o f Code
e ct .i O
At.
(SA /(S E Qu at io n
\6)
83,100 piping
95660
Oil
62470 Ol or
ISnD
13100
~6875
32750 1. 91
piD~ng
{or
S~'/(SA
Se
eee
T r 6 s 3:7
~15000
produce
given t.emperllture Pip ioi .. Pressure atr.,. MlD~ SA 1.25 Prcpceed Ru leaw.......•.........•.....
iv
p to i p e
T1i;"~6
Author.
1 C under Allowabl
Sla ....esa
Carbcc Olcel re de
SPIV).
Spw)I'.
2.22
2. J..I
1. 67
2S
35
(201.
115)
reaction
th
computed
thn esti
te
as
twee
8.
th
esults of calculations base
on simplifyin
assumption
to undergo 7000 week over 20
ar evaluate JJ fa
estimate
of
ar
tota
properly th th saIety
it
uignifieance
of approximatel
2 50 ,0 0 factor
",;11
to
pa
le
on
1000 cycles
upward
th
nc
BL
contingent
following-de-
assumptions
plie proper specificatio
an
supe vision
of
one has little practical problerns.!
ported.
wbicb
JW
liberal ullowances velopments:
u bl i
io
of
on atrain-
TIONS
fl
sensitive piece of equipment.
COD
allowable
ct on is i n o nn e o n u ip m n t ta in in parts such as pu ps also requires ns io ot n - n si t v e qu pm nt ch va le
ub oo
gi
n dl e it in ip ng
limits th
take equa to po ot of be ea on
lo analysts
of blanke
expect to
ly
resultin
n t directioas, higher to lateral to
ly
co di io
the design ,t
encountered
ing st.l-ain ar
DO
disappeariag,
in
oz te
that th
os
o se w
02
at
theeffects
If
cent to th equipment.
purpose. tabulati
pressure
be
piping ha
ut
pansion.
as a.
hi
pulsations.
the PSP<'I type of informatio
of desired.
45 of
of expressing
limitation
the
ny sp ific case wh
degr
pproxi
ti
will
ep a-
to
in
is
or ul ting
to
is
claim
unpredictable,
form will ways ne ss ry as designer; if in B. is on it he ufac ur portant units. WBAT
SYSTEMS
roup
or on
evot
consideration
earnest
thes
to
to
ping
gine rs major classifications:
rose-s tion
ro rties.
ANALYSIS
REQUIRE
that, even afte
considerable
modulu
simplifica
assume primary
orta ce
su es
resp ct ve y,
resistance
be uorea.soo.a.ble
thei
effect
ques
strength
and a.t
de
CiI.II
in the
by visual inspection
or
mathematical
analysis
intensifications present. le th oreg in
or tests. 15
refl hi oi of vi in th fo lowing ge er in paragraphs 6£0(a) and 6£O(b):
us
rope ti
nt
ip ng-f xibi it
lc la
co ta ne 8.
It will be
that
ul
or ul
system. to the conditions.
line length an configuratio
to a.
simple an
reasonably accurate first approximation
100
\~
:3
\I\~ '. 10
~~
~,~~"
~.
......
.~:\\ ~~~ ....
.2
:'
0::
"'
'3:~
61-?:~
II''''
in
....
,_ r - _ _
--.::
~~
-.:...~ I.
Rotio ot Oeveloped Axial Length FlO.
SffAP£
Ls to
Anchor
is
F.'CTORS FOil SIMPLE SUo/CLEO-PLANECONFIGGRATIONS
12
to th
CONCLUSION
distance 11'1lS
by :.IS C.
(105). ,.
n31.1
ip ng
-,
ratio
to that
vestigated
ill
operatin s ys te m
to a.
latest advunces in theoretica It bas
L./U;
.:
task forc
t.c
0.
explai
certai
.S
that
·1231
openly
referred
to
dral
numerous that,
mmo
applying
proportions
of
00
al
h e p re se n
may
estimate
will be This has
(L./U Obviously.
nition this
r es s square-ccrner
Rules
solution
means os
vide a. reliable
fr
to
paragraph
additional
to uncover
calculation
to
to the clauses
to assigns
represen
to
dent thB.t
lc la
aign.ficance of the various
v'2),
StO(e)
r ac t c e
of
a.
stress
an
I n t e i ge n
to p ro mo t
intended
u ni fo r t y
of
e n o rc e e n
ratio ACKNOWLEDG~IENTS
U' 1.05)'h···········
where
and
respectively,
(24)
to
x. B la ir ,
aguin
J.
c Cu tc ha n
re
E.
