ML20073T037
| ML20073T037 | |
| Person / Time | |
|---|---|
| Site: | Limerick  |
| Issue date: | 04/18/1983 |
| From: | Hu C, Huang A, Khlafallah M BECHTEL GROUP, INC. |
| To: | |
| Shared Package | |
| ML20073T027 | List: |
| References | |
| SR-8031-SS10, SR-8031-SS10-R, SR-8031-SS10-R00, NUDOCS 8305100281 | |
| Download: ML20073T037 (76) | |
Text
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m k CALCULATION SHEET [ b cai.e.NO.Sl8031'55/9 REV NO. OnioiNAron c. k. Hw DATE 4 -/ / - P 3 CHECKED sf DATE- // 83 ( rno;Ecr Nm e v sc l<
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SFP.22768 Rev. (606) E D-69 (5/76)
C k CALCULATION SHEET 4 catc. no. Sege31-SSig aEv. no. O
^
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[ SFP.207?8 Rev. (6/76) e
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SUBJECT C f a '* *F [ d" MM 6MM* b SHEET NO. ,, F (sej,6
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& pr +he pr.b lem under con gde rakon.
'Flevi Lility +1,e ett w u, .11 & veaau d beca of cf & ase of 1he clamp . floue ve r, hmd o"
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I h Pfm f 52. nggIe cVed. b . KFP-23768 Rev. (676) ED.69 (G/76)
A ( CALCULATION SHEET r Sb CALC. NO. bI 80)I.*hb[AdV. NO. O ; ORIGINATOR C' - bl" DATE ~b3 CHECKED MM DATE - //!b b M f Y C Id
- JOB NO. 8803
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( x CALCULATION SHEET (- CALC. NO.bN SN!'SSlO R EV. NO. ORIGINATOR C- - DATE 4'I I- E 3 CHECKED ' YM DATE M! b O I O ** I PROJECT b I M # Y ' C Id JOB NO. SUBJECT [ o "',0 le d u tf t1 StM L 5 f _S , SHEET NO- 23 1 y ,' rg gy f f 's S S' (b) .M Eg. 9 8 I[{ * [h M 6 [ . 5 5,,,
. s =,ses. em 6 g,s o. C 7
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] = w s e 1 (, e -tw fhe km
.H*
D,. 9 = C R+ pjg + 6, 7 + B t 2r P (R4 R '>t = %. m du n so w < ua p I C%%Oo pt l lO P = i g g o l < l r b = 2 eq e r f si h' hO b' . SFP.20730 Rev. (6/76) E D-69 (G/76)
( CALCULATION SHEET (' CALC. NO.$f gejg.S$10 REV.NO. O ORIGINATOR c. M . H" DATE 4 'I l ~ 3 CHECKED DATE / 3
/' PROJECT N e er [c I4
- JOB NO. #88 !
SUBJECT (fAWD $M f R CLd I b$4 b SHEET NO- < I 0). fa&y E VA k hs'o n IoAd on fot * ( Un i f=* yre ccure ) x ( Pad Area) X (Centu7 reo) 042 % snakber l o ad = ( 4, o o o t6 he tr Ther = I . dis c on L' nd) = I261 X zz. 5 x i. 3 = 3 7 il P i b Dae To pre w are dis conh*'$ ~= 321 x 22.s v13 =13 e 9 ft i Tht to<t = M- o+ 37 ii e +O 8 9 = Go To 7 16
.Q ..)/3700 = 4 2IO esi I stresse s i., AuucA by civp =[
Cz=16?I
- C , = 1 2 5 2.
y, I ( l 2
- fM l
l Si.c. (M,et + M.,_ + % ) '>'M ,,, l l l M=t 2 C M,nOy + C M se g + ( M se,O f l
= .2 7 I t e " 9 ) + t 2 i 2 2 + s woo]
= cone w- , 8 l
l C i i SFP 20768 Rev. (6/76) ED-69 (G/76)
c W gisd C CALCULATION SHEET CALC. NO.SR83 -5510 MEV.NO. OR[GWATOR c. M . Hw e -o - f 3 S OATE CwECxEO r 2,, M, DATE _ PROJECT bi W1Mi C d ' JOB NO. OOOI! ' SUBJECT O!A**1C a ' M M 9 SHEET NO. IAy = ,2 (( 13! * >-+ Qu cv 3 I
- 1]
1
= 433 7 g M-t k, Up= 2 S c 19 'L ) + t.s- ac 9 ' i n t E] -
= L2398 Ft-Ih '
M: / G o 37 P '-t- 4 3 3 9 ft zz3 7t"
'O p = nez n-a '
~-
h QO b $n- IL k c, P'P* + q r1 D. g ,, ci,, p g 3,1 1- cd stre s s.e s z* p = u. m s u \ 1., c v.u 4 g. , , , o 2 .o.a e , 9 ,,,4 P
.um. n P
P = / 2 9 9 r+ 209 73 4 59 tf o P h p5I ) 3( T S I 9 70 fCi [f[ id d - l0 >3b, ut %er (Ob $idf Y k W CC Yf M' O. ncc.n., s c. u . l ) SFP-23768 Rev. (6/76) ED 69 (D/76)
D,
?
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. m a r o'c k '
JOB NO. 080 SUBJECT 8'd M k MS4* b SHEET NO-CfA**l' 1 2
- Fent ,
cosidered a t, U 2- ) is 4 . . - - _ _ . _ _ . _ - . _ _ - . . _ . . . _ _ _ . _ . . . . . . . _ _ _ . . . . - . _ _ _ . _ _ . _ _ _ . . . _ _ . . _ . _. 5 - l 2.W Do_
^
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- s
- g Eg. 13 ...
1 7
<; , m v g ra- v p o -
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- d -
h SFP-20768 Rey, (6/76) E D-69 (G/76)
. ,> T
( ' CALCULATION SHEET (- SI ,/ CALC. NO.S D@ -S IO H EV. NO. O ORIGINATOR c. k. H" DATE d-H - El CHECKED r I DATE /#M3 PROJECT l I
- e ~/ *' C k JOB NO.
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'1 2
n g;, g_ ,9 +u g,,A g ;sg5% p,, % p , p,,, 5 3 4 _ Sy-he - e der con se de rak/o r , # is che,*ol t ht g.il _ 0 0 CM b CR ! CR k AIC hm par o% f f ela k l oad Sd q;r.9 7
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pa Je pressu re co n sWar'n f = p.t xQ x 2 2.c xl.3= 7p t 'il u
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/,cd sfa u.es = 4 3" } /s yao = 3 9 m c %z e4 = c ( "*21- ) + C ( q_t ) H^ + 2(I-LI) E K lel l Ylod SIed#5 I
2
# # i" #
- p g cy u s (, -
=//6oi f 2623 L 2(I-o 3)
= ' ~
- (O ce76 o SFP.20768 Rev. (6/76) E D-69 (5/76)
-mL a> (' CALCULATION SHEET ('
tBIk [ CALC. NO. 3I" _ REV. NO. O ORIGIN ATOR, C. N -
- DATE IM-Eb CHECKED I / DATE M'N3
(- PROJECT 1- " *d ( kC JOB NO. ON / SUBJECT C ! A ** !,' I "2 i* t MW ') SHEET NO- ,1 2 w -Il he l.OY 3 h(M-t) ~6 %
- 4___.__. .. . . . . . ._ ._ __. _ _' _ __. _ .
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g(t d) I 1 +IOf*k SIf#53 2 g, 7 ,7 4 o _g. 2 e.1 x4 it x 4- L 3 (, e '( b o -+-l L R
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'8 9 bA Vfb y =
(3-$18 } C F9 ~}
= 13403& /
~
A J' 0' 0 E b 9 5 rx y e
(
$t CALCULATION SHEET (
S- I CALC. NO.SEfou- SS ( O. REv, NO. O OR INATOR C' N k DATE # I O ~ IE CHECKED e YN DATE N/ b b PROJECT I " " f JOB NO. ON3l SUBJECT I ! 0 **' i2 Ead u d ON 14f 6 SHEET NO- EY t 2 (s'i> 06 E
- S ft 'l l ca. ding s ( Load set 4$8 k A ) , n = TO Cy cles a P= Tbo PSA e Sim a (%st'+Hwl} -
-+ M rs e '? H n ,
5 s M/ : 2 ' ( H.e[ t Hse.v'[' + H sAs ] 7 0 . . _ _ . _
= "Eb ~Ib 9 'O _ ( =- Cg ( P2 } CE [ E- )Hy +lo ca.& stass-e s 1
11 1 3 2 = @flW{.G ? \ [/\ 2 + 417-9 T ? 9 3 2 fo E* loCad @res4e5 3 1 8 E M-t-P o i I 9 + l C Cd NTNS4*5
. hy lord @ % 6+ S . *(.%) w au.h 1.tA =ta00 sw .
7 Yheve d o v p au 4.*ma. Cow 6YrAi I~~: 570 k 21. E #l . 3 ,= l b 6,3 p
, (T= so o'F)
Ob $* (E}, f Ot$$u M C 0 v skyg g% k t )73l
, f,p i i e e 4 = [ u. oo o 4 [ r,(, q g .9 g 7 g j s 3 g , g (, gg
) eed citw sse s = 3 E L E g,,, V 13 7 *: 37360 fst L= 771'[+ 10 H 14 ? 7 3 L P
= 6?3 04 k'e = 1. o + ),M -il =2733
( (g = % io s = + 1w - m YC {$ 00
'4J 8036 (FP 2*,76% Rev. (606) E D-69 (G/76)
CALCULATION SHEET l C CALC NO. 648031-5510,,gy,no, C ORIGINATOR (k N DATE d-Ibhb CHECKED N DATE D/T2
', F ROJECT '&* Ck
- JOB NO, 8N3!
SUBJECT I
'*d*d b S$*b SHEET NO.
O # 'l 1 2 g) ggy L x d i, 5 ( Loc c1 set d ( e ) ,a276:ro ey c l e ,5 3 h* CR ( ) [ bsRE)nE 4g t f o CcA k SIM 5 4 *
- b Y ' ~
6 7 Mg: Q@ } y g A'n - \ V s lg *t,E
- Me,gg C 28989z ia-ib i b6RV 8 2 \ M-F
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- 1*
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/m 64 I StNS4e5 clu e. -f;; SgV '
.8 f oCad 6b e69f5 c{we. M S R\/ = [ 3 'T o o y o. go Lt M se,y 64< ) ro$e = 2 n ., c b ), b ~r l X g, p 2 (9&ln T ) A Lq L g
= ta'6-
~- f n b g ~ \. 0
< c) sg + s 1=_a-6 tJ 710
*/g % O SFP.20768 Rev.16'76) E D-69 (G/76)
- t 1.
PtI CALCULATION SHEET <' S. CALC NO.N M! d5lk <4EV.NO. O ORIGINATOR 0' *
- DATE 4 ~ II' b - CHECKED 'y M2 DATE b f PROJECT l ^^ * * f IC JOB NO.
SUBJECT b + ' e dx Md E 5
- 5 .
SHEET NO- ! 1 2
'Tn t Y bwo k rg $sMA (&& b s'+ $ Gr &k 'res, f of 4.__,.._. _ _ _ .
5 Of 6 Mk] C/ C k e 5 ( [a clgf( ghh g g gag 8 p;go.pgf T2 E 2 L' hs 7 8 __ hw Ci ( )4 C ht )N W h ,k 0 C d 6 M 5 5 C1% b NfM L k 9 yY e 5 5W 1 lC C O h$tt%$ { + f ) ~~~ Y D E k 5 V po, -3 kr [ ( 6'O l ', I I' b E \
~
II gg 0 sm, [=T ,m
=
c- K y., i- " 2 n c --o [ 3 5%._i3 ~-
, l-93
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- # /7@
tJ =- l9' o o o m
)'= 000 00
,O a..,;<k=o'oz~2-t - 3e r- + o' t- o eoC SFP.20768 Rev. (6D6) E D-69 (GD6)
' CALCULATION SHEET, :
CALC.NO.$fdO3l-33ID REV.NO. O ORIGIN ATOR O'b' DATE 4dl-h3 CHECKED l DATE // S
/' x PROJECT 'Ya#fi N JOB NO. O AO3 j SUBJECT Cla ed inolnatel Sf M ? S-P 9 SHEET NO.
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~_ ,. . ..
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Bmd o" word- c wu , &-- c'l c *l ed ' " Owa M# 4-lu ca t ewl alt sbu e r me# h c(a g. ._ l C"- AlIou die S. T ,, ,J d i h%, if S I,a n l ef p o ;,, 3 4 oa+ th& fla re salts n calcaix.t very ___ cce cer vo3:aI , % ~. of +4> co. cerv &c n _ anz. Sw,,mr,3,1
+11 in F !! a:"] t ... .. .. - .. _.. __
v L i.; Sud on prog'eeDJ cimg pad Me'a3 AM% owlg Gs3% - of W vah%r loak w.UI k opplied on centyd fack.. k vre.d , sy. % . Ca.{c af hrn.. l00f le ad . - . N U) S M ss b cli a.: can frHer k Ye olu Cul af +-W wWd o J-I:ad on ORNL 's kporf " End efe c$S On e/ Low S % Lg'ec % ! $i h' o hr e n-)- L o aot is3 s c r-f ? s tics:in d,? u pa vihd a n ~ic b!(.$ WB 5 6 9.5. I-I a>> d - 2 iS u:G d y . 6 mu.>nc saneh- Iol k w c) % cateJ & cla.,p h b f,,a us /oca cm <se c . m ,, af,,a a p,, h fp laa" ( in+c c v d he b mL ti) On STftd]h$ f fA , f ifess 8) I hQJ p 5hesIJ hs lowe y joy cla mp ( non -inteya I drich n,en t) ) ee el b e vK. SFP.20768 Rev. (6/76) E D-69 (0/76)
'iYil CALCULAT10ld SHEET-7(9J')
ORIGWATOR C'k* b^ DATE d ~II b3 CALC. NO. g R203 l- 45l 0 R EV. NO. CHECKED /__ DATE /O O -8 PROJECT - N' *M il N JOB NO. WON SUBJECT IM CI D le S h 44# 5 SHEET NO. O!d "'[
' (jy rt,- y ro+.) te q evs k it & C lo " f i;
I a
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i 5 6 I' WA
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9 10 +lo lo e J 5 % :os cvu. uwJ a bso la +e g Ia . % 11 12 31- v< ry co mer voNva s. th e ven/ A % of 13 is 5 M ss 4,f en si ke s . is , 16
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' 18 L i ,, .y,f u, ;-k A. C l* ~ p e ft'e d h- sa "'" e r y A A~ 2 20 A> / t. jf., ys 1hikle. , l 21 1 22 C'"'
- P'* 7 '*- -
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*3 -
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F.T gE f CALCULATION SHEET'- D CAL.C. N05U611 -5510__. R EV. NO. OniaiN ATOR C . k' - H8A OATE "'I I '~ CriECKEO L DATE
\, r' PROJECT ' F T' C IU
- JOB NO. 088
' SUBJECT C f # "' P 'adb d 6S' b SHEET NO- 1 l
1 2 3 C. ._ ~ _ _ fff M i k ._ ___ . _ . . _ . _ . . _ _ _ . , ____ 5 _ ._ A"d Pv. #ress 6 1. R oar k R. T. 7.v- i A < @r a .' 4 " , 8 M e (g yc u) hi !! y E d i h[W . D $ k sge$
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g-.. g g.g... ntm-OS P!3*tt A*di*P5 N s.vegw:e vant:r:s c: .vn1 Screenme ru1cs andprehmmary desien cf ffTFriping uere developeJin 19N hascd on n.c.w: .w G, j* expccted behanor and engmecring p.Jment, approximate nalculations. e wrn. ASyl detailed melastic analyses offi rehnrs Th:s paperpriaidesjmdmgsfrom six aJdasonal
- ' dctadedinelastic anah ses u nh correlanon s to the simphfed analysis screenin g rules, in adJason. simphficJ analvsss methodsfor treating weldment local stresses and strams as i self as fabrication induced flaws are described. BascJ on the FFTF expertence.