Mattimore, of
hi
to Messrs.
p ap er .
BIBLIOGRAPHY
this modulu
(In
appro
i rn a e l
c h. ro o l o i c
o rd er )
of elasticity to
to to Harnmable,
wise
il
c i . sc hr -i /
bullet.in " 0 1 . 5 4 1 91 0 p, 43,
"U~r
vo A r a n Zr:i~cAri/i. 1911. 1889.
des
e.
Verei~. I,
e Te i" "
deuische
d eu ts ch e
Lnoenieur«
441-457.
Dinold.
e;"
restraints.
it is proposed
it is expected
to
to
to !1..5
company
Journal,
Stromeyer,
Er1{li~rin.o,
c to be r
to method
(l05),
such
a.
Septembe
Pollltuhnic
7.
, p. 8
1 91 5
Sanford.
!o
F ur na c
an
gaud,
14. 1912,
I nO l i r T e
ecAanicalEnqinurino, S te am .
Journal
0/
an o ih e a t c »
an
hl na
Masaachuset.te
Institut PP 69-
118. vol.
11
Th Enoi~
J. R. Finniecorne.
ipin ,"
OCtober. 1928. pp L98-238.
0/ Mtuhemsuic
Journal
an
Hovgaard be 1928
Phtl~c~.
PI}. 239-209.
io in 17 "Design Shipma n, Tr ans,
\8 Bowley
l.
"01. n;
SM
G. Back,
ll.IIJ
1, 19 9,
41
l,
B.
p.
l. 8,
.,
Ph//~ia,
an
ecember,
it
li 331-341.
22 "The HIUlli.n,o, Pipin.r; and Ai Cutchau,
PD 647-650.
ad M.
Cnrulitumino
Sweden,
te ber,
K. W. Jernstro Engineers. 1939
rans
HuJ. i 1 l( ) ,
of
in
aM Air CcmdiJ.ionino, 25 "Creased Pipe Poioer, vol. 73 JUlI 2.1931
1931
W. Paul, Longitudiual
L.
in ," 19
r,
t, Mechanical
to th B. .s im L940, pp 443-460
Pipina
Blew-Knox al Pip
ends,
tr io
li
vol.
l,
4, 19
62
J. R. 1941
aM Pdroleuni
Erurineer
41
We3tinoMtUI~ EnoinurirLO,
i5
ino, "01. la
Medvxnic«,
Applud
M..· itim
1931
Enoineerina,
in
vol,
inie to
Heaiirui Octo
Trans. SM "The 55 ip in
0/
Conrad, Power, OCLOber. 1940 pp 58~L
rschber'g, Power.
lOooF Air Cona.itioning,
"St.resses a.nd
54
rc it ts
., 1940. eflections of Three- irnensio Snively, JOIJTncJ. 1940 PD A-17-21. te it in t. re
Pipino
Combllstion,
J. Baggerud an Marine
of Naval
of Society
Journal l. 61, 1939. pp. A-21-24. ip il
53.
1930
is
1938.
itts
4-
pp.
49
51
Meche nics. Stockholm
rose,
A-89-.-\.-91.
ecember.
vol,
ll
Applud
H.
Peiter
T.
.tl.
Marchant, Journal 9, 1937 -{I8-A-74.
1929
52-25, 1930
0/
J. vol.
William Hovgaard,
Jou'fTU11 0/ M~ic~ pp, 293-344,
ti 1930
Architecture
Sheds Applied Mechania,
823-828,
te
4.
of
44
Enginurirt/J,
,litclWIl'Cal
El\{)i1l-'ering,
io
4.6
ecAanic.!. Wahl. 1, 1929,
0/ .\'aool
is
!>.farc 13. 1936.
Nuval
m, 9,
\I
\\
t.
Enoinurs,
Mechanical
94
B.
19
Ert/Jinur-
ossheirn
rg l.
4.
4-12 t, Power, ib
t,
ip
19 le
l,
an '-
19
it.t
Cona.ilionino.
stig
4,
JUly-A
40 Ksrne os
ly
is
it
0/
Ut
rm t.ri st
Nooal
19 4.