l recommendationsforfuture Code and Technology worls to reduce design analysis costs l f areidentajicd. N0'd.ENCLATURE b a = heuber equivalent grain half-length w = Poissen's ratio f 0 = Flow shape parameter V C _2 = Stress index = 1.95/A4 /3 'TE = Maximum thermal expansion secondary C2 = Weld shrinkage stress index bending stress Do = Outer dia eter of pipe 'aT1 = Maxinun radial gradient thermal E = Young's modulus h = Noten depth stress KN = Fatigue strength reduction factor 'DW = Dead weight stress op = Pressure stress K2 = Local stress index oe ff = Effective stress Kt = Elastic stress concentration factor C KT = Factor applied to peak thermal *eff ==Effective Total effective strainstrain strain creponent T ce = Elastic strain Ke = Elastic strain concentration factor ' = Plastic strain N = Number of applied cycles 'PF Nd = Number of cesign-allowed cycles
= Peak thermal strain P = Primary stress intensity INTRODUCTION Q = Secondary stress intensity R = Bend radius of elbow The Fast Flux Test Facility (FFTF) piping r = Mean pipe radius design activities have progressed f. cri the prelim-I = Screenins stress limit inary design in the early 1970's through detailed
! 3Tm = A11cwable design stress intensity ASME Section III code analyses including detailed a rance limit inelastic analyses for elevated temperature ccera-Smc = Stress limit at colo end of stress tion. Design activities concluded in 1979 with range final as-built reconciliation of stress reports for Srh = Stress limit at hot end of stress constru:ticn and installation modifications. An range overvien of the flow cf these activities is provided T = Time of applied stress by Figure 1. As described in 1975 [1]*, signifi-TD
= Allowable time for design cant project cost and schedule benefits can ce cb-
! LT1 = Linear thermal gradient te'rperature tained if <creening rulas and simplified a-aiyses
; range tFrt :;*i wall can be used to ecnfidently identify a pipelire cen-j t = Pipt wall thickr>2ss figuration that will p3ss detailed stress an3 lysis
* = Coefficier.t cf thermal expansien code lirits. The screening rules for preli inary S = Carry c.er facter design [1] usad on the FFTF project have served 1 = Pipe f a:ter = tR very ell. Detailed AS"E Codc analyses usi~: alas-y tic mc* hods [ 2] and inelastic ectnces [3 - 5] have deicnstrated that all Co;1e design rules and limits g are met. AccocJingly, a correlation of t M 4taile:
e inelastic analysis findia.as with the sirulified l roru huicJ h. n.c htor i en.iccruir ti.... .n .4 tts, Arnerun wien .,r analysts screcning rules >:111 be presented. htch ui : n,.;ners. s. , p...c, Li . .n ii., e enim : % ,a , n o n,,,,,,,,
. C.uur:rna bi i eme.. . 4 al.t . Aucu.s 14 :l. l'** 4tanum rept s..cs.cJ at As%It ItcaJ.quarists 4t.:: h 17. Ihf l . . . . - ~ . . . . . s - . c ,, . , 4 a;,.... ..co ,, ..
.s Before presenting the correlations, a short m,ve, i ci sn m rw
$ cverview cf the screening rules and b6ckground will er o av
" i i i i i
./ be given. After the cceparisons, simplifications st zs. . a m,,6 L7
' in tfc detailc<i irelasti: m iyte; and supplmrntary jn t s.. [
y s ii..p i 4 ! t ed i re i n'. . c ar.a ij . . .I w c.:,:.n.t;. G Finally, the paper concludes with recomendations . is for future code and technology work to reduce design - /
- e ste m -
d l analysis costs. so ( ys4=gti ein - e s , SCREENING RULES A';D BACKGROUND N l - N N * ' 5, n
'
- I CN
g
; The preliminary design screening rules and * -
\ -"
i limits [1] for primary stresses, shown in Figure 2, 3 N, . s N ." a were easy to meet due to the icw design pressures of the FFTF piping. Thase lcw primary stress levels L , helped control ratchetir.g and stress rupture damage [ t ,3' . 3'" _ s at lw levels. E* 7 , ,, E E - 1 g j Screening limits fc- cricary plus secondary 5 . g stress ranges (See Figure -) censidsred limits J asscciated with creen ratchet, creep f atigue, and .. These limits v.ere applied to the very - l i s hak e cc.<n. simple screening equatien of: [
- s. LI.IT 51* 11 13
- 2 4 -
' Or c Ast 13314 l ,, _
(1) tm un.! m: rm 1
'TE * #a1T 15 - cactua i cmtna where: . , , ., .
rx e a in its tze in TE = Maximum secondary bending stress in pipeline, usually at an elbow. nvmarat t'n _, m r.-I :. l j =.u:e l FIGURE 3. Primary Plus Secondary Stress Limits for 316 55. j r - ,, , e w. i.....
'*"' --N -" L aT1 = Maximum thermal shock radial gradient stress
, Q-d. considering a_11 of the plant thermal transient
/3 l :*.t.;%.. l ! .- 7.* :r.~; ,
and equal to
.j 1 1 ,
' n .:T -- j 4-
- :=.: r '-: :=~- ~~
I ., E a (ST)) I C" C' 1g $-3*))I .L :TC":" I { . .. i 2(1-v)
.=0 F 5 = An allowable stress intensity considering
- .; j ,9 *,Q~ - j creep f atigue, creep ratcheting, and experi-
,;;,= I.
ente factors. g.g FIGURE 1. General Ingredients and Flow of Piping A major feature of the screening rules and System Design Analysis, ASME III, I. limits is the shakedown and relaxation of stress during the hold-time providing the transient stress
""^*RE 'eC' range is always less than the " elastic action
- range. This is depicted in Figure 4. " Elastic 16
, f - 100 action" range for primary plus secondary stress range P + Q is m ed @
; PD '3 + P, s c,5 KSg oR US, g 12 -
?
Df 3 T, = 1.5 Syg +S rh [ [ g \ % A s l z (2) z where the standard AS"E Code terminolocy of the g
! g N s 16 55
- ; \ 's g 33
~
50 ; ASME Ccde Case 1592, Paragraph T-1325 Test No. 4 N NV [18] is used. 0 O l 'N \ / l
$4 - - 630(ni -
s If the (P + 0)R exceeds 3 5m, then the N.,,]',::m oco - relaxation of stress cculd be as shown in Figure 5
- 60. 000 1
,2T, oac , o and not similar to renctenic relaxation and not g
IG affected by the transients as shown in Figure 4 rm gr.c lxo llJC 12:C 1%C TIMPERATURE t'n B3 sed Cn approxin3te calculations, expected behavior, engineering judcment, and a fcw detailed FIC'J RE 2. Preliminary Design Limits for Pressure inelastic analyses of pipelines [9],[3], it was
/m and Weight Stresses Using 50j of Co::
deemed irpcrtant to previde enough flexibility into
'g')
1 Case 1311-8 Primary Stress Limits. the piping iscretric designs to satisfy Equat'icn (1) 2 i
i 6* and keep the (P + Q)R less than 3 5m. Results E 1000 2000 3X0 (h) f ' frcn inciastic analyses of pipelines is given in ,, , , , , g p Figures 6 and 7. - 17 Additional background is presented in Refer ence [1]. 7 MPa Q 10
%' / 0MDE -
69 a ( L5s,g -- = t E
- f v.
}
l N y0 - 1; 0 i N :;; , I b rH O t J ' (P.Qi g iIME
-10
[ l3 1N51DE
~
I -17
-- AB CD e .. , , , .
- - - - - - - - - - - - - - - - - - 01S0 1000 2000 2560 us* 220 11C0 3E j Tlt.'.E (h)
FROM A-B 15 TEMPERATURE CHANGES: 1200 0 F+ 3500 + 1200 0F FROM C-D 15 TEMPERATURE CHANGES: g FIGmE 4 Typical History for Pipeline Primary Plus M F Secondary Stress When (P+Q)R 1 1.55mc + SrH-
-]
J FIGURE 6. CLS Pipeline Inelastic Analysis Results n5 (Ref. 3). 15 13 mH h
,Al% 0 N to ,
s - r %, Nww $ i 3
.O -
e't i $rH b U
, -S ,
.y l TmE $ \ ) j , $
10
~
% l 's ,! -
-se 10 m0 LN 17.2 tsi Gli6 Wa;
-2D i . lat 0 120 to (P+01,
# P05I110% LT _
FIGURE 7. Hoop Stress Distribution in Criteria
- - - _ _ _ _ Elbow Inside Surf ate (Ref. 3).
L55 y- - - - - - - - - - - - m .= i= . CCARELAT::*iS CF DETAILEC INELASTIC A*.A' Y!!! FI*. - . INGS WIDi SIMPLIFIED A*;ALYSIS SCREENING P.U:.ES i ' l : l FIGmE 5. Typical History for Pipeline Primary Plus Table 1 presents the correlaticn data. TN if ig% Secondary Stress When (P+Q)R 1.SSec 1 detailed inelastic analyses ir:1uda picelir.es c' simple, short rt:ns as d picted in Figure C ac::
) + SrH.
i 3
. P I
and conscrvative modeling. The simplifications in TABLE 1. CORRELATION OF DETAILED INELASTIC modeling include: f* i ANALYSIS FINDINGS WITH SIMPLIFIED ANALYSIS SCREENING RULES I . Um cf constant bending elbnw elemts (Type s.,.r mn v ~. .. ....3..g,,, h # " W*E *
- W W N
~
E M *E* , a. TT"fAM.%* 'E%::Cr 's F"it*/T:r ~ . Extrapolating elbow midsection stresses and a F: ! !! !! r; Wi ,: !!! !!! ;',' ::: ::. strains to those f or tha elbow end weldments
; ' *: T U !! O M M ;; ;E ;;: ::: ::: by use of " carry-over f actors and indices to A E; .'- !! !! '!! i;! ll! ;;; !" M' lR ;g account f or nonunif ormities introduced during the f abricatien and welding of an elbow to a 5
- 1- .: * '.'.T* f*?j..*1'*?, **i/~ ';};Q ",'f*y[.3
., ll;,'i$ "'" " " . Use of indices and fracture techanics crack-5
- M' 8 .,n...,>. grcwtn models to assess local peak stresses s ,,,,,,,,,,,,,,,,,,,,,,,,l,[,[,,,,,,,,,,,,,,,,m,,,,, and strains c . ... .. ..... ..
... 4 . ~ :.. - . . .
In eenera1, detatied ine1astic analyses of a
~
'C*:.C:: :.*::. " ~ l1.. *J "'* "" '"'**'"'" ~ *--"' "* "-
. pipeline systcn provida prirary and seccedary stress
.. .. , ; .y . .,, .. :
. m. . .. . r .e. m. . .. effects. hbstructuring tecnniques er use of in-dices are reeced to acccunt for peak stresses and strains. The simplification in inelastic analysis 9
, procedures include:
g Envelcping and lu ping cf thermal transients l z e .. , I. u o
,dJ . Extracolating ratchet and elastic follewup 2,'*
i @4'a . is7 strains to end cf design life f, U8 in , 8lb ia D.9 i The technical bases for some of the simplified 9j" methods identified above will be discussed in the r:s i.ms ,.= rv following paragraphs. L ON M 3 Constant Eendino Elbow Elements 8
@ The technical justification for accepting use
'Is f of the constant bending elbcw elements depends on b N "*nd. each pipeline analysis application. Considerations k) N include findings frcri prior elastic analyses of the pipeline such as the level of stress expected, the i
{ .m==. ratio of in-plane to out-of-plane bending en each I elbow, and the nu-ber of elbow elemant se;-ents FIGURE 8. Primary Crossover Piping Mesh (Ref. 4). used to codel each elbow. Hibbitt [9] and Pan and i Jetter [3] discuss the limitations of the constant I bend element. Figure 13 shows a typical model of a fairly' complex, long runs as depicted in Figures 9 900 elbow using three 300 segments,16 elements and 10. around the circumference and 11 layers through the I wall. l The simplified analysis screening values for the pipelines of Table 1 are cross-plotted on the A basic step in justifying the number of seg-screening rule limit curves in Figures 11 and 12. ments, number of elements around the circumference, and the nu-ber of through-wall layers to codel each The pipelines chosen for inelastic analyses elbow in a pipeline was the comparison of elastic had the highest simplified analysis screening values stress levels, mcnents, forces and displace ents and the least design margins. The design carcins computed using the inelastic pipeline nodel to those were identified by detailed elastic ELTEMP [2] and computed using conventional elastic analysis pipe-simplified inela tic analyses such as the full line models typical of analyses to F.3-35:'3 of Sec-relaxation Bree f7] and the O'Donnell-Porowski (8]tion III of the ASME B&PV Code. Correlations to l methods. Accordingly, since even the most severely within 5% .to 10% were judged acceptable. I'creover, i loaded FFTF pipelines were de onstrated to meet all for large diameter, thin wall elbows typical of
! th2 code requirements by inelastic analyses, many breeder reactor plant piping, cc parisons cf elbow i other FFTF pipelines with similar but less severe detailed shell finite element or finite difference
, loads and themal transients are also cualified. elastic analysis findings with constant t,ending
-e However, for these pipelines, some of the very con- elbow eierent findings were also utilized. As seen servative code elastic analysis limits (such as the in Figure 14a, the degree of ovalizatien varies Sq limits) were exceeded. See Figure 12. around the elbcw arc. Ovalization cf 50% to 60% cf the taxi :' at the elben ridsecticn exists at the SIMPLIFICATIONS IN DETAILED INELASTIC ANALYSES junction cf the straight tangent pipe. Pczever, the elbcw cet elastic flexibility has been shown by e Detailed inelastic analyses of oiping do tests [10 - 12] to be adeouately predict:d by use h require sa':e simplifying in codeling and analysis of the sirale f en ula of L = 1.65h give : in tFe procedures to keep the analysis costs within rea- ASMECede,NB-3600[13]. This fer ola r7 1ects sonable li" tits. These simplifications are technic- local flexibility distribution and varying ovality ally justified by the satisf action of ad hoc rules 4
l
it Mn = Aw ('t) along the elbow arc. This ovality also pcnctrates _' 8 8' **
- u2 u
' cne to two diameters into the tangent straight pipe , ' ' ' '
portion (Figure 14b & 14c). The code approach in- M * "t % " %' .,a - u volva. tM flexibility f r_tne as a enn* tant f.v.tcr n applied to the elbo.s arc portiori (Figure 140). /,,trun. n,,, ne sic vm. niv i eu Accordingly, it is an " effective flexibility f ac-6 tor for modeling the total c1 bet and eff ective tan-gent pipe flexibility f or use in the total pipeline system flexibility analysis.
" i j
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g' . . > l crane:m vva NT * $e A .%a. (u[ . ( Af tL( ,,g
,.- .L. , -A. . l*,r./ W g ,
L .e uva a Extic .t.c 3
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o . tto 1 oa:T n5se DE'AQ c=t t,wtic
- u. :s A.3 uv.t' fit 014uis*4C ac.Austh
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FIGURE 11. Primary Plus Secondary Stress Rar;e 8-inch SHL Inelastic Analysis Finite Limits for Preliminary Design of 3:6 55 FIG W E 9. Pipelines. - Element Model (Ref. 5). ttum Arx ('c) = er a2 na se sa As previously noted, test data [10 - 12] have # ' I e i been used to develop and have confirmed the simpli- . 4 fied flexibility methods and models for elbows with g3 sj p*
;r _-
N,
,33ti, 3 ,,it3sg
- 80
!/i straight tangents. The highest elastic stress in- -
^
N) dice in the elbow midsection has also been shown to so - / ,3sm stt in - be adequately predicted by use of the Code formula [13] of C2 = 1.95/A 2/3 Therefore, by assuring that % D the constant bending elbow elements used in the - pipeline model provide numerical values of stress ss, m sta vus. olv. '
- l and deformation for elastic loading that correspond s ec. tnN -
j c - with sufficient accuracy to those computed using " T the standard Code fomula and flexibility methods, = 3
+ '
J.- the model is deemed adequate for use in the inelas- / *%,,, E
~
- muuny / +'o,, , .
E tic analyses, provided plasticity and creep effects _ are limited as discussed below. g, _ OtSICN UMIT. 5 +,,,,
++
g as ;
,'^
i + 4
~
I
, f : h
_-* b
/
.sks er [eiW of, T ga y ".w'kk . . .
sguMIT Pit ta 13 OF CASE 1731-8
'T%
'%. ,_ T_'
i
..g"~
Ut* ' v 7.$*
. '*..'P+ .
4. e 7 ,
- e. itv.uimitv e.
~ C8tTE*la ' CRITERIA
- AND PAh5L3 CCM uvlT5 gd I- .-~.. *
! f f ' f g 9*
l ' ' i
- *- l*n-5 O
rz ac so in uz in tw
<Q. p.g. ' "
., ityeArx 6, 5
_ .- - D FIGURE 12. Preliminary Design Primary Plus Secondary
- -- .- " - Stress Limits for 316 55 Fipelines.
} '-1 '.-
QF ( The thermal expansion and thermal radial crad-l 1 tent r axima elastically-calculated stresses ihposed l lb. on the This elbows were,the for FFTF, keptand lesscreep than the 3 %'s i b ' FIGm E 10. Analytical Model of System 61 Primary level. limited plasticity effect l Hot Leg Loop No. 1 (Ref. 5). to local and small pcrtions of the pipelire w311. j t 5
Thus, many elbow element segments necessary to cap-ture stress redistribution associated with gross plasticity and creep throughout the elbow ware not a ner"!rr!. In Mditiria. .M '6a c ia^ 1 i an re*ptm n w i e. . expected to "shakedcwn (Figures 4 and 6), good r., c _8 margins between the Code limits and the calculated $ ' # ~,,~~.I.N3'/ I
. 44 values of accumulated inelastic strain and creep- *o : "' -* ' :/., /. - .
N ,'"7 f atigue damage were expected to offset possible i limitations associated with the approximate elbow model. , , , , , , , o e s 129 1W . See details of the elbcw models uted in FFTF ,, m eg g f relastic analyses are given in Table 2. Generally, the FFTF analyses [3, 4, 53 found tvo or three elbow FIGURE 14b. Typical Distribution of Axial Surface eler.ent seg .cnts with la to 12 elements around the Along Pipe for In-Plane Benjirg 1.oad. j circurferences and 10 o- 11 layers through the wall I were sufficient at reasonable cost. a i I . 66 ., n [
.I ' ' ' '
.I g EE N . t ' ,, $* *
- l wc 'cita i c .t ca i c .t on a QQ kj" $ / -,
y - s 80 -
--
- 2 e -
EP.3 l
. \ tsu n;.trso GO .a gr s' T s p to 31 2-2 13 4-4
-s 3a 'g o'W'M ol5T ANet ROM cc.TIR oF 80 3
.: .x =====.
2 R"u f FIGURE 14c. Typical Variation of Ovalization Along
,, ~u ane d [ Pipe for In Diane Bending Lot.d.
. _, m ,, <
ELkP 802. EL M M ,. VARIATICN USED IN CODE
"" FLEXIBILITY ANALYSIS r' N g _
D --- Ek 7 k.1.65/x.>f
; I i
- - , l FIGURE 13. Typical Constant Bending Elbow Elements. g _
l TmCAL ACTUAL VARI Ail 0N j _ g INCLUDING OVAllZAT10h EFFECT3 l
- BIND 1 1
- b i 1 STRAIGHT t TANCEt.T I P!FT g 0-0 1-1 2-2 3-3 4-4 DISTANCE FROM CENTER OF BEND smu u3:us FIGURE 14d. Flexibility Factors Along Pipe for In-PlPE BE!.3. R!r = 3 o Plane Bending Load.
ca.t on c .t on cNE em Stresses a'nd Strains at Elbow End Weld ents o 2 3 4 Elbows are 'of ten attached to straight portions of piping by girth weldnents located at the junc-tien of the elbow torus and the tangent straight pipe. Stresses and strains at the elbow midsection a were fcund by fiarkl [14,15] to govern too f atigue life of pipe elbows tested below temperatures where 1 2 3 4, creep effects are significant. Accordinoly, the AS!<E Code {13] in NB-3600 provides stress indices for butt welding elbows that are based on midsec-tion stresses, but a Dc/t 1 100 is required. For
] FIGlf!E 14a. Typical Variations of Stress and Ovali-zation Along Pipe for In-Plane Bending, FFTF, the largest Do/t is 64. As the D /g t ratio gets larger, the stresses at the elb w and weltents 6
s.
.83 . L e tocau.rmt' e, ; irregularitics were mur.h milder than typt a1 manual g . wite 5,me,aca racica -?;-
welds. Fabrication aliarrrent and mismatch toler. 8 ances and tho welds wore all kept within Code c,. ctsan mitt os ms c,e, I [. limits. Accordingly, tha ere stre n iniire'. tici
.m i d. ' , ;.r cpr i .
, . *,. , 3 e , m eir . i - a i .*
{ to tk f Wr ienion li >' . .c
' * '. " 's ' Cr ate to account for local stress concentrations and a,=fe, ron ca s sia g fatigue strength reduction factors. Thus, a local ef,> e. N . aq indice for the girth welds Lased on the Cede [13]
, t.*'srh::f N,f' ,' 2' was taken to be 1.8 in regnitude. Tte Ccde does o o m not have a f actor for radial weld shrinkage effects.
I , -i j \f,a l Discontinuity stresses of the type decicted in N
; Figure 16 and due to racial shrinkage in thirwall le f
% ' - i piping, were approxi ated by clastic analysis of a
,a
/ nu .ter of shell shrinkage distributions ar.d R/t j
w y :a ratics. Based on these fi,r.dir.gs and coce ir. dices
. / 'a ,-
fer girth welds, the ::: ciel ir. dices of Fi- re 17 j FIGUTtE 15. Relating Weld o and c to Elbow :lidsec. .ere adcated. These ir. dices were intended for use 5 tion c and c Cue to Mcment Loading, in predicting the mari u stresses and strains at welds in the pipe axial directicn because t6e K2
= 1.8 iccal f actor was censidered an axial f atigue i
TABLE 2. ELBOW fic"Et OESCRIPTIC:0 strength redacticn f a:te . An apprcpriate 5:2 he:p dirc:ticn was Y3 ejdtobe~1.1to1.2. l s
-s'_.T. T"2 t .2 .c a_
., w . ..
.= .. .W~1.*M,q
_.1.- -3._ y . :.C;C.
.,.7; ., N}'e relctive to the ;i;e/e'bc.:
l j i u.. u .i en . m - , j i n.. n u to . w u .. , ,,
. us..
. u .. ..
u en no. 2 u g ._., ,, , 1.T , g Qs e . ur u in ea a u g. .;y ; u n.m u n.. .. == = n , a e.m u er e as e a w 3; e, . 7 a y
..a_.. * ~ .i ,,
may beccre larger than at the elbow midsection. *I" Considerin; the limitations of Markl's test data, a
,8 , I g, ;tl4 max. n oemt scuet it was decided to also calculate stresses and strains at the elbow end weldments, in addition to " ' * " ' ' '
those at the elbow midsection fer the FFTF. FIGURE 16. Discontinuity Stress Due to Radial Detailed inelastic analysis of pipelines using Shrinkage in k' elds, the constant bending elbcw ele =ent (No.17 of the MARC finite ele ent computer program) [6, 9] do not To obtain approximate values of elbow and weld account for the secondary stresses due to f abrica. maximum stresses and strains for comparing tc the tion mismatch or radial shrinkage at the welds. In elbow midsection stresses, the method was as addition, peak stresses and strains due to weld sur. depicted in Figure 15. The 1/4 factor is based en , face irregularities, etc. are not directly included the 1/2 carrynver f actor and the maximum axial in the pipeline inelastic model. Accordingly, a stress of ~1/2 of the raximum hoop stress. Table 3 simplified method of evaluation was devised and con. shows corbined indices fer the various FFTF pipe ceptually described in Figure 15. sizes for both elbow cidsections and elbow end i weldments. Note that as the diameter gets larger, The simplified method consisted of using the the weld indices are larger than for the bend mid. pipeline system mcdel to predict inelastic response section. These indices were used with the elastic for primary and secondary stresses excluding f abri. flexibility analyses of the pipelines and are based cation mis 7atch and weld local effects. Stresses on shrinkage and mismatch data of Table 4 and strains at the elbcw end weld joints were then approxicated using the values ccr7puted for the elbcw To obtain stresses and strains at elbow end midsection cccbined with carryover and shrinkage weldments for use with the inelastic analysis cede factors. evaluation, a simplified methed was used. The hoca ar.d axial maxist:1 stress and strain values computed The carryover factors were determined from for the elbcw midsectier.s. using the inelastic pipe detailed shell finite ele ent, finite difference analysis, were first examined. The values at the analyses cf the FFTF elbcw designs, and f rom con. elbow end weldnents, eFClusive of weld shrinkage sideration of the experimental data [10,11,12] and configuration peak stress effects, were taken on ovality distributien such as shown in Fiqures as 1/2 of the nidsectic, values. The radial weld 14b and I":. Fcr the FFTF applications, a carry. shrinkage produces stell bending under axial mem-over f acter of 1/2 .vas found conservative. h. trare load. One arprcach is to acply the stress
! ever, higher f actors may te needed f or larger and ir. dices of Figure 17 as rultipliers with weld peak i thinner-aalled pipe elbcus. stress indices to the calculated effective stress and strain, exclusive of weld effects. That is:
Radial welds on FFTF to join the seamlru pipa and machined elb:ws were cane by an autnciatic wald-m ing machine. The weld reinforcement and surf acc welde o ff ' 1(7 0fK)g 2 y eff at elbow ridsection (3)
TABLE 5. pipit.G STRES5 RA*CE C0'JNDS 1 'O.".?i - Ia P t '+4xPBValun
+ Op Opnr T en Max I " ~T Cycles
~
L,.r e t n PQ Q 71 - 0
.. l e en . - . 4 345 843
. ..o ., d .7.7.'.D.'" Elbow I'idscc. 800 427 50 e4
.w,....m.-
566 35 240 843 4 " """ 9' ' Elbow Midsec. 1050 d i.'l*.'.'.'"d l 800 & 427 & 4 20 109
" Elbow tildsec.
' co .e c- , 1050 556
,$ ) ".M77ML 172 843 EE" ,,
Elbow Ends 800 427 25 1050 555 18 124 843 d *Uk .,, Elbow Er.ds I m.m.4... c. 109 I" ' * * ' ' " Elbow Ends 800 & 427 & 2 14 1000 566 FIG'JRE 23. Analysis Prcgram for Develesing Accept-ante Criteria fer Fabricatien-Induced 18 124 843 Surface Flaws. Straight Pipe 800 427 Straight Pipe 1050 566 14 97 843 Crack-Grewth Analysis Straight Pipe 800 & 427 & 2 14 109 In the design of FFTF piping, the range of pri-mary plus secondary stresses in pipe fittings such_ 1050 566 as elbows and tees, were limited to a value of 3 Sm as given in Table 5. Due to the radial shrink-age of the weld .ents joining the fittings to the .,
..e straight pipe sections, the welds also represent ,'~ .
location of increased stresses. Outside the fit-a*- .M tings on straight pipe section surf aces, the maxi- ' mum applied stress range _ is about half that of the .. - fitting (i.e., 1/2 3 Sm)- ,, _ Tre evaluation of the flaws were divided into " , ,- two stages; crack initiaticn and crack propagation. - Normally, a non-flawed smecth surf ace will require ,, _ many cycles of stressing before a small crack will - develcp. However, a notched er flawed surf ace can
- initiate a crack very early in the part life and , .
then the question shif ts to how f ast will the crack ,, _ grow. Figure 22 shows the threshold flaw size cal- " - culated for tre crack to grow under various applied n,. . u ,, stress ranges. For maximum allowable design .. . stresses the threshold sizes are given in Table 6. ,, The crack-growth fracture mechanics analyses ,a ' were accomplished conservatively assuming that the u, og , ;, ,;, ,e ,e .. surface flaw, which is normally not as sharp as a . . . , , crack, to be a crack. The determination of the applied stress intensity, :.K. was based on the l methods of Section XI of the ASME Boiler and Pres- FIGtRF 21. Typical Fatigue Strength Reduction sure Vessel Code. Other fctmula based on the work Factors Kg fcr Defil-Induced Flaw of Hsu and Liu [24] and Shah and Kobayashi [25] St. apes. were also employed for further insight. An example of the creep-fatigue and crack-Tte crack-grc.ith analyses indicate the growths growth analyses findings is given in Table 7 As l are fairly sensitive to stress level (see Ficure 23) shown in Table 7, the high-temperature elbow mid-but very little growth is expected below 8000F sections are located where such flaws may cause ( (4270C). See Figure 24 non-satisfaction of the creep-fatigue criteria, However, the high-te.iperature elbow ends and i The crack-grcwth rate and threshold stress straight pipe sections do have adecuate creep. l l Intensity data (see Figure 25 and 26) used were fatigue r.argins. When a drill-induced 0.010-inch based on work by Ja es [22, 23) . To account for (0.025-m) deep blemish, which is not as sharp as a long-time high-terperature eff ects, an environ ental crack, was asstried a crack. its growth was predicted rate acceleration factor (Figure 27) was cbtained at ~ 0.042 inches (0.10 ed for the high ter perature
% by extrapolation.
10
up to 10 mil deep may be tolcrated with no signif t-j cant adverse effccts on thri piping f atique integ-m - n ., rity, provided all operating vibratory inMed J - ' - ,l stres:cs are as les r ret 1 I a -
[;/
.. ,ig a,,,,)*
a, _ For operation below C030F (4270C), where creep effects are insignificant, the crack growth j, _ ie - j.t.,**6r u-- is slow and the ir.,a-cycle f atigue life for a given cyclic stres level is greatly increased. Thus,
, ta -mb" e low temperature (below E000F) piping flaws any-g "I"_ $p i a-a nn m . nu ss where on the piping, up to 10 mil in depth, could
_im % i e. . LD be tolerated. g ,,
, ______a__
_ i= . ir e j
?
~VTb l
, , J ,,
E,s
] -
A ;- l . , , , a n " e a a a se s w re .,. s m - smss ec. x a , .* . -
.. a *8 -
a .* . en - FIG'JRE 22. ~Nstimated Thresholds for Flaw Growth. I, TABLE 6. THIESHOLD FLAW SIZE FOR CRACK Gh0WTH ! ' e,>- .m.m
~
Stress,sa = 3 h, Stress, t.0 = 1/2 3 L , '" " "" Elbow Tee, etc. On Pipe Straigt.t Section .. _ . - (OF) (mil)* (mil)*
-ca. .
70 6 25 l 800 2.5 *, ,', : 10 ,, ,, . . .i - 1000 2.0 8 1,m . .-, 1200 5.0 18 ni.u m tin. ass-e -a,.... FIGURE 23. Crack-Growth Rate vs Stress for 10500F.
- 1 mil = 0.025 r:n elbw midsection. The other locations had very &?? 432 528 5 93 704 C small growth, < 0.001 inches. The wall thickness, 08 a 4 , 6 in this case, was ~3/8 inch (9.5 m). s,,e o The high-temperature crack-growth results are fairly uncertain due to the v;ry rapid change in ' ' , ~ l in
- 25.4 mm _
growth rate as the applied stress and effective stress intensity change (see Figures 25 and 26) and the cyclic time change. This time-dependent effect . is of ten referred to as a " frequency" or " hold-time" effect (see Figure 27). Thus, although the crack - " ~
% = 0 020 3a .