Sociel1) 0/ Nasa
AmeriULn 4. rl
rs hun
tu ge
."
r in e
n o n e. er in o
ril. 1934 Absorber
leg
ets and
an
S hi p 1 ,r t/ J A o • .
l, 39
to
de,s lnoenieurlD.u1U,
1941
EnQinurin{l,
41
Journal McCormack, 1942 pp -38- -42 58 "A in
0/
40
Applied
Mechanics.
Appl~d
ta
Mechanics, Journai '"01.
ra s.
4, 1942
L. Snyder,
in 43
l,
M;,cutchan, te
ino,
16 170.
43
ril. 1935
"1\ ielv te
nd Octo
Ka r.
"01.
de rn rd
rg
[o
-8
1935. 43
Eruriruerina
19
Spielvogel, POIC~r.
19
;,
41
Pouier,
Noyes, Journal: 1941
19
Pipino
Heoiina,
Spielvogel.
r,
ic
HlUlliTlo. Pipiru;
and
Ai
1943
ig
ta
l. ..
1935 l, 06 1944
11 18
10 Conditionisuj,
igness
14 He ustin, 56 1944.
of !.he
Journa
er ca
S oc ie 11 J o f N av a
n c n ee r
vol.
ietr ti is tu s. eHart, Applied MecM.nic.s, Trans. St R. AS~! E, vol, 66, 1944, pp -240- -Z44. it "Elaatic Str ight ip an ti nds, by rocker Pipino Handbook nn A. McCutchan, cGra -Hil oo ompany p. 754.-860. 77 "Bending urve Thin Leon Beskin JourTl4l o] Applied Mechan~. vol. rans ,194 -I 7. Tests C. Andrews, Healing, Piping arui Ai ugust, 1945 Conditwnina. Aims ip tr ti ti ," ld th Paul. Powe Plan Engineeri!1{), ptem er 19 15pp 103-104. Het(myi. University ic 1946
Peiroleusr Engineer tr 82
in
ip
Refiner, Octo er wick, Petroleu -, 105 '·Z-.
ro Exoanaions." by 19 0, 103-108.
ark!), A. It in in 4, 'ur a, ll Ke tu ky ce ber, 1950 10 '· tall ti ," stru ti Leaflet IL-llQ-75 urbines. estinghouse Electric orporation December. 1950. 107 A. lark E. Reissner Academic Press, Inc., 951. '·~Iethod of bsorbing Exp ..nsicns of Long-Rang lO Transipin ." rnissicn F. E. Wolosewiek, Petrol e-"" Refiner, February, 1951 pp 9-74 vogel, P D V : ~ ,
1946
No em er
19 1.
Figuring
1' te in o t o na l P e r o e u Ne u, 9 46 , st C. Andrews 83 "£tude de Is. ef'ormat.ion sana Tuyaux igrie Il. H. arth le an iri. ll ti I' ia io Maritim et Aeronautique, vol, 4 5 46 411. 84 "C ra (} '2 47 13 0.
1.
23;-246. 04
inforcernent Enc-inurina
ip
Ju e, 1952
III
J. iq 4 7 p.
Pa tial
W, Spiel-
"Easy
vogel, PO",", October,
1952.
W. E. Cooper Atomic Energy Cornmisaion E. 113 Test," by L. Andrews. 'Tra na, ASME vol. 74 19 2, PD. 123-133. Trans.
1946 lair
J.
PCIJJtT,
in
AS~!E,
l.
4. 19
911,
7-303.
is .n
11
C.
le
ic ts
is
ti
7, 194.
in H~aLino, Pip-i7UJan
lish
Ai
J. is 1946 ndre s.
gus t,
Coruiitioniruj
te
R.
0-
r,
1946 rt
series initiat-ed
83-8 Januar
94
v 0 1 . 75 19 3, pp 1051-1072. ,. te ," J. Ex rese te meeting London gla.nd ecem er
l.
4, 95
01 16
it 12 19 2.
in
1947 gineere. Lo don,
19
Wilbur, Peiroleum
0.
1.
ecem er
in 12 19 2.
Refiner, March,
4, 19
953.
ti
io
ic
143-168.
ta
ic
9t
869-879. Jesse Yeakel, Petroleu
no an
1947 PD. 113-116.
Refiner,
i r C o d iL ib n n a
H.aLiTl(J, Pip-
94
le il in MecAa.nical
in ,"
47 by
by R.
ta
leti
J. R. Einniecome.
s. 1948.
Comb-u.!Libn, Proceedings
Lewaren,
in-W ll
s,
ly Th Oi and G a . & Journol; rati
,"
.A
19 fficie ts 19 su 151-159.
rm
ic ip
pp 369-;384,
49
TE.JCT OF PROPOSED
is
CODE
RULES
FO
C!;!AP"TEIl
01" Sf;CTION
ON Fw:JORILITY
PD 8(}-88.
to
(NOTE:
Poure GUleraLion. Decem-
gas,
Assern
to
a.
iv
loadings Peiraleu
Of
FOil
im
rl
95
1948
(Loudon):
49
01
ic
ic Constanta te l. lish in this
Engin.u-nnc,
it
which aignificant
Refiner,
analysis:
,
kl):
4.
1
expansion wick, H uu 'n IJ ,
P ip in g
an
wick, Petroleum Refiner
o -n d o n n IJ , , p . 8
19
02 06
which by conventional
to
ar
valu
15
parisien,
sufficient
01\
magnitud
initial
ak
ha
will appear
will ac
10 paragraph 6£1(11)
ol spri
as
6£
sp ifie
B CL 5
sed. Requirements. (a Formal calcularequ re on.l here re so bl oubt
A S~ l £ mp l n s
an
tiOOBor model tests shall
the conditions
to
Standard assumption an paragraphs (a) to (q). testa, in lc la ions od
requirements
(b
cycl will remain subst.o.ntiall
su
t.
is referred to is th deter-
shall be ak
nefi ia
(b
ffec
udic ou
co
sp inging
ssis ng is recog-
th system to
than th stress ev is warran ed it eg rd
(c
re te
shall solid hang rs
guid s, sh cons er d. shal take into accoun
(rf) Calculations
wit.b close clearances, th tim rather than thei rang ar significan an credit accordingly is spring th lcul ions ru ts 8. om ts aierials. (a 61 ls ch pt appl es to al ss of rn
stress-intensification
such 10
be used. (e)
In
terials expausio
(b
the maximu
as
in
calculating
unit expansio
show fo that [or (for bo lines,
normal-operating temperature
in
account.
normal-operating
ma.xi.rnum
nominal irom th
"rang
temperatur
shall
dimensions. th
be used
calculations,
expansion of
movements
angular
this
materials
shall
be
l'11.AC!e
to
(g elasticity
Bureau of Standards. and
(e
!, respec-
tb
Eo at room temperature.
stresses
to
at al significan
Us be bove as um tions, expansio shal be investigated
points
(b
with the foUowing formula
of the National
of Str ndards.
Bureau
as 0.
(d
s,
oo
al
for a.ll ferrous matewill be
Th S-values and to pera in pe atur s, sp ti el terminin th allowabl expansion-stress range S... sh
where
S. S, M,
(e)
ke
Mb/Z M,/2Z es ta tors on
vis.·
orsional stress si be ding nt., lb in nt Ib in
stress-intensification
factor Sll. shall co
(c
exceed tb allowabl
stress
A, where (1.":15
disregarded.
be
48,1
S.
0.
subject
S.)
6ee(b)
where
s.
quip
nt
su ti
ro
cess
thrusts
iu the
Flexibili
(b
S•
a.nd momenta
a.nd are to of th od
in the applicabl
shall
If desira le
the
fl xibili
ay be
of
va ue Total
(c)
shall
no. oi full
temp
le
more applicable following
catalog
of thc~ properties will be provided the meantime data puolisbed in ay be used.
this case
anchors
be installed to provid
causee.
Or tics of sufficie or nd forc du
upon adoption oCthese Piping Handbooks or
strength nd rigidity shal to Jluid pressure an othe
7000
and ... ... .. ... .... ... ... .... .. .. ... .... ...... .... ......
250000 an
data
table:
Stress-reduction
over
expected lite
Tables
5e{:tiODS
factor
the
16 R; and R,
(d)
e qu a o n
I'
In,
In h e o re go i
restrained
r;~n 1-.:,
ft.
r.
to
or
sionless.
Standard assumption (f) to (i).
(d
graphs with
arid
(e
the
9.
signifi-
1,
where
(f)
110
expansion
(a).
th paragrap
if the piping system
stress
to to
E,
E. t.
E,
data, the
Ic, and R.
factors
flexibility
an
Iactors
stress-intensification
be (e)
(g
s af e
ca
6&2 Supports.
based
s us ta in .
ts no
(a)
expressl
tota!