- 88 "'
extension for a 0.010-inch (0.025 m) crack-like '
. i flaw in a high-temperature high-stressed elbow mid- 3, section is calculated to be 0.042 inch (0.10 m), g it could actually be much larger or much smaller. 73 A 50% increase in stress level would increase the predicted crack growth to 0.13 inch (3.3 mm). A yu
w - ~ 50% increase in depth, 0.010 inch (0.025 cm) to 0.015 inch), (0.037 m) results in a predicted crack growth of 0.27 inch (6.9 m). ' ^ - ~ Above EC30F (4270C), creep effects can f greatly enhance the crack-growth rates and reduce the lm-cycle f atigue life. If the maximum allow- %,", 'J N" able code design stress is developed during opera-tion, a very sna11 flaw, as little as 2 to 4 mil o ( # . , deep, may gr:u during tte design cyclic life to " ) " " 'n "N 82 5 unacceptable levels. Thus, elbows, which do have , ,%, % local areas stressed to the Code limits, should have all surface flaws removed. In straight pipe ,qog m,,3ci.io r sections, tre operating stresses are usually less than half these in the elbows. Round bottom flaws [v] Figure 24. Crack Growth vs Te perature. 11
~
t o .; gye AuntAlf D tvet 3N 55 Tf 5f tD At 1 Corp,
/ - 330 < f 4 400 spi, o.oS < P
- o.So g
scATTie esno rog , j e . , ,, ,.,,p. t ut a[ At! *. '<5 m . q . O SPiciMLN 234, n . o.oS
,[ / e p' 10-5 ;
e urciugn 234, n . o.so ug,ec,n v - vacuw tr. i.s.t.lo.6 ,,,, f' gnyisonogy, '
/ / 4 - 0 5picwin 2c4, e - o ou
/ Sconvu
. s urciuto 214, e o.n) 7 */ {
_ c.5erciutn 2ss. e o.500 j tuviroNMENT c ' **cu'" I nn,osen ,,. vt,,>. e i . - J , s to. - l ! io-+ - evant a UICWEN 247, e o. c5 1 E O UPPt 880UND l g - 7 SPECwtN 267, e - 0.5n 2 - , SercWIN 271, t . C.oS a; LINE gyFO,R ANNE AtED g 3i,33 .* l , s - { f I
- suvaoNunni
- .: } h s I Semi. nua rea : a _
,/ _
l @ia '. Al4 ENVIRONMENT r Lg ANNIAtto !vre 304 u g Ig . O I 1 in 25.4 rnm 1l
~
I" ,o-' -
'l I
t"f CTIVE STFf55 INTENSITY FACTO *, K 11-e1 0 , It./tia.M 8 I l lI FIGURE 26. Fatigue-Crack Growth Behavior of Annealed 304 SS in Sodium Vaccuum Nitrogen, and Air Environ ent at 10000F. e oATA AT LOWER EFFECTIVE STst55~ INTENSITIES (Speciaea No. 92. im ' ' ' ' t e o.67, f 400 cpmi 3 \, ,-{ 5;cei . .i.o
! *' ' ' ' \
lo'8 I lo *3 10' y i= _ \ m.gou .o EFFECTIVE STRESS INTENSITY FACTOR, K, n t1
'3, Ib/(in.) y \
* .pe*s
=1 % 1mm .t.AL.fD.
.... mews 5.t.iMill 5f t EL .
HEDL 78c1-301.2 h se \ , U N' , , m ' a += = FIGURE 25. Upper Bound for Fatigue-Crack Propaga- 33 tion Behavior of Annealed 316 55 in an j Air Environment at 10000F for the Full w Range of Effective Stress Intensities. L 9
.viaire.."."I'.3 h 3
From the findings presented and from other ,, , , , , , , , , analyses and considerations, it was concluded that, -> w. w wa ..-i , .# ,g ,g ie in general, high-temperature straicht pipe will i m c.4sa ng "'C"'C"*"' tolerate drill holes and surf ace flaws on the order 8 8"
- 25 8 m" of 0.015-inch (0.037 m) deep. Low-temperature m mi-mi.
(below 8000F) large pipe and elbows will tolerate 0.025-inch (0.64-m) deep drill holes with no need for blending. FIGURE 27. Frequency Effects on Crack Growth for Stress Intensities Over 15000 lb/(in.)3/2 Based on the creep-f atigue and crack growth fractJre mechanics stress analyses, limits were 2) For high tegperature pipino with operat-developed that depend on whether the flaw is located ing temperatures above 8000F (427oC), on a piping fitting (such as an elbow) or on a
- straight section of piping, and on the intended a) Any surf ace defects of any percept-operating temperature. The acceptance criteria able depth in elbows or fittings, developed called for all of the following surface defects to be blended out: b) Any surf ace defects with sharp bot-toms of any perceptable depth in
- 1) For low temperature piping with operating pipe surfaces, temperatures 8000F (4270), or below c) Any smooth bottom defect over 0.010 a) Any surf aces def ects over 0.010 inch inch (0.025 rm) in depth in pipe (0.025 m) in depth, surfaces b) Any arc strikes o* weld splatter. d) Any arc strikes or weld splatter.
L 12 1
1ABLE 7. SU'?'ARY OF CREEP-FATIGUE AND CRACK-GROWlH evaluations. However, sirrplified analysis ruthods ANALYSIS RESULTS were needed and developed for weldment radial shrinkage and local surface stresses and strains. The use of K indices. as in clastic analvsis, seem
** t W tM onh pr.ictical day tu treat & .uc.
*f .
a,y
.m .t.2 t
e .U.,.
.o. ,..
i.,m . O..r..utrt._.:. Simplified analyses and clastic analyses pro-o .. == = .. .a u u ..we . ., vide significant insight for designing a pipeline em . . I" and they help provide valuable data useful fer corw paring with detailed inelastic analysis results, s w e.. n . . .a i. u n.we . . o.a Af ter adequate comparisoas of detailed inelastic si m u . ui n u ..we m .= analysis response for lines limited to P + Q 1 3 h , a ... m a we . n u - - . where the temperature hold-tir.e relaxation continues w.. u .: i u u - . monotonically unaffected by the themal transient, ii .v . m :. . .. in u e.- -- . the development of less consevative elastic analy-w.w .. .m a me . .m u - . sis rules should be atte steo by ASME Code bodies. Moreover, it is our excerien;e that by keepire tne m . n e c a . . m .. pipeline primry plus se:ondary stresses in the
~Z."#.*U t' L U.4M." ;'n".*J' " *" *' "*' "" * *" '" " '-'"*"'" range where shaxedown in crees occurs, the (i.e,
-..,.o .. .
P + Og 13 L) creep-f atigue life will be governed by the stress-ti: e history and very little usuage will be consu ed by the cycle fracticn related to the strain range. That is, the N/Nd fraction is small and the T/TD is designed so The depth of blend was also centrolled so that the that elastic followup is not significant and the residual wall thickness was adequate to neet pri- P + Q stress ranges are less than the elastic shake-mary and secondary stress limits. Defects greater down range. Then the creep damage will correspond than 0.025 inch (0.64 m) in depth were given case- to monotonic relaxation during the service life and by-case evaluation and repair treatment. be acceptably low. Of course, elbow end weld ent radial shrinkage, mismatch and configuration rust The 10-mil limit in the acceptance criteria be controlled or the weld will become design was a conservative limit chcsen with the recogni- controlling. tion that considerably larger flaws could be toler- r ated. But the field inspection technique was.too Scratches, dings, chisel marks, etc. inadver-crude to allow the limit to approach the maximum tently get imposed on piping and equipment while xalculated capability any closer. Moreover, most the plant is under construction. Accordingly, cen-of the flaw types experienced previously in con- sidering that such flaws can reduce the operational struction were less than 10 mil deep. Flaws greater fatigue capabilities, an acceptance criteria should than 10 mil, but not greater than 25 mil deep, are be developed for identifying what flaws can be tol-blended out. Flaws deeper than 25 mil are given erated and what flaws should be removed prior to special evaluatica and the appropriate action insulatir.g and placing the pipe into operation. determined on a case-by-case basis. For future designs, to orovide a sacrificial layer of material that could be blended off, it is recon-i High-temperature piping elbows should be free mended that 0.025-inch (0.64-m) allowance be { of defects as they are generally tne most vulnerable applied in the design like a corrosion allowance or i locations for effects of surf ace flaws on piping wall thickness tolerances. Moreover, more high tem-integrity. This is due to the uncertainty in the perature cycle f atigue and crack-growth data are time-dependent crack-growth rates, and the elbows desired in the ASME code to assess fabrication 1 are locations of maximum stresses, and there is indt In particu-potential f or vibration-induced high-cycle stresses. lar,,ced flaws and threshold vibratory t.K and da/dNstresses. crack-growth rates up i l As it is difficult to accurately predict system to 1200cf are desired. Smooth bar high-cycle l vibratory response, measurements and inspection for fatigue data to 109 c' .les are also desired. pipe vibratory motion have been taken and will continue during FFTF plant startup testing. This Significant advances in methods and technology
; will assure that the piping has sufficient margins forelevatedtemperaturepippingdesignhaveoccur-against high-cycle f atigue. red in recent years but irprovements are still ll expected and desired to reduce design costs and to enhance the reliability of the piping.
l ?I CONCLUSIONS AND RECOP?ENDATIONS l r Simplified rules and preliminary design limits ACKNOWLEDGEMENT ! developed for FFTF piping in 1974, based on expected behavior, engineering jude ent, approximate calcu- This paper is based en work performed at tha lations, and detailed inelastic analyses of three Hanf ord Engineering Develo:nent Laboratory (HEDL), pipelines have served very well. All designs based Richland, Washington operated by Westinghouse Han-i on these simplified rules and limits have been con- f ord Company, for the U.S. Department of Energy.
? fimed by detailed code and inelastic analyses. The author is grateful to the HEDL Plant Analysis j staff who carried out cany of tre analyses provid-Six additional FFTF pipelines have had detailed ing input to this paper. Special thanks go to l trelastic analyses and cmparisons to simplified M.J. Anderson, W.L. Chen, S.N. Huang, i
*- analysis finding have been performed. Accordingly, H.R. Lindquist, G. D. Sumers and E. O. Weiner, detailed system inelastic analyses of pipelines are l b)
( practical for primary and secondary stress / strain 13
' REFERENCES 13 A'NE Boiler and Pre..ure Vesse! Code, Section II'l: ttuclear Po<rer Plant Components, 1 Severud, L.K., " Simplified Methods and Division 1: Metal Components ASME, New York, NY,
" Application to Preliminiry Design of Pipirr; for 1971. -
t, a n. ' .t t*4 s El m t A i :".rctue. s . x Second National Congress en Pressure Vessels and 14 Mark 1, A.R.C., " Fatigue Tests cf Welding Piping, San Francisco, CA, June 23-27, 1975, / Elbows and Comparable Double-Mitre Bends," Trans. Advances in Design for Elevated Tercerature ASME, Vol. 69, 1947 p. 7. Environment, ASME, fiew York, t.f. 15 Mar kl, A.R.C., " Fatigue Tests of Piping 2 Sampson, R.C. and Jagels, R.E., " Stress Components," Trans. ASME, Vol. 74, 1952, p. 301. ,
' /
Analysis for the Desi5n of Liquid Metal Piping in the Fast Flux Test Facility," 75-PVP-21, Presented 16 Liebowitz, H., V2e?Wth, n., T T at the Joint ASME/CS"E Pressure Vessels and Piping Sanford, R., " Stress Concentrations Due to Sharp Conference, Montreal, Canada, June 25-30, 1978. Notches," Exoerimental Fechanics, Dec. 1967, pp. 513-517. 3 Pan, Y.S. and Jetter, R.I., "Inciastic Analysis of Pipelines in FFTF CLS Module " Pressure 17 Juvinall, R.C. Stress, Strain, a~: Vessel and Pipino Ccnference, Miami Beach. FL, Strencth, !'cGraw Hill, Stw icN, f.Y . 1H 7, June 24-28, 1974', Pressure 'tersels are Picing: pp. 265259. Analysis and Ccmouters, ASME,t;ew York, t,f. 18 AS"E Boiler and Pressure Vessel Ccde, 4 Chen, W.L. and Weiner, E.O., " Inelastic " Class 1 Case Interpreta m ns: Ccde Case .331-5 Analysis of Pipeline in FFTF Heat Trarisport System," Co por.ents in Elevated Terperature Service," and PVP-PB-028, Presented at the Joint ASME/CS"E Pres- " Class III Case Interpretations: Code Case 1592," sure Vessels and Piping Conference, Montreal, New York,tiY, 1971. Canada, June 25-30, 1978. 19 Maiya, P.S., " Effects of Notches on Crack 5 Huang, S.N., " Inelastic Analysis of Two Initiation in Low-Cycle Fatigue," Materials Science Pipelines in the Fast Flux Test Facility," PVP-36, and Engineering, Vol. 38, 1979, pp. 289-294 Presented at the Third U.S. National Ccngress on Pressure Vessels and Piping, San Francisco, CA, 20 Chow, J.G.Y. and 500, P., "Develepcent of i June 25-29, 1979. a Procedure for Estimating the High Cycle Fatigue Strength of Some High Te perature Structural 6 MARC-CDC, "Non-Linear Finite Element Alloys," Methods for Predictin; Material Life in Analysis Program, (User's Infcmation Manual)" Fatigue, ASME WAM, Dec. 2-7, 1979, New York, tit. j Ref. F. Control Data Corporation, Minneapolis, MN, 3 May 1974 21 Jaske, C.E. and O'Donnell, W.J., " Fatigue i Design Criteria for Pressure Vessel Alloys, ASME 3 7 Bree, J. " Elastic Plastic Behavior of Journal of Pressure Vessel Technoloay, Nov. T977.
, Thin Tubes Subjected to Internal Pressure and i Intermittent High-Heat Fluxes with Application to 22 James, L. A., " Fatigue-Crack Propagation Fast tiuclear Reactor Fuel Elements," Jcurnal of in Austenitic Stainless Steels," HEDL-SA 1051 Strain Analysis, Vol. 2, 1967, pp. 226-233. Atomic Eneroy Review, International Atomic Energy 6 8' 0'Donnell, W.J. and Porowski, J., " Upper Bounds for Accumulated Strains Due to Creep Rat- 23 James, L.A., " Frequency Effects in the cheting " Welding Research Council Bulletin No. Elevated Temperature Crack Growth Behavior of 195, June, 1974. Also, Transactions of the ASME Austenitic Stainless Steel - A Design Approach,"
Pressure Vessel. Piping ano Materiais Conference, 78-PVP-97, Presented at the Joint ASME/CSME Pres-Miami FL, June 24-28, 1974 sure Vessel and Piping Conference, Montreal, Canada, June 25-30, 1978. t 9 Hibbitt, H.D., "Specia! Structural Elements for Piping Analysis," Presented at 24 Hsu, T.M. and Liu A.F., " Stress l Intensity Factors f or Truncated Elliptical Cracks,"
; Pressure Vessels and Piping Conference, Miami FL.
June 24-28, 1974, Pressure Vessels and Pipino: Handout at the Seventh National Spposium on i Analysis and Computers, ASME, t.ew York, fiY. Fracture Mechanics, College Park, MD, August 27-29, 1973.
; 10 Pardue, P. and Vigness, I., " Properties of Thin-Walled Curved Tubes of Short-Bend Radius," 25 Shah, K.C. and Kobayashi, A.S., "On the i Trans. ASME, Vol. 73, 1951, pp. 77-87. Surf ace Flaw Problem," in The Surf ace Crack: Phy- ' sical Proble-s and Cocoutational Solutiens, ASME, 11 Gross, N. and Ford, H., "The Flexibility New York, t Y 1972, pp.19-124.
of Short-Radius Pipe Bends," Proceedings of the Institute of Mechanical Engineers, Series B, Vol.1 l 1952-1953, pp. 480-491. ! 12 Imamasa, J. and Uragami, K., "Experi-mental Study of Flexibility Factors and Stresses of Welding Elbows with End Eff ects," Proceedings of the Second International Conference on e'ressure i ( Vessel Technoloay, Part 1, San Antonio, TX, Oct. i 1-4, 1973, pp. 417 426. I 14
- r. Sg gob \ - SS IO L, 'I, ytterch me,d 3 c Ac.c. . e, %.o -
. 5 Pipina-Flexibility Analysis O V v Br A. R. C. MARKL.8 LOUISVILLE, KY.