The
(h
to
temperature
nll calculaexpan-
(b
l.()
assure that the
and
the equipment
considered,
S, but E, a t r oo m
elasticity
SA
A'
e mp er a u re . The
6!?1
maximum
sball not
rated
It CHAPTER
Of
EC'l'IO:-; TilE
M.
(1.25
KE
or al
Maximu
for pipe line
re re c on di ti on s
0.25 S~)
where
COMPA..'1Y
or mode test sa sf h e o Uo wi n
s,
whic
S,
a na ly s
simultaneously
normal
S. are to
(S and
800 F.
stress-reduction
ti in.
[actor
IS psi.
nppropriately
conform
with
(b
te
syaterns
record
Stress-reduction factor,
cycles over expected life
1. 0.
of satisfactory
service.
0.8
(c
paragraph
0.7
(a),
0. 0.5
250000 an
approxirnate
criterion
i~not
satisfied
tudinal
If than
S~,
to S A . -
DY
1.05) The
well as
and
622
0.D3
'I
checked
pipe.
eupports
shall
be
to
S..
to based
as needed.
stresses
Sh an
re
the
17 '-.c
c:~
-on
....
'"
u;
01
tP.x
r-f--'-.
..c-
~~ .>..::
.-..::
-e
.~
2~
)j JOI:KJ:j ,(II.IIQfl(iLl pu
1"1
JOPD;:II.I.J!'lJ&~UI
N'"
or
~saJIS
:>
JOI~D;I
01
0{)
'JJOQ
tl
~~
!:
i=
-e
'-'
.t
....
H.
t:
io
b~
O.c.
""""
~I;!.
NI"' ..c:
;;
'"
f-
a: .<
!l:
....
'".,
'"
co,",
\J
18
to al minority F...ross
FLEXl131L1TY
viewpoints
al kinds
au
of criticism
F'OR CURVED PIPE
nlthough
In
flexibility
Karmlin's
are
factor
least
in reformulation
(1I7)
gone Iar
ha to
k,
Flexibilit
10
12h'
--.:.
Eaclor an
Stress-Lnieneificalior
12h'
Factors,
0.
12h' 4136h'
105
k,
[2
Formulas
48OOh'
4800h'
536h'
in years
to c o
J .Y s ug ge s
o d c o. -
O.255000/h' 12h'
73,912h
252
k,
1.3400
O.OO7500/h'
2,446,176h'
3280h'
2,822,400h! 2,822,400h'
329,376h' .f- a.3OO306/h'
1.4004
12h'
0.00 l058671h'
O.013946/h'
having
O.OOOO!276/hl
II
Karrnao flexibilit k~
reference
(114).'1
Formula
I
or
constant
12h' 12h'
W:l.S
10 12h'
where 10.762 0. 684.
0.3014
o u - o - pl ao e
o.~
.176
ex bi ty
In
0.11070.074880.035260.0202
Inteosification 1.65
h,5;1
It
Fluibitity
eba".ct.eriotic
VOQ K a r m 4 . n
fiI'!lt.
von K & . r m . . 1 n eeeoc VOD Kirm.(o. t hir
.s
ro.J:im.atioD, &Pproxima..LioD,b
k8
0.1
9.;4
9.04 16.6
26.4
::
r- :r
nth .~pro:EiDl.&t.ion. al Beakiu, pproxilllaho b""e
.Jenke
0.05
17.3
34.0 34.6
[7.3
33,0
[6.5
D",•• to
0.
3.25 3.2Q
3.29
3.29 3.30
69
69
1.69 1. 6Q 1.65
nalysis.
Discussion JOHN
E.
BROCK.'"
is
that i s r ep re -
its
to to
as to
em
AS E.
parentheses
aut.hors
bibliography.
I~
t.vngcnts, is us to make
will enable effects
other developrnen ing a.
t.q
not particularly om in One indication
op
tion
an overestimat
will
however,
governs
mation.
flexibility Iactor k, int
be
the
approximations
solutions.
analytical
fn
is
th
he
[ustn fe
ve op ts ea s, though
or
will
symmetrical
ay
ut tt
•.
he
t ho r i nd i t e
er ns th n e t s l l o f w hi c ca wrench, as 8. motor, as to
or
es
ki
neutral axis. nt co on nt p re s e d
hi
p-
he ul an th om o u ways, namely,
as
ccrrect=-if
have been mainly with stationary in tall ti r. Baker is with marine installations. 8J compared to 8. square comer, ha tw opposing effect on flexibility. On th on hand th K6.rma.n-Hovg(l.[).rd-Vigness-Beskin etc.,
axis
violence
in accuracy
hand,
"short-cuts"
curacy Buffer ba been explored adequately compared
81T1All
representa-
to
etraigh
consequently
ig
configurations radius
e sp on di n effect predominates.
nt iv
.