A steadily expanding literature bears testimony to the individual problems, and assist in arriving at a final formulation growing recognition of the importance of the problem of assurmg uniform interpretation and intelhgent enforcement. providing flesibility in piping and to the many diiliculties At the same time, the author was invited to prepare a paper to besetting efTorts at establishing a simple rational approach explain the basic philosophy and scientific background underlying for its solution. This paper aims to outline the various the Proposed ilules. phases of the problem, with particular emphasis on the phenomena of plastic flow and fatigue which distinguish the behavior of piping systems under thermal expansion The objective of piping-flesibility analysis is to assure safety from the ordinary room-temperature steady-state strue. eainst failure of the piping material or anchor structure from tural problem and lead to the concept of a limiting-stress overstress, ngainst leakage at joints, and against overstrain of range rather than an allowable stress as the criterion of the connected equipment, without waste of material. While expan-adequacy of a layout. In treating his subject, the author sion joints of various types in some instances prove useful for this has sought to present the consensus of the Task Force on purpose, by far the more common and generally preferable prac-Flexibility charged uith reformulating Chapter 3 of Section tice is to provide for thermal expansion by utilizing the inherent 6 of the Code for Pressure Piping. Their Proposed Rules fleubility of the pipe run itself acting as a spring in bending or are included as a focal roint on which it is hoped broad torsion. discussion will center. Piping-flexibility analysis resolves itself into the following: 1 The calculation of the forces, moments, and stresses (and Irraont cTioN desirably also, displacements) at all significant locations in a tubu-lar structural frame under the influence of thermal expansion. IN Pressure the course of a ingeneral Piping, initiated 1951,aTask review and revision Forre on Flexibility: 2 Their ofcomparison the Code with allowable for limits. was appomted by ASA Sectional Committee B31.1 to study The frame can be in one or more planes. The number of and report on the adequacy of the current provisions of the redundants will vary with the number of branch lines or inter-chapter on " Expansion and Flesibility" included in Section 6 of mediate restraints (guides, bracca, and so on). For a space sys-the Code. Two subgroups 8 were formed, one to deal with tem, there will be six unknown reaction components (three forces stresses and their allowable limits, and the second to digest and tbree moments, or three forces and their lever arms) for each available information on physical properties entering into piping- anchor point in excess of one; intermediate restraints introduce flexibility analysis. a lesser number of unknowns. The former group, with the findings of which this paperis solely As compared with the parallel structural problem, the evalua-concerned, came to the conclusion that a complete reformulation tion of the reactions, stresses. and deformations in a piping system of this chapter was desirable to improve its clarity and, more under thermal expansion involves a number of additional con-importantly, to bring its clauses into accord with advanced siderations, of which the following are the most important: theoretical concepts, new research results, and accumulated 1 Piping components other than straight pipe, notably elbows experience. A working group
- was charged with the task of devising rules which would realize this objective and still be and hends, exhibit pecuhar stress-and-strain behavior under bending which generally redects itself in increased flexibility, readily understandable and easy to apply. A draft effecting a ,
satisfactory compromis,. between scientific truth and the sim- usuaHy accompanial by intensification of stresses. plicity so essential to any body of rules dertined for wide applica-2 Piping systems are not intended to behave elastically in their entirety. As a result of local creep (at high temperatures) tion was produced and accepted by the Sectional Committee. r I cal yickling (even at ordinary temperatur(s) relaxation anay Ilowever, since the Proposed Rules depart appreciably from take place whereby the re.tetions and stresses in the operstmg past practice in reveral respects, primarily by their open reengni-tion of the concept of stresa range, it w$ia thought desirable to condition are lowered and substantially equivalent rehetions and stresses are made to appear in the cold or ot!-stream condition. publish them first in nonmandatory form as a Task Force Report (121)6 to permit piping engineers at large to familiarize them- This process can be anticipated by cold springing. ,, selves with them, test their suitability by application to their 3 Owing to the cyche nature of the operation of all pipmg systems, fatigue becomes a factor requiring consideration, par. 8 Chief Itescarch Eng2neer. Tube Turns. ticularly where the fluid carried is corrosive to any degree.
' For membership, ace nource (121). Numbers in parentheses refer Tue CsENERAL PROCESS oF SoLtl TION to the Bibhography at the end of the paper.
- Under the chairmanship of II. C. E. %!cyer and R. 31ichel, re- In the flexibility analysis of any system of given line size, con-sp" ,* y f guration, and material, with a predetermined amplitude and
. W.8p elvnect as chairman, and N. lilair. II. V. Wallstrom.
number of temsn rature cycles, the following steps are involved: and the author as members. a The original fornmlation by Subtroup i is transcribed in Appendix 1 The significant physicaI propertire of tInc material, such as 1: alternate point claufes areviven mtrodu mced later in deference to a diuentma view-vparately Appen<hs .. E d M4 Nm's 6 } W Contribuicd by the Power Divinon and pre ented at a joint session stress, creep and relaxation stress, and endurance strength have L of the Power, Apphed Alechsnien. IIcat Transfer. 8afety. Aletals Ensi- to be determined. This paper will not concern itself with the
- neering, and Petrolcom Divbions. Joint ASTa!.A8itC ltcscarch
! Committee on IMeet of Temperature on the Propertin of hietals, and NoTr.: Statement = and opinions advanced in papers are to oc Research Committee un II:sh-Temperature 8tcam Generation, at Se understood an individual erprmion, of their authorn and not thn e Annual %fecting. New Ycrk N. Y.. November :mDecember 4 of the 8oriety. Nianuscrept rimved at ASNIE Ileadquarters. July 1953. of Tut Aurmc u .N..rn.rv or St ren u.cn Ehutsta.as. 27, 19!,3. Paper No. 53-A.51. V REPRINTED FROM ASME TRANSACTIONS,1955 M
t t Srst three constantz, for which the values and the Isis for their The inen ased tiesibility of curved tubular members resulta selection have been covered by a arparate per by the chairman from their flattening along one nr.the other axis under bending. of the second subgroup of the Task Force (120. The way in The flexibility factor k in common uae in this country wa. which the strength properties enter into the solution of the prob- devcheped by von Karman (:1)in 1911, from a first approximation lem under the Proposed Itules, on the other hand, will be dis- of an as<umed Fourier-series solution. It was redeveloped on a cuaned in detad at the appropriate point in this development. di6erent basis and experimentally checked by llovgaard (11) in 2 Aasumptions have to be nwie regarding the dimensions of 192ti It is usually given as i the piping, notably those aswiated with the cross section. For I simplicity, the Propmed fluhs disrertrd dimensional tolerances p , 1248 + 10 t and the uncertain and erratic changes in thickness caused by 12A' + 1' i corrosion or emsion and permit use of the nominal dimensions i throughout. where A = tR/r' is the so-called flexibility characteristic which 3 Conditions of end restraint have to be assessed. The Pro- depends on the pipe-wall thickness t, its mean radius r, and the posed Rules give no prescription in this respect, but general radius of curvature # of the center line of the pipe, practice is to take the ends as fully timiin the absence of detailni Originally this factor was used only for correcting the deflection analysis of the rotations and deflections of vessel shells, pump or of curved members bent in the plane of their curvature. This turbine casings, pipe anchors, or other structures to which the practice continued until Vigness (70),in 1942, demonstrated that line may be connected. Ilowever, equipment expansions must it applied equally to transverse or out-of-plane lwnding. be taken into account since they may cause increased forces, The first-approximation Karmsn-flove tani factor has been moments, or stresses. used generally for both twes of loading until Heskin (77), among 4 The significance of different forms of intermediate re- others pointed out the need forusing more terms in von Ktrm.in's straints has to be appraised. Major restrictions to free movement Fourier series for bend proportions where the characteristic A falls of the line due to guides, solid hangers, or braces are usually below 0.3. The following close approximation suggested in taken into account in calculations or other forms of analvsis. Beskin's development commends itself by its general validity
- Secondary restraints, such as unbalanced spring forces or 'fric- and startling simplicity tional forces at supports, usually are ignored; however, caution should be exercised in extending this practice to systems whose k . $, 2 g, A, . [2l g weight is great in relation to their stif! ness, a condition often encountered in pump or turbine leads because of manufacturers' This formula strictly applies only to the central portion of a limitations upon t hrusts. curved tube of relatively large are under bending, and does not 5 A method of analysis suitable to the importance of the consider the etTects of intern:d pressure or end restraints.
system must be selected. The solution enn be approached by The etTect of onlinarv steam pressures on the tiexibility of 6-in. analytical, graphical, chart, or model-test methods, or even by and 12-in. bends has been investigated by Wahl(12). Ife foitnd comparison with past successfullayouts, and may involve various the tendency toward restoration of the circular form to be of a degrees of approximation. Ilowever, for approximate solutions low order, and as a result it has become customary to neglect this an allowance for the probable errer should be included. etTect. This conclusion may need modification for thin-wall 6 Finally, a comparison of the results has to be made w,th i short-radius elbows of large diameter, + tilowable limits. These are clearly established in the Proposed With regard to end restraints, it is obvious that even straight Rules for the stresses, but left to the designer's judgment and tangents will tend to reduce ovalization of the curved pipe and consultation with manufacturers of equipment in the case of reac- therewith impair its flexibility. The restraining influence of end tions, because of the diversity in shape and design of connected tangentthas.been demonstrated by diameter measurements re-structures. gorted by the author (87) and more thoroughly explared hv page pm Pansue and Virnen en). Its etTect, however, was found to be It has been stated earlier that the calculation of the reactions . relatively minor for arcs ndeg or greater. For smaller arcs, the
~
reduction in flexibilitv would im e pected to be more pronounced, and stresses in a piping system is complicated by peculiarities of but since it is known' to be accompanied by a commensurate re-stress-and-strain distribution in certain piping components under duction in stress intensification, it is igncred in the interest of bending, one of the etTects of which is to endow such fittings with keeping calculations reasonably simple. (usually) greater tiexibility than would be predicted from the The effect of the attachment of stiff rings or flanges to the ordinary beam theory. ends of curved pipe, on the other hand, was found to be quite In calculations, this is commonly taken into account by the marked in .the tests conEcied 6y_Pardue3Q@ ness; .sav'h rpplication of a so-called flexibility factor. Thi= cm he defined- flange appeared to cancel the influence of approximately 30 deg' as the ratio of the rotation per unit lenttApf.1heprt in question of are of the licGl.'In the Proposed Rules [the$ d'aEhaife'lan'
~
produced by a~niMiFiif, to the rotation per unit _I,engthAn used to derive simple empirical-correction factors A% and A% straight pipe of~the same nominal size ~iDni"sCedule or weight- designed to reduce flexibility factors in the range below A = 1 to produced ETthe-same-momertt---ftTs~ajTdied either as a multi- j j plier of the length of the part, or as a divinor of its nominal mo I ,, 1 65 I ment of inertia (the moment af inertia of the matching pil w) or 4%" i of the elasticity modulus. Available information on its magni. l tude for ditTerent types of fittings will be discussed briefly in the g ,1.65 text following, h% g Carted Elboics or Rends. These are by far the most significant - group of piping components from the ktandpoint of providing
- The more genernity known femulam for the flanhility factor of increased flesibility. At the same time. they constitute the only
'"""I PEP' "'d'"d h'"V i" d 3 It mil be noted that bquation 12l rloselv sppruaimstes von ^"P""
K arm"an a third appromirnation group for which tiesibility factors have been dern.ed theoretically and hki propo*d formul. ne originally given in the ducummon of j and confirmed by an adequate amount of testing. Shipinan's paper (17). , i Ua i f I
- _ -~ v
lar interett in this connection. The stiffening effect of flanges
**, i j j, '
placed close to the ends of the bend is equally evident as in the i ' ' a _
' case of curved Imnits, but as the tangants are lengthened to 1 !
approximately two pipe diameters, the flexibility factor asymp-h M t t t cally approarlu-e Imr rent u that computed for a corre- { k f Mb6% p = i6%*. f epsmding curmi bcnd. In the absence of a theoretical development, the rearse availa-o y 3 l ble test data on mitre tends, including the results of unpublished
- ,o
*N .h r
- k%f 6%** ,
load 41Hlection tests secured in connection with fatigue testa re-l 3, . \l3 l ported by the author (Il1), have been evaluated conservatively o p j j in the Proposed llules as {3 , p C ; q p .
, 1 52 .[3]
s NM ! k=g. jg I
-2 I
I I l The characteristic h herein is as defined under Equation [1], 3 3. , except that an equivalent radius R. is used which is given as
. [3al R, = 2 cot a for s < r (1 + tan a).
a . . ~ . .
=- = 1 l -
reyes own .a o ca. e p.a,.a e --- I b - and a.m e ae e --- }
,s e ss e no a zo r
;;-(1 + cot a) for a ? r(1 + tan a) .[3b}
'oTas os ce a o < ;
R. = Re ithhty Chorocteristic h = y,, , where s is the mitre spacing at the center line, r is the pipe-wall s ' N l lll I radius, and a is one half the angle between adjacent mitre axes
,, c 8-.-h "
g ,
' ( r the angle detining the out-of-squareness of the mitre cut).
It should be noted that, for wide spacing, Equation [3hl, the mitre a s' j( s , k. Ji == 09Ch% ! bend is to be taken as consisting of a number of arcs with inter-
\ J iw 090Wt l g i" = 09%% j l
vemng tangents. 3 h K' o Corrupated Pipe. Straight or curved corrugated pipe and g l2 N7ta (N gg I creased bends are the only other shapes to which increased flexi. bility is assigned under the Proposed Itules. The limited test 1 [~'~* C " Q~ j
) ,
g data available on these types of components are summarized in a y( p,.' I j paper by Rossheim and 51arki (55) on the basis of which a uni-9 , g '7 t form tiexibility factor k = 5 is st.ggested as a first approximation. 8 N This should be used with caution, since the tiexibility of corru-
- o. 1 FLtxtsti.try Ano Srness-Isressiricarios factors FoR gated and creased pipe may be expected to vary with diameter, thickness, and bend radius of the pipe, and height, pitch, and con-nnect i nt. r a ermee. o g. a. tour of the corrugations. The effect of some of these variables (tm and an: rocce era arb. u e.er .a rs ofsvermae. of As tower poini .tna are. a. eiven in ratae.f A3s Na# o I E[u$"f'[r InllM[eIn*7 '.T.N.N[InNJeM"7e'Yy",$r*J$'l 12 an.: is at the am -rc Donnell (26) and IIetenyi (60). It alsohashas beenbeen demonstrated the found experi-mentally. Dennison (45), working with 6-in. standard-weight pipa. reports a value of 5 for the flexibility of creased bends and for 9041eg elbows flanced at one and both ends, respectively. between tu and 7.2 for that of corrugated tangents and bends, A comparison of the test data with Equations [21, (2al, and and tests reported Ly Itossheim and 51arkt gave values of 3J
[25]is given in the upper chart in Fig.1. It will be noted that and 2.0 for specially made 2-in. standa'd-weight corrugated Equations [2] and (241 are in satisfactory accord wich the results tangents and bends. of thcee specific tests, while EquaGon (2bl overestimates the flexi- OtArr Components Forged or fabricated tecs or screwed or bility factor for low values of A. A study of the lower chart flanged connections comprise some of the components which leads to similar observations with respect to the corresponding may exhibit increased or decreased flexibility as compared with streeintensification factors, which are obtained by the applica- straight pipe, depending upon their individual dimensions and tion of the stme correction f.tetors. In view of the limitation of contours. 13ccause of the lack of a sound basis for even a crute tvailable test data to a single pipe size, bend radius, and flange empirical formulation, the Proposed Rules assign unit t!exibility type, attempts at a more refined correlation appear unwarranted to all such parts; the error incurred by sa doiag uill never become ct the present time. The corrections are to be regardad as no critical since such littings usually constitute only a small part of more than first crude approximations, detiensible on the basis theline. that inaccuracies in evalu stion of both tiexibility and stress- It may be worth while to draw attention to the fact that the intensification factors tend to cancel cach other, at least with re- Proposed Ituh s do not make it mandatory to use the specific speet to stree calculations. flexibility (and stree-intenstication) factors given therein for Mitre Bends. On the basis of isolated test data and service any of the piping components. This represents a tacit admission . l experience, these piping components are known to possess in- of the tent stive nature of the evaluation of existing data made by creased flexibility appratching that of curved bends, particularly the Task Force, and points up the desirability of a more thorough where both mitre spacing and mitre angle are small so that the theoretical and experimental exploration of the tield. mitre be'nd comes to resemble a curved elbow. In-plane bending leet datit on 4-mitre spaarter-bends with tangents of various " I 'engths fullowed by !!anges at each end, on which Zeno reports In discussing stress intensification factors for piping compo-(m in o discussion of Pardue and Vigness' pap r w'J), are of particu-s ! 421
\/ ,
t 2 1 . l . 4
4
-t t
nenta, it is necemry to distinguish between formulas or valurs de- I rived from theory or static strain-gage tests anil such <>btained creek Iccation and direction obtruded themselves ulum tha fmm full-scale fatigue te ts. author's obscrystion. It seemed as if all these fittings c..n. - The primary ihtference between formni to some extent to the behavior of curved cibows or bcnd. them lies in the tunt of reference. Theory refers to an ideal This Icd the author to suggest a common empirical expreW..n g homogen.sius notch. free material, while the results of fatigue for the stress-intensification factor (Ill) which is + tests of commercial preslucts preferably are related to parallel ' results on commercial pipe joined by butt welding, which itself g.N.>g, contains stress raiacrs in the form of surfare imperfections. This A,% - , [74 change in reference point, andTwissibly also the redistribution where and attendant relief of peak stree occurring under cyclic hul-ing, accounts for the obsers ation that stress-intensification factors h, - <- (tA/r8) = caective ficxibility charaetcristic (dimen. - ! aionles4 ! derivnt from fatigue tests are cenerally lower than those pn-dictnl by theory or measured in strain-gage tests. c = (t,/tju = scetion-modulus correction factor (dimension-3,,,) Since pipe in the primary constituent of piping systems and { service failures of piping are almost always assnciated with the - I wherever fitting has same thickness as matching pipe I f, = eHective fitting thickness,in. j effects of cyclic loading (generally aggravated by corrosive
= average of crotch and sile-wall thickness, for wchling -
influences) the stress-intensitication factnr will be defined here tees
- as the ratio of the bending moment producing fatigue failure in a I
= pipe-wall thickness inemased by one-half excess thickness
, given number of eveles in a straight pipe of nominal dimensions, to that pmducing failure in the aame number of cycles in the part provided in either run or branch, by use of thicker piping
- tender consi leration. or pad or nldle, for reinforced fabricated intersections This definition implies that the curves of failure stress versus - i for webling cibows, curved or mitre bends, or unrein.
number of cycles to failure parallel cach other for straight pipe forced fabricated intersections of a thickness equal to that of matching pipe and other piping components. While this is not strictly true, test t = thickness of matching pipe,in. i data conform reasonably well to a law expressed by r - mean radius of matching pipe, in. s ' iSXL 8 - C. . .
. [4 }
R, - effective bend radius, in. l where idesignates the stress-intensification factor, S the nominal = R = radius to center line of curvature for elbows or smooth bends endurance strength (cyclic moment' applied at point of failure !
= r + r, for welding tees,'where r, designates crotch radim i divided by section modulus of matching pipe, rather than titting), = r for sing!c-mitre hends and unreinforced and reinforced i N the number of stress reversals to failure, and C a materials fabricated 90-deg branch intersections constant. j ,
s r t { From Rossheim and the author's tests (55), later confirmed by 5 i cot a; f -(1 + c t a)f rmultiple mitre bends,where
' tests run by the author's preaent company (114), a value C =
245,000 nas established as suitable for Grade B carbon steel at s designates mitre spacing at center !!=c, in., and a j room temperature. From additional unpublished test data in designates one-half angle between adjacent mitre axes, < deg the author's company's files, a tentative value C = 281,000 was < deduced for stainless steel, type 316, at room temperature. The condensed information given in the Proposed Rules is t Finally, Stewart and Schreitz's tests (116) suggested a value C directly derived from reference (114). The correction factors
= 183.500 for stainless steel, type 347, at 1050 F. l AWandh% proposed to account for the effect of end flanges on '
In view of the all too common misconception that fatigue is the stress-intensification factor for curved or mitre bends have i I always afariated with a large number of loading cycles, it appears been discussnl already under the heading Flexibility Factor. pertinent to point out that the author has found Equation [4 l to Note that the higher of the stress intensifications for the flanged
- be as valid for the determination of stress-intensification factors elbow and the flange itself must be used. l at 20 as at 2,000,000 cycles. The author has observed no evi. Corrugated Pipe. This type pipe and corrugated or creased i dence of leveling off of the S-X curve at either end, except in the bends have been assigned a etress-intensification factor of 2.5 in case of straight pipe which to some extent tends to follow the the Proposed Rules. This substantially follows the recommenda- {
l trend of polished-bar tests. The endurance limit of commercial tion given by Rossheim and Marki(55)in a paper evaluating the ; piping compe,nents is not reached as soon as in the case of polished information availdsle up to the year 1939; the value selected is i bars. The thought suggests itself that possibly the number of that for "noneyclic" service since correction for definitely cyche ' cycles defining the knee in the S-N curve is the higher, the higher service is etTected under the Propoel Rules by the application of the stress-intensification factor, a stress-reduction factor. Considering the important influence The foregoing gives the general approach used in setting stress. of the diameter-to-thickness ratio of the pipe, as also the shape, r intensification factors. In the following the detailed sources thickness variation, height, and pitch of the corrugations of any 3 are given from which the values of i published in the Prnponni specific manufactured product of this type, the assignment of a , Rules are taken. At the same time, isolated additional test data constant stress-intensification factor obviously represents a gross' ! are adduced from the fatigue-test files of the author's company oversimplification. A more thorough theoretical and experi-
- to round out the picture. mental exploration of this type of construction appears urgently Pitting for hirectional Changre. These can be treated as a needed, if it is to be used in severe services.
group becauge of the'ir striking similarities in behavior under bend. Bolted Flanged Connections. These present a dual problem ing fatigue. In the course of evaluating and correlating fatigue from the standpoint of pipingdicxibility analysii It is necessary testa on mitre bends, forged and fabricated tees, similarities in not only to guard against ultimate failure by rupture but n!*
' Where the strew smplitude applied in the testa exceeded the yield against disablement of the joint through leakage across the strenath in tendinir. a fictition* moment bnaed on a straight.hne ex.
tension of the clutic moment-derlection curve was computed to con- e For welding teca conforming to ASA Standard Hin.9. amurnpri.m form with naual calculation practice. of R. - 1.35 r and i. = 1.m e u*us!!v wd! produce conservative esti-mates of i on the basis of represer.tative measurements. f .
- D ,
. - _ . , _ _ _ , . . -%,.... _._-m _
?
gasket. The values of the stren+ intensification factors r.hown in stress in its hot or operating condition, and will not undergo the Propoel Rulen are taken from a paprr by .\!arkt and George inelastic acti.m leading to relaxation, the consideration of which (97) and nerve to predict ultimate rupture in joints bolted to will be dincussni in another section of this paper. b about 40,000 pai strean. With lower bolt strem+s there is the The evaluation of the forces, moments. and strenses existing in I possibility of premature leakage. Alti ough there are no pub- the initial premtresmi cold condition evidently reduces to the I lished data on the subject, the authm judges from isolated test analysis of a tubular-frame structure under the influence of given j runs conducted by his comp my that frmiom from leakage can end and intermnliato lieplacements and rotations. This is a ! be aneurnt by application of a factor i of the order of 1.5 regard- standant structural problem, but for the need of correcting the [ less of the type of tlange, except in the active creep range where deflection and computnl stresses of certain members by the appli- . periodical rctightening may become necennry. cation of the llexibility and stress-intensification factors dis. I Pipe Joinh. These joints when made by butt welding form cusanl in the text preceding. the basis for comparison for all other fittings, and hence take a The initial cold reaction' R at the line terminals and the con. factor of 1. Fillet-welded and screwed joints are assigned the trolling stress #s in the line for 100 per cent cold spring are given t same values as single-fillet-welde! and screwed flanges, since the by the~ following generalized expressions i failure of a tlar. red connection of a ductile material usually occurs in the attachment to the pipe. g ,,gy 7, E ,= FS,. sF, S [6al e Tapered Transitions. Components such as are used for con- ! necting pipe of different wall thicknesses or fer the hub ends of j flanges or valves can be given the following approximate stress- S,=cEJ ' . .[Gbj intensification factors on the basis of isolated unpublishmi tests Z. ' run by the author's company: where e is the unit expansion from installation temperature to 15-deg taper, i = 1.1 maximum operating temperature upon which the amount of cold 30-deg taper, i = 1.2 spring was based; E,is Young's modulus at the installation tem-4kleg taper, i = 1.3 perature; I and Z are, respectively, the moment of inertia and section modulus of the pipe; iis the stres+ intensification factor Only the small end of the hub need be considered in such an at the controlling point: F, and F, are shape factors expressing analysis, smce possible higher stress intensifications at the large the over-all erTect of line configuration and axial dimensions, end, of course, are compensated by the relatively lower stress including flexibility factors; and F is a composite factor relating level corresponding to the increased thickness (which also ex- the reaction to the controlling stress. plains why ASA welding neck flanges always fail at the attach- While general solutions of this problem have long been availa-ment end, never at the root of the hub). Incidentally,it will be ble, their application to piping-flexibility analysis has been noted that the factor of 1.3 for a 4bleg taper is the same as for a restricted because of the specialized knowledge and formidable fillet weld, the two representing the same geometrical shape expenditure of time required to carry out a calculation. Eoua. OtAcr Components. Components such as reducing elbows and tions [6a] and [66] are deceptively simple, but the shape'faciors tees, box-type httings, anchor structures, and the like, in the F, and F., appearing therein. in themselves generally represent absence of directly applicable data must be evaluated by analogy extremely complex mathematical expressions. To reduce their with fittings for which factors are available. computation to practical limits, some of the foremost piping-It already has been pointed out that neither the flexibility nor stress analysts have exlwnded considerable erfort and ingenuity the stress factors given in the Proposed Rules are made manda- in devising simplifications consisting either of preorganization of tory. While the formulas and values given are based on the best parts of the solution without affecting accuracy, or of making available information, they are by no means to be taken as sci- approximations of greater or leser validity. entific fact. The prime purposes served by their publication are Among devices of the first kind appliNi primarily to strictly to call attention to the existence of such stress mtensifications, t ma:hematical solutions, the following are the most importants' provide standardized asumptionsin place of complete chaos and, finally, to stimulate further research by all connected with the 1 Preintegration of recurring shape coefficients (17). piping industry. 2 Introduction of virtual center of gravity or elastic center (38). PRIMARr Amysis 3 Introduction of conjugate axes (41). For the purposes of a brief study of available methods of analy. 4 Application of principle of cyclic permutation of co-ordi-sis of piping systems under thermal expansion, !ct it be assumed natesu to reduce multiplane problem to single-pl2ne problem (61). that the system be installed with 100 per cent cold spring, i.e., 5 Exploitation of symmetry of simultaneous equations to that members be cut short by the full amount of their anticipated reduce number of operations required (61). expansion and then pulled into line, Fig. 2. I.et it be assumed 6 Application of matrix method to provide ch arer visualiza-further that the pmportional limit of the material should not be tion of components entering into the problem (117). eteceded at any point during this initial prestressing. It follows . l'or clarity the developments in thin and the following section from thew asumptions that the sy stem will be free of expansion refer to a ningle end force which is all that i4 needed in the case of a single-plsne bend with two hinged ends. The drainition of R can be L , expanded to relate to the a(n - i) rorce comimnents and a0. - ti e moment comimnents created by col.1 *pringma or thermal expansion f
'**P* Y" " h m-- -.
Rg the conclu.,'mn* derived." points of timation without loss of validity of w The ,. cope of tbc paper permits no more than a brief enumeration
+eL-., of various naproaches. To enable interc-ted rendern to ac<piaint themselves wit h them. paienthetical references are riven to the better-known sources emplovis.g ttwm without however. smplying that they are neemanly the urional proponents.
[ u First application of this concept is credited to G. W. Watts and Fro. 2 Srstru Ct r 8aont ron Coudeninosso W. It. Ilurrows. 423
+d Among apprmimate assumptions lea. ling to a variable degree two companice (1211. Once the oprations are coded prop:rly, 1 ~
of arcuracy, the following are probably the mont common: which is a time-consuming task for experts in this field, th., ! 1 Sub lisi* ion of line m. to short elements, the man of which is machines are capable of solving any problem of the same typn concentrated at their mi<!-points Gl h if the c!cments selected and thus serve to exp:md gn atly the number of systems which I can be calculated within a given time. -) are short enough, this method is practically precise. 2 Substitution of square corners for curved members; this 81 ELF-8PRING AND COLD-8PRINo ErrEers ,) widely usrd approximation iem>res the mercased dexibihty of ' In order to focus the reader's attention on " methods" of an dv-elbows and le+1s to an overe timate of reactions and either an sin, the problem of c dculating forces, moments. and streses in ' over or underestimate of the strews depending upon whether the foregoing has been refun*1 to a familiar structural problem the stress-intensification factors are conaidered or ignored. by imposing speci:d con <htinns. In what follows, the scope of the 3 Corn ction of leveloped squan -corner lent:th of system by investigation will be bro:ulenn! to embrace all conceivable n.n-addition of a virtu:d length reprewnting the excess !!cxibility of ditions of installations and temperature or stress which might all the elbows (10.5); in effect, this distributes the excess elbow be encounterni in actu:d practice. i flexibility uniformly over the entire system. The accuracy of the Let it be assumni that a sptem te installed cut short an arbi-
- results is considerably improvnl as compared with the foregoing trary :unount, so that a gap crL is left between the end of tho approach. line and one terminal. This proble n is identical with that show n 4 Concentration of the excess flexibility of each elbow m. a in Fig. 2 and is solved in general terms by Equations (Gaj and Mhl, except for the intrmluction of the so-called cold-spring factor single point located this modification at the intersection or the square-corner ofsomewhat solution is ity tu;o tangents more (120); e a hich ranges from zero (for no cold spring) to unity (for 10 complex and more accurate. cent cold spring). Equations (Ga] and [66) are based on c = 1.
Obviously, both the initial cold reaction and the initial cohl 5 Introduction of two or more weighted points for cach stress for the more general case will differ from those given by elbow; this further refinement of the square. corner solu- these equations by a factor c. Actually, since reaction and stres* tion leads to almost precise results with proper selection of the are interrelated by a factor F, which is constaat for any line of weights assigned to the points. given shape and dimensions, a study of the behavior of the system 6 Assumption that neutral axis parallels line connecting can be restricted to a study of the controlling stresses created anchors (20); this produces precise results for symmetrical ttunhi by changing temperature conditions. The mitial cold cases, but the accuracy very rapidly diminishes as the shape de- stes is t parts from symmetry or becomes antisymmetrical. sj _ cs,. . . [7;
,7 Assumption that neutral axis connects the anchors directly; this, m effect. assumes a hmged system, and may lead to major As the line is brought up to temperature this stress decreases.
error where the ends are rigidly anchorni. becoming zero when the line has expanded by the amount ce per unit length. Upon further exoansion by the amount (1 -c)e re-
~
- f. 8 Assumption that hending and torsional rigidity are identi- .maining to give a total of e, a stress of r'eversed sign"is produced 1m cal (30); taking the shear mo fulus equal to one half the ehtsticity (initial hot stress)
(" modulus in tension simplifies the solution of space probicms with-out leading to excessive error. l gj , (g _ ,) En3, , ,[gy 9 Assumption that the stress-intensification factors are fe identical for m-plane and out-of-plane bending (II4); use of the )* higher of the two for either condition lemis to a conservative m . is ungs m u us at hot or maximum opera % error not in excess of 20 per cent for elbows and common full-size temperature. In the absence of-v. ic iding or creep in either the cold or hot intersect. ions. The suggested stressin. tensification factors tabu-lated m. the Propmed Rules utih.ze this assumption. condition, the controlling stress thereafter will alternate between the two h.mits given by E.quations [7] and (81 during successive In addition to purely mathematical approaches (to which the cycles of cooling down and heating up. This is generally true preceding text primarily refers), there are graphoanalytical of snoderately stressni lines operating at temperatures at which methods (7ti) of equal range of accuracy, in which the momenta the metal is not subject to ercep, and also of lines operating at are built up from one enil to the other with the aid of precaleu- elevated temperatures which have been cobi sprung sutliciently lated solutions for cach element of theline. Furthermore, a num. to keep the initial hot stress below the creep limit. i ber of chart solutions have been published which represent more Where these conditions are not met, initially high streers, or less complete precalculations of entire systems of unit stiffness particularly in the hot condition. will relax with time until they and displaecment (33,37,10 >); the latter obviously are restricted reach a level which can be maintainni indefinitely; this phe-
,to simple confieurations. nomenon is illustrated by the recordirgs traced in Fig. 3 which While many metho.ls are theoretically suitable for application are taken from laimratory tests of a small-scale expansion loop to systems with any number of terminal and intermediate re- which was alternately heated to approximately 950 F and allowed straints, the computation work increws rapidly with the num- to cool to atmospheric temperature. It will be noted that the ber of redundants. For this reason mathematical and semi- controlling hot stress (and therewith also the hot reaction) mathematical methods rarely have been applini to systems with dropped off to a constant level after the first few cycles; the line more than three points of tixation. To supply t.' c nent for a has sprung itwif, whence the de..ignation "wlf-*pring." If the means of evaluating the flexibility of lines with many branches or asymptotic value toward which the hot stress tends be desig-intermediate restraints, such as guiiles or wind braces, model- nated as S,, then the ultimate hot stress after adjustment be-testing methods have been deviel wherein the reactions causni enmes by given end displacements are measured bv cit her sprines (52, M, ,
sf . 3, , .[9] tio) or electric stram gages (78). Of late, memory-cndowed clee- , tronie or other computing devices have been utilized by at least " All expreanions are shown as absolute vaines. - 404 i
r 31 {g' p.i.. .t.t. I' 5 l l i) { ] te.. Q
= ! :'
I. 's
]g{ ,No cold sprjng h a
%n et operahng icooHe$ of oseroting coci w atco. cot'ng coodPeat temperotwe ide we temperature W wol temperatur. , coq up Q Se gg l ; tomi ian.d . tat. ! j
.- i 6 2L /_ 1 Ff 1 !/7 -&
g .s.7/
= -
} l y50% cold sqryng j Fso. 3 l'rrEc7 or RetuATroN UeON IttMCTloNa AND STREM*ES Upon cooling down, each unit length of the line contracts As one limit, applicable to lines of small temperature change, again by an amount e, the stress reverses, ami the ultimate cohl set E. - Eg then stress becomn gj 4 g,, , gs, , ,ggg,y S*' + S.' - S, . .[12a]
3,' = S, E*E' S, .