':.1;
:~
'~i
MIW
'F
.,
1.,
MP
SO
OP
1.0
~u.:~_-.,~ .~
.(
. .. .. .
EQUA
the
ho
reaction and the
,.
ApPROXTMAT10N
AN
vears,
oe
he
ha
pa ti ul
as
ir
ng
carefully
is
values withou
on
cold spring If becomc
is is o, th
l c
or 1953.
or certai
EXACT
L-BEND
If
ri 29
designs
_ .
rO
LeQ
[17J.
1,-
communication.
In
what
L/R
Privat
system.
different
be counte
of hi
m:J.Y
.~
. 1. . I I
SQU.
SOLUTION FO
ia a. single quantity
is
.,,-.,_..,_
IL
... ... ... .._~
~I~~.;~.~.~
using
is
cc.u:v. .I~n:CII CI IoQQ. I.&I U4 IQCU. L 1<:JII,. pT.. "I-" I'0Il
u::tI a . . I o C T
L •
of na
c(~aI
~;)
:::;:
.,
::;:--1-'
"~
e-
-r..
in
account
ho
"'hien ch ct riz in ua de gn
~~
""~o--
~~
V~
.~
great
nd oo
',,-
o r t ig h
short-radius
taking
BO
.......
/.f~
involvin
it
i me n o n
ow ve
grea
r'
re re
p.
BO
E.
E,
ld
gg
R.
3E ized deforrnation
R. The
Iuilures
service
nrc associuted
it
us
Wa.9
allowed
to
c yc li c .'
na area
rnn.l- or nonfu
its strength
good
0.
approach
rather
stress
an
USUo.lIy
to
established tbat
very thin-wall
components, OCCUI"l:l
cases.
l lo u a b
to
Range.
S tr es s
design.
of
it
Report, It
gree up
that
par
The last paragrap
gerous.
the
its
an
Allouxibl
to
Reactions. rirnitaat an
of
ment. ha
Require Analysis1
Sysum
S uc h if
to contribute
piping
to
r eq u r e e n At
ulso
aystems.
appnre
Task
will tend
to
to
Conclusion,
ts
stress ?-ray i-
which
with
th
rest of
various
as
pretation
.sh
f1
became
in
as
evee if this implies
rm
as
able to That
KAI.{A1!CK.14
that
617
Section
Hovgaard,
6, Self-
to
lysi
following
comments
ro
D. Sherby so ar
offered;
Smith, &: "Gibbs
s.
ic Problems
DOrn.
o!
ig
ratu
re
,"
Temperature,"
by by
21
light
is
La
concerned,
Th
mere difficulties invol fo
Hovgaard
developed.
nsic equati ns
ul
fo
ea ng
st ongl
it
thre
th se
a.ct ons.
unda
ta
has kept
prin ip es
(a)
ould he
determining
8.
to
(b
stress rang
ca
was
ub om
te
nt
regulate
prom ne ce
accept, was till very
Flexib lity
regulations
of he opin on
circumvent unreasonable
regulations.
m.ination, as to th to when such sa.tisfactor-y
wh re tbey
re ppli d.
same is
an
stress-range
ve
to of
a.
ha
ie
par~
indicated.
all the
III
pro-
and
circumstances. year
dra.ft of th
Messrs,
refrain [rom atat.ing
L.
Th
PACH.
author's
paper
uuderstanding
whic
ft
he
tt
as
a.whole met,
and
wa
of pipe-stres
analysis
the rncmbership
result ha
as
but enthusiastically come Iew mental images in us ng stress rang
as
cb ni ll
calculations
tion seem wort While the
while.
moved
hi
pr du
disp
en
thicknesses, substituting bend length corner, than
very tirne-consuming, large approximate assumptions.
(R 5D "r whos virtual This will be the case when th virtua square comers L' 1.571 KR 2R al nds, hose 1c:d ilit ac or re less
Wa.8
1.571
!L
hile ther ar
spring in al was
lOa
ar
was involved
on ept.
if ould oc by xt rnal forc
correc pipe-stres om to cc
per
would be
nd
fe
it su
K-va ues, th ir
such bend pipe.
will
to predict.
Beside th flexibilit
th
factor an
utra th forces assumptions
will to el ev
he
stress-intensification it
stresses as com100
xist nc corners for
Oi
is ts
o.
hift
ns de bl
of the sh also ma result finery
Mem.
ivisio
ASME.
Arthur
wh
he square corn 8-'1 well t....
22 tha t, the
neutral
arnoun
of relaxnt.ion is un-
If
to
very
o.q
stress
condition
iLh
;l.t
i nc or r c t
well
If
c. than
to minimize
rd ri
to
o bv io us l
re
of
piping
system, relaxa-
th
be
to
assure B.
rnay
TIOSSHB1M II
AND
F.
to be
SHEAFFER."
te
has
used to
accepted
If
facts,
to
to be desired. strains.
what
thei
periodicities.
various
and
as
.s
calculations
or
statement
im-
well
an nn
may
BO.
physical
because fabrication, less,
metallurgists. should like
to h er mu l- st re s
to ell!
to
attention de ai s.
be
Our
to II')
ERNEST
ev where flexibilit
highly
flexibilit
to
very
process,
Using
to
factor
Poisson's ratio
II
valu
characteristic of
to be
II
to 101\·er
regions.
k=~
stressed
ry
given
these
121.
0."
In well to
Iorrnulo.tious
eva (a) ho condition;
cold condition;
(b
total o ca l
(c
range
of stress
or strai n ;
r ee p ru 1l
JO
puny
Schenectady.
N.
Fellow ASME
Mechanical
Engineer,
Factors,
23
700 cycles.
to to
be
DO 0.
rnater
li st 8of abou 0.33
nt ns fi
io
or ug te
pa si
joints wh re an
pone resp ns le os st inge an
fa to 0.813' "\11
(I
l)
h'l,
DO
I'h o woul be oblige to t.ion, here hose ho ha no re ut loophole afforded cnlculation whatsoever. 62
L80
h'l,
If
prepar
ufac ur terpre
ro
th stress-intensification
nt
si
ha ge
factor definite requirements
factor of 2, representing
th stress-intensification
to
stipulo.ting that certai
piping be calculated.
factor inherent to
0.9 wh
ot rs
rtia
ubst .nti tion
of he uthor'
Fo
ul
(51.
tool
it
hi
to nc urag
sounde
T110RS
om ts
so sh ul
of whic
ds togcthr-r throug dist high-press re urhiuc ad pa ha foun itexpedien
ar carefull
SU
to
i>P.
gen
(11.9
pu ling th spring ng th writ rs
gine ring
deht of gratitud
to
cL).
sp to appl
nf ur ons, such counter-
calculated
averag
engineer. to
invite so
cornrnen ts.
author's closin
re arks
in
nf ed prim il
hose hase
sion of good judgment
bona fide material property
bl wast
of ip rnut rinl
Vie
C{l.5C
Chart draf of LheT;.L..~korce Report to
th
no pipi
re ct on "-5
it ow expansion. provid
fo re sonabl
im
of
lowa le piping reuc ions
1954,
24
ulti
te
hibitive
ondi ion)
nd finally
so
ould re uire th
enti
were relate
allowa
analysis
believes it If
formance to
Robinson's
rr
hi
excellen advice
rather
than
property),
physical
to th
No separate limi tation
ss estab-
too
to
is sufficiently which
E.
is meant
to
onfigura ions
ch ra te iz
by small 8.
to
fast,
pr ce nc be us nl to take
ov
soun
engineering
judgmeot;
J.
they
H.
fl.'
le
or nl ghte ed
forc
nt
to brin
ithe
an
uoundary
nt
ould be xhaust d:
(see Apri 1, 19 4, Mr. Kamarck, while approachin angle, appear to
too
in
line
should
too
(which
to cove thes
this
that
this about.
While still
a.tI
baa been
J.
fe
of
squure-corne
cornplcte
assu ptions.
flexibilit
factor
It
(up to
if the
it
Iong-radius
to to
questions,
ld-s ring
syst
prop rly,
ha
S€.veral stages or Factors sinc he ld-s ring maximum.
TTGG7-3-255-prinled
ac or
by definition is limited to