.[10]
As a second approximate limit, for hot lines where the relaxa-tion limit S,is small, set E. = %E,; then The preceding four equations fully circumscribe the extreme stress conditions enc 9untemi during the service life of a sys. tem, gj 4 g,, ,2 + c S,.. ..[116] whether it be installed with cold spring or not, and whether it be 3 subject to relaxation or not. Now, as Stromeyer (ti) pointed out in 1914, and Dennisim (45) S,' + S.* - S, - f S,. .[12b] re-emphasized more recently, service failures are associated with cyclic, rather than static-stress spplication. Fatigur, with cor- Note that at one limit the stress range equals S,; i.e., is constant rosion usually an important coatributory factor, must he ac- and independent of the anmunt of cold opring, and that at the cepted as the primary cause of failurc. Itesistance to fatigue is other it is lower than S and atTeeted only to a minor extent by measured by the so-called endurance limit (fully reversed stress the values of c and 4 surported over an indefinite number of cycles, in the millions) h de following four equations the corresponding reactions or by the endurance strength (stress supported over a given are given as obtained by multiplying the right-hand terms of number of cycles), the latter being of more direct significance t Equations 17] to [10j by R/6, the present problem, since even in the process mdustrws the num-ber of major temperature cycles rarely exceeds six per day, R/ = cR. .[13] corresponding to approximately 40.000 over a 20.yr life. Actu-ally, the stresses usually are not fully reversed in actual piping installations, but since the mean stress is inileterminate, particu. R/=(1-c)b',R. E
.[14]
larly where relaxation occurs, and of subordinate importance to the stress range, the latter is taken as the sole criterion in the R.* = #3, 8 R. [15] Proposed Ruh a. For. simplicity, these cet the value of the *
" calculated-stress range" equal to the stress S, pnxtured by 100 / E, S, }
per cent cold spring; that this is a reasonably correct or at R ' " (I E. S, / least conservative assumption will be shown in the text that follow s. Detailed discussion of the relaxation limit 4 has been deferr d ~ For the initial condition (which is maintained throughout to this point because, under the Pngmed Itulei, it is considered where no adjustment occurs), the stren range is given by the to affect only the computation of reactions. With the establish-summation of the stresses given by Equations [7] and [8] ment of the approximate stnwa range S, as the primary criterion of the flexibility of the piping system proper, individual stresses g, at any one time during the temperature cycle have come to be S/ + S.' = g' S, + 1 cS,. . [11 l ignomh in the case of the reactions. on the other hand, the E, E, extreme values in the hot and cold conditions are taken to control directly; the reamn is that strain- ensitive equipment, such as For the ultimate condition in the case where relaxation does ir Nrbim m he miely dawd liy ninhM4 occur,it is given by the summation of Equations [9] and l101 even though thia may be promptly relaxed as a result of yiel.hng or creep nomcw here in the aptem.
'\ S,. The relaxation limit S, can be defined as the asymptotic value S,* + S ' - S, + \1 .[12] toward which the stress m a prestressed structure with a hxed t i E./ %.)
425
U I distance between ita terminals tends as the material flown as a Ar.tAWAU.3 STRras Rancs 1 a result of yiel. ling or creep. It is not gwihle to a+ign an accurate value to this proiwrty, at lea.st under bending (the predominant It has been suggested earlier that S, = 1.6 S. representa a ' type of loading introdum! by thermal cipan ion) w here higher conservative estimate of the stress at which flow starta un ler a I stnsees are necepary to pm hace flow than under tension (the bending moment at elevated temperature. By the same token type of loading for which mo t of the yacid and creep data have S, = 1.6 S., where S, is the S-value at the minimum or (umallv$ installation temperature, might be taken to express a suitahl . been developed). Ilowever, it appears conservative for the pres-ent purposes to sat sta value e< pad to the leser of the tensile condition for flow at the minimum temperature. The sum of . these two limiting strenes or yield strength an t 160 per cent of the strms prmlucing 0.01 per { cent creep in 1000 hr at the given temp rature; this corresponds S.. = 1.6 (S, + S.) . *
.[19l to S, = 1.6 S., where S. is the allowable S-value at operating metal temperature. The
- election of S-values in the Power then could be considered the maximum strens range S. to which Piping Sectionu is based on the ru!o given under Table P-7 of {yst m e uld be subjected without producing tiow at either Section I of the ASME Boiler Construction Code, which states =
that the S-value equals the lesser of 25 per cent of the tensile in:the Proposed Rules, the allowable range of the expansion strength,62% per cent of the yield strencth,100 per cent of the stresses by themselves has been established tentatively as fol. , stress producing 0.01 per cent creep in 1000 hr, and 60 per cent . of the average or 80 per cent of the minimum stress producing Ss = f (1.25S, + 0.50s.) . .[20l rupturein 100.000 hr. Actually, the Proposed Rules rest on a much more conservative IIerein fis a stress-range reduction factor fer cyclic conditions, basis; in effect, they assume S, - S fn addition they credit varying from/ = 1 for X < 7000 cycles, tof = 0.5 forN2 250M cycles, as shown in Fig. 5 The variation mughly follows the law only two thirds of the designed cold spring in the computation of the initial hot reaction, while requiring the use of the full fX = 6. .
.[21[ .
amount of the cold spring in computing the corresponding cold reaction. The ultimate hot reaction is, of course, ignored since j it is never greater than the imtial hot reaction. This leads to the l i 2 3 6 12 24 cycles perday following equations: . for 2 Wide 3 1 Extreme hot reaction, paralleling Equation [14] 39 8-u. { t R,=(1S)E,R. 3 c .f17l 8A I I g - l' . . 2 Extreme cold reaction, greater of values given by Equations j.7 j [13l and [16] after substituting S, - S., with the further proviso g- l { tR ' b'
- _ 05 , I l,
1em! u nber V t l of cycles N diJ e .5 wg - - --= h s e, . 5
- =
10*- 2 5 10 5 2 5 ; E Ni u, y-g o N e. g Fro.5 PLOT or ETaEWREDUcTfoN Facron Courrixto sw *
". 4, ra Paoeosto RULES '
E Y
% N 2 2 N a:" l n- N which parallels the correlation of fatigue-test data on piping com-
,n
$ 0% 2p \
M g Wcow spong ponents suggested by the author (87) in 19 86: see also Equation
,g. l g 7 $
[e [41. The motive for selecting 7000 cycles as the starting point for au - 2 ! $ g the application of the factorf was to free the calculation of every. E j g 2 day systems from this added complication: 7000 cycles roughly i g I conform to a cycle per dsy over a period of 20 years, which is more than most systems are subjected to. I l l To obtain the maximum combined-stress range, the allowance Fro. 4 Ret.rtrox or Rmacrious Cosert rso av Paoeono Rev.Es Sir = 0.75 S. net aside in the Propwd Itule< for pressure and m Turnarricu. Rr scTroms ' weight streues has to be addni to the allowable expansion-stress range given by Equation [20): this is done here on the that (S /S,)(E,fE ) not be taken greater than unity (reaction assumpti n that f is unity, which covers the usual range of otherwise would obtain same sign as R. which always is higher) " " * """ a E, S. EA + O Pr = 1.25 (S, + S.). .[22l R, = cR or (1 E. Ss R. .(18) By comparison with Dptation [191, it will be noted that the Fig. 4 gives a qualitative comparimn of the n actions computed I"P "I N"k' " "Ti" "'ili'" ** *"st 78 per cent of the by the Propoed Rules (hesvy solid lines) and the corremon line ""*il"hI" "l'"*" '*""" S.,""leduml m. the opening paragraph of theoretical values; the dash lines indicate the maenitude of the this acetion: however, schetion of a proper value for the reactions in the alwnee of r"laxatian, while the dash-dot lineg I*"'"'"n the n,ght Me of the wiuation is open for discussion and
'"'I"**
illustrate the mo.tification of the latter as a result of relaxation. ! An estiplate of the aver. age efety factor ag:dnet ruptureinher-is The author would prefer basina the espansion stresses for all ent in de WopM Rnles in the range betwen 7000 and 2.MW servicce on the S-values in this section, cycles is derived in Table I from the limited experimental data r f l b 426 t I r l t i l I
- Se etWip-eme* =usse - ..w-e-
__ + _- _ __ _ _ _ __
--7.,_ _
I TABLE t I'.STtSI ATI: OF FAFETY FACTOR FOR A LIFE OF 7tD3 CYCI.ES Carhan eteel 24t4enleen steel hteterial.. . Uraile 16 Tyce 3 tti Tyce 387 G rade. . . . . . . . . . . . Itonin nuo V Conesant te=t t meerature.. Hoom Testa conducteal t,y. . . Auttanr's A uthori (*o. Stewart snel coencany 47) (unceable l'c i) Nebreet 4 I ten 21,0u0 Ostouo IE.no
' Factor C in forenula 3XA8 = C. . . . . . . . .....
Averase stre== ranea N e' = 28'J<wup ' ta crednee fl?47o failure nn.l r revermt heniline in hun 8 cycle s. . KI400 95660 Section of Cosle for l'resimre l'esna. I'u er Oil oit Od or
$ apant piping piping power Allowable strc== 8, = #n tai at eiven temce-rsture 13 00 under sven necamn of Cuile for Preaure l'irana. . . 15000 20000 18750 Allowable *tren rance 8 e + .srir = 1.2518, + .N 3275o poi sier Proce c.4 Itulev . . . . . . . . . . . . . . . . . . . . 37500 50000 4r.873 Safety factor in terms of stre== = A#/t# 4 + 8Pich . 2.J2 i Gr 2.ol l WI tiefety factor an te rms of bic = iN.e*/(Na + .srwsp. 44 13 35 25
- See Equation 120).
trailable. In terms of stress, the safety factor is found to be of allowable thru3tn and moments for their standard units (106, the order of 2; in terms of cyclic life, it is of the order of 30. 115) or are prepared to m! vise whether the reactions computed The very least safety factor available, cim>idering the 25 per by their customers for a specific installation can be tolerated. cent spread encountered between individual ti+t data, ndght be In general. even they are inclined to understate the capacity of estimated as 1.25 in terms of stress and 3 in terms of life. This their equipment, primarily becau<e of a fear of discrepancies be-emphasizes the need for making a conservative estimate of the tween the results of calculations based on simplifying assumptions Lumber of cycles of major temperature change a system is likely an I the reactions impoel upon the unit in actual service. It to undergo. . would appear that a chance in policy towant permitting more In the range below 7000 cycles, the safety factor provided in liberal allowances would be contingent upon the following de-the Proposed Rules increases. For example, for one cycle per velopments: reek over 20 years, or a total of approximately 1000 cycles, the 1 3Iore general adoption of assumptions and methods of safety factor in terms of stress would increase by roughly 50 per analysis of proved accuracy or conservatism; to foster this is cent. The minimum safety factor probably would be close to 2, one of the purposes of the Proposed Rules. which would be more than ample, provided the actual stresses 2 Improved understanding of the necessity of realizing the am evaluated properly. . assumed design conditions in the actual instailation. This im-As far as the zone from 250,000 cycles upward is concerned, no . ph.es proper specificat. ion and supervision of cold spring; also, a estimate of the safety factor wd. l be ventured, since the propor- clear realization of the fact that edculations based on the as-tionality between the moment supported by pipe and tittings will sumption of a weightlesa system and frictionless supports can be progressive;ly lost. Fortunately, this zone has little practical grossly underestimate reactions caused by thermal expan> ion significance with regard to expansion problems." where these are small in relation to the weight of piping sup-L, A note of caution is n order. The provisions of the Proposed Rules do not take into account corrosion which would lower the 3 Publication of information on the order of magnitude of the b endurance strength an unpredictable amount. various components of piping react. ions expected to be produced ALLowantz Itcaevioss in well-designed piping syrtems leading to and from strain-
.. . sensitive pieces of equipment.u The degree of flexibility required .m a pipmg system is often controlled by the forces and raments the connected equipment Until better infonnation becomes available, piping designers can sustain without becoming inoperative or requiring excenive uill be forced to continue to resort to rules of thumb to guide them maintenance. 31ost frequently. the problem of setting allowabic in preparing their layouts. Some of these are given in the form reactions arises in connection with equipment containing moving of blanket limits upon thrusts: as an example, Baggerud and parts such as pumps or turbines, but it sometimes also requires Jernstrom (51) suggnted 3000 lb as an upper limit for ships' considerati.m for other strain-sensitive equipment, such as larce- turbines. Other= provide limits for both the resulting thrust and diameter, thin-wall prevure vessels or exchanger shells with the resulting moment, the moment in foot-pounds often being removable tube bundles fitting with close clearances. taken equal to the thrust in pounds. Others consider the com-With good logie, piping-stress analysts expect to be able to piments of the reactions separately for ditierent directions. higher turn to equipment manufacturers for guidanec in this matter on limits usually being assigned to downward hals than to lateral l
, the premi8e that the latter shouhl be in a position to advise thnut s. All of the rules citnl emingly di< regard the size of the l what provisions have been made for ah* orbing piping reactmns in unit, although they are actually intended to apply to conditions the design of indivithnal parts of their units and the completed customarily encountered in specific fiehls of engineering. amembly. The attitude often encounternt in the past, thas pip- To take care of the size etiect, some ndes are given in terms ot ing strains are no direct concern of the equipment dnigner i< fast pounds thrust per diameter inch or peripheral inch of the noule. dienppearing, and it is becoming more and more nrogniwd that Paul (79), for example, -nege ts 100 lb per peripheral inch of l lines connecting pumps or turbim s or similar crpiipment wouhl turbine nonic aa a rea*mahle t hrust. Annihrr nde of thi* present no more of a problem than other line*, but for the fact rharacter, w hich has been propo<cd hv LL*wirk (102). relates that the piping ha< to absorb not only the expansion of the line. the thrust to the sum of the nominal eliamrtet* of the suesion and but also to protect the ciptipment from the etiects of its nu n ex- dscharge piping and at the same time di!Terentiates with reapert
. pension. If this were not the case. the piping engineer couhl to the anchorage of the tmit. Rules expres*nl in terms of kiloa att very simpiy discharge his ta3k by rii: idly anrhoring his line adia- rating or equipment weight attempt to accomplish the same .
- cent to the equipment. purpo e.
Unfortunately, only a few of the major manufacturers publish n The tabulation of nycraec reactiona against pumps on p. 411 of s* The rulea are not intended to cover transmitted vibrations or the paper hv D.11. Ito -heim anel the nuthor tih is indientire of the prensure pulsations. type of information desin d. l
.t:7 l
I i
N 3 m Finally, there are a number of advocates of expres<ing the in any specine case, what degree of approximation will be accrpta.
- limitation in terms of the piping strm at the terminal. I'or ble, and how it is to be compensated for; furthermore, they d.,
example, lloath (90) suggests a nomin:d lending stress of 9000 not indicate w hose judgment in this matter is to be accepte.1, th.. poi (with no credit for cold spring) as a nati< factory denien basis; engineer's, the cu*tomer*s, or the inspection authority's. Th.. other experienced stree analysts have establishni individual formulating gmup devoted earnest consideration to these 9p..- limits depen.hng upon the type of equipment connected. tions, but came to the conclusion that the variables involve.1 m The foregoing recital of different approachen has been given flexibility analysis are too numemus, and their individual ettre, with the thought of stimulating discuwon by those who are more too unpredictable, to permit the establishment of a simple see .,f familiar with the subject than the author can claim to be. It is explicit rules, observance of which would assure protection i., his thought that reasonably conservative empirical rules of some life, health, and investment without imposing an impossible hur. form will always be necessary as a first general guide to a piping den of work on piping engineers. < designer; if the reactions obtained therefrom should be exceeded Variables fall into three major classi6 cations: ; in a specifie layout of visually alequate proportions, consulta-
- tion with the manufacturer is advised, at least m the esse of im. , g g ,
portant uni A 2 Cross-sections! properties. ! 3 Shape factors, i.e., properties associated with the dimen. ; Wan Soms REomas ANat.Ysts sions and configuration of the line axis. 8 The foregoing review of the theoretical considerations and ex- i In the first group the expansion coefficient and the elasticity perimental data underlying the Proposed Rules inescapably modulus assume primary importance as measures, respectivelv. Icads to the conclusion that, even after considerable simplifica- of the amount of strain introduced into the system and the clawir tion and idealization with resultant loss in accuracy, the flexi- resistance opposed by the material. Yield and creep strength bility analysis of any but the simplest piping system presents a reflect modifying intluences of plastic flow upon the resistanc., formidable task, and that accordingly it would be unreasonable and at the same time provide important yardsticks for the .hw to demand that each line be analyzed by the most precise ap- termination of the allowable stress range, which is further con.fi-proach available. Approximations must be permitted, provided tioned on the endurance strength of the material. their effect can be at least roughly evaluated and compensated Among the cross-sectional properties, the moment of inertii for. This is not enough; in many instances, perhaps in the and section modulus of the pipe similarly provide measures of the majority of cases, appraisal of the tiexibility by visual inspection forces and moments generated and the resistance of the pi te or comparison with similar layouts with satisfactory service thereto; the influence of the latter is modified by any stress performance must be accepted in lieu of a mathematical analysis intensifications present. or tests. While the foregoing properties enter piping-flexibility calcula. The group formulating the Proposed Rules has attempted to tions more or less directly as factors, the dimensions and configu-reflect this point of view in the following general clauses contained ration of the line axis an.i the shape of its components (as reflecte.1 in paragraphs 620(a) and BM@): in their flexibility factors) exert a much more complex eEect on 1 Formal calculations or model testa shall be required only the forces and moments, and therewith the stresses. where reasonable doubt exists as to the adequate flexibility of a It will be apparent from the foregoing that any rule or formula intended to provide a demarcation hne between flexible an.1 2 Each problem shall be analyzed by a method appropriate stin, or understress.31 and overstressed layouts must contain to the conditions. act n upmsentatin of de matand & knymtum, and & 3 Where simplifying assumptions are used in calculations or une size, length, and shape. The first three major variables can model tests, the likelihood of attendant underestimates of forces, be taken care of readily, but attempts at reducing the effect< of moments, and stresses shall be taken into account. Ime length and configuration to a simple and reasonably necurate shape factor meet with almost insuperable difficulties. These clauses admittedly are vague and oder no concrete guid. The most promising appmsch toward a first approximatina ance toward arriving at a decision whether analysis is necessary is to express this factor in terms of the ratio of the developni i k l i l l N i 4 r 10 b - O ' Vg ; i 6 l i 71 1 i s l Mxn M. 2 '3d\ 6 $ Tfe,, i i l 3 Ml l l %l l ll l C8 s s
% ! Nb ! l ll l
, f qiN+w x .llll J '. l
'j i 12 l to l 16 i
#8 2 l l l 76 6' 3 4 Ratio of Deveicoed Axiot Length Ls to Anchor Distence U
( , l
,( Fro. 6 Suser licrona ron sivett 8rsntr.pL LNE CoNrmUntvfo8t4 l k
cs f,
_ _ _ _ _ e s.a., - f l r line length L. to the distanec U twtween anchors. What can be CoscLt'siow accomplishid by this appniach is *hown in l'ig. ti which was Tla pnym21 Itule* pnwent an atte.npt hv eiome of the coun-3 developnl from a study publi ljesl by the author m one of his try's leading piping engineers gathenst as a ta k force eperating
; compan); s buktins (10*>). l his is b.6-ed on squsre-corner tmder 8ectional Committm ASA 1131.1 to rnluce the comph x g
assumptions and embraces almost all nincrivable pn> portion" bh m of evidin M yuw flMiility in a piping system to a F of smgle-plan. n.nfigurations of ahe I . / , l. , and expansion fm 3 m Ic gu de lines n (Iceting the late t advances in theoretical U-types. The abarims are ratios L,a . the onlinate* read th" undersianding and accumulatal practical experience. It has ratiof of the controlling stnw in a hend of any of the *hapes m- W tiu amor's a*ignnwnt to as-mble the factual evidence vestigiteil to that in a >quare IAwnd of equal am hor d&tance, underl3 ing this d.wnment and expLin n rtain concepts, such as pipe size and material. arut temperature rhange. It udl be noted stres-intensification factor, stress rance, self-spring, which have that been inhen nt in past funnulatic ns of the chapter on " Expansion I and Flexibility," but are more openly referrnt to in the new
/ " (L jy _ g)s 53I draft.
On reviewing the evidence, numerous gaps in our know!nige roughly describes the upper Imundary of the entire family of of the magnitude of certain properties entering into the problem curves except that applying to imrotumon proportions of a have hensme apparent. On the other hand, not all the present U-bend with unnpsal legs, for w hich it may produce a gnws under- knowleilee available on certain phases could be utilized in fram-estimate of the etressca. As a rule, however, the stnwes wdl be ing the Code Itulcs because of the nerd for keeping them simple. overestimated. For example, a stre-* ratio of the onter of 6 is This has necessitatni a weighing of the significance of the various obtained for the i.quare I, bend (L,/C = V2), whereas by defi- factors and their elTect on the over-all accuracy of the prediction nition this should be unity. Obviously the criterion is too in- of reactions and stresses.
, sensitive to prnlict even the results of a square-corner solution While the Proposed Rules repn=ent the group's best effort, with any degree of reliability. Sinco the latter itself often pn* the interpretation of the facts given therein is not necessarily the vides no more than a crude first appnnimation, it becomes evi- only one possible. Publication of the timucht processes leading dent that a formula of this simple character will not serve to pro- to their adoption is intended to provoke discussion by engineers vide a reliable means of distinguishing systems which must be at large, to uncover additional data not available to the group, calculated from those for which calculation can be waived. and ultimat4Iy to lead to an improved formulation, particularly This same criticism applies to the formula given in the alternate with regard to the clauses intended to promote uniformity of version of paragr1ph 620(c) of the Propomi Rules" which practice and intelligent enforcement.
assigns a definite limiting value to the stress ratiof AcxNOWLEDG1 TENTS U8 1 [24] The author wishes to recognize his indebtedness to 11ents. 0.03 DY 2 (L,/U - 1.05),^. N. Blair, A. SicCutchan, J. D. Atattimore. II. C. E. Afeyer, and where U and L., respectively, again designate anchor distance S. W. Spielvoget for encouragement and wholehearted assistanee and developed line length (ft), and D and Y are the nominal pipe rendered in the preparation of this paper, size and the resultant of the restrained thermal expansion and net linear terminal displacements (in.). The left-hand term in BIBLIOGRAPIIY this case also contains approximations; specifically, it assumes a (In approximately chronological order) constant relationship between the allowable stress range and the I Formandcrung und Beanspruchung federnder Ausgicich-i modulus of elasticity. . rohre,,. "by A. Bantiin. 3!ittedungen nber i erschungsarbeiteo.
) Assuming that it would be possible to establish a criterton bulletin 96, 1910; al,o Lituhrift des l~rreines deutscher Ingenieure, enabling the piping designer to climinate amply flexible systems vol. 54.1910. p. 43.
from consideration, the next problem is that of distinguishing 2 " Expansion of Pites." by it. C. Taccart. Transactions of the Aniencan Society of Civil Engineers. paper no.1167. December,1910. the remaining systems with respect to the accuracy required in 3 Ober die 1 orm mderung dannwandiecr Rohre by Th. their calculation. Systems carrying flammable, noxious, or other- von Kirm4n. ZeituArift des rereims deutscArr Ingenieure. vol. 55 wise dangerous fluids, or failure of which would entail a maior 1911. p.1%9. Enanciallo8s, obviousiv are more in need of precise analvsis than 4 "Flexibilite des Tubes." by h!. Starbec. Bulletin Association those where a break is'merely inconvenient and readily 'repain d. Tech,niqi la it 1 1 L pp. 4,H 5 to In the latter m>tances the application of approximate methods Polytechnical Journal. September 14.1912 p.577. would appear economically justified from a standpoint of time 6 " Elasticity and i:ndurance of secam Pipes." by C. P. I enving; the u# cf approximations also may be necessarv for more stromeyer. Eauincerino. June 19.1914. p. h57.
~ '
I critical piping systems involving branch lines or intcrmediate cham? eal "Lupert's Department of Crane Company. The rulre World.ppe Ben l ( I i restraints. October.19:5. Wherever . approximate methmis are used. the question imme- 5 "!/ Aptitude l'.lutique den Tupiutenc< A Vapeur au twint de diately arises hew to compensate for the attendant error. Again, vue Dilatatmn." by II. carher, obtainable throuch author. Wandres, no simple rule can be advanced. The only advice which can be Binche. Hainaut. Bpsmm 192o,1923.1925.1927. 9 "TI.e lhtwity of Pipe Bends" by S. Crocker and S. S. offered is. to compare t.oe results obtamed by the approtimate Sanford. Verhanical Equinterina. vol 4's.1923. p. If,9. method it i4 prolwed to use, with those of precie calcul.stions in "thpan, ion 8 team lleml*," by P. M. Gallo. The fila.t i . for a autlicient number of casca covering the extreme conditions Furnace an.t .Ntrans IWnt. Alay, June. July.1925. IL "The Elaatic Defortnation of Pipe llen.14." by Wm. Ilov-it is expected to encoimter, and to derive correction factors then, gaard. Journal of Mathematics and l'Airsars. N!a ichusetts Institute e
; from. In some methods, such as thoe published by the nuthor.e of Technoh.gy. camhn. lee. Atmm. vol. 6. Lvember.1926. pp. m-company (10~,1. such a check has already been nude by the its.
i proponent of the method. 12 "Streties and llenctions in Enpan-inn Pipe Bends," by A. h!. Wahl. Trans. ASM E. vol. 49-50, paper FN P-f,0-49,1928. l 8, ( " See " Study of Shape factor." 13 "The Flenibdity of Plain Pipe llen.l ." 1.y J. It. Finniccome.
% as Transenbed in Appendis 2. The Engineer (London), August 17,24,31 aml September 7,1928.
429 ! s I I t
..,~~.-,n_.. , _ . , . _ _ , , . , . - . . - - - - , . _ . - _.,_..,e _ - - , , ---e-
__ . m . . _ _ _ _ . _ . i t f . a e 14 " Deformation of Plane Pipe Bends." hy Wm. Itovgaard. k f Bend Piping." by it. f Denni*m. Journal .tmerican Socirtri of Xar,d - Jewrnal of .11athenintics and PAvsirs. St.I.T.. vol 7. October.1929 Engineers. vol. 47,193h also Engineering. January 24. February 2M, pp.194 2'tM. . h! arch 1.E. IRM. ; 15 "I urther ite-carch on Pipe Bends." by Wm. llovraard fournal of Jfa:A. m,gira and PArnirs. St.l.T., vol 7. December 1925. DL " Load-Deflection Tests of Beveral One-Plane Es pan
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.430 I'
l. I t
?wN v' gD .y==uy w--m g-Wywf**->7m-me-++hM9--mec'--m.~ g---dvme- y ge w yp,%g>m-p-su*-- isryi e , y,
- 9 w ,,w,9- 4m. y-r-=- 99% -4 m.- m-_ wnNw-.m==--mm---- ww m' '
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- Radius." by T. E. Pardue and I. Vigneas. Trans. AsM E. vol. 73.
- 1951. pp. 77 s7. 1 Precure, internal nr external.
100 " Introduction to Piping f leubdity" (by A. it. C. Markt). g n*right of pipe, (ittings and valves, contained fluid and { Piping Engineenne Paper 4.01. Tube Turns. Inc.. Louisvdle, hy . insulat. ion. February,i m o. 3 Thermal expansion of the line.
- 101 "Mesur d Force.on Pn+ure 1: chef Wh c*." bv F. E. Wol.w.
sriek. Heating. Viping and Air t'ambtwnnna. July,1950. pp.102-106. The first twoloadinge prnduce =ustained stre*=en which are evalu. l 102 " Equipment 8trer.cs Ingwwcd by Piping." by F. E. Wohine-srick. Petrattun Regarr. Au, rust. 89'al. pp. W 91. sted by conventional meti.ods. The 4rces due to thermal ex. f 431 t i I
pansion, on the other hand, is of sufficient initial magnitude will be reined as a result of local flow in the form of yiel. ling or in runs of pipe may be cold sprung. Cold spring may be taken I the form of creep. The prem rmhweion which he taken place account in the calculation of the renetions as shown in j will appear as a strew of rrverwd sign in the cold con.htion. tuf(d) provided an e:Tective method of obtaining the de igned ' coh! 8pring is specified and used. This phenomen m is designated as acif-springing of the line and is similar in etTect to cold springing. The amount of such self-sprmg- 6JO Rasie .ls umptians and Iteg,,imnents. (a) Formal calcul., T ing will depend on the magmtu.l. of the initial hot stren nnd the tions or moilel testa shall be required only where reaso temperature. Accordingly, while the hot atnms tends to diminish exista as to the silequate flexibihty of a system. Each prnhlr i with time, the sum of the hot and cold strews during any one sh:dl be analyzed by a method appropriate to the condition eycle will remain substanti:div constant. This sum i4 referred to (b) Standard auumptions and requirements are given in
- as the stress range. The fact that the stress range is he deter- paragraphs (d) to (g). Where simplifying assumptions are net mining factor leads to the selection of an allowable combined in c:deulations or model testa, the like'ihood of attendant un.h
- stress (range) in terms of the sum of the hot and cold S-values. estimates of forces, moments, and stresses shall be taken into account.
(6) The beneficial e:Teet of judicious cold springing in assisting - the system to attain its most favorable condition sooner is recog- (c) In calculating the flexibility of a piping system betwwn nized. Inasmuch as the life of a system under cyclic condition anchor points, the system shall be treated as a whole. The depends primarily on the stress range rather than the stress level significance of all parts of the line and of all restraints su at any one time, no credit for cold spring is warranted with regard solid hangers or guides, shall be considered, to stresses. In calculating end thrusta and moments acting on (d) Calculations shall take into account stress-intensi equipment containing moving or removable parts with close factors found to exist in components other than plain straight - pipe. clearances, the actual reactions at any one time rather than their Credit may be taken for the extra flexibility of wh componenta. range are significant and eredit accordingly is allowed for cold In the absence of more diractly spplicab!c data the spring in the calculations of thrusta and moments. flexibihty factors and stress-intensification factors shown in Chart I may be used. 618 3faterials. (a) This chapter applies to all classes of ma- ; terials permitted by the Code, (e) Dimensional properties of pipe and fittings as used in (b) The thermal expansion range e shall be determined from flexibility calculations, shall be based on nominal dimensions.- Tabless (f) The total expansion range from the minimum to tha as the difference between the unit expansion shown for - the maximum normal-operating metal temperature and that for maximum normal-operating temperature shall be used in all , the minimu'm normal operating metal temperature (for hot lines, calculations. whether piping isNot coldonlysprung the or not. this may usually be taken as the creetion tempersture). For expansion of the line itself. but also lincar and angular movements materials not included in this table, reference shall be made to of the equipment to which it is attached, shall be considered. authoritative source data, such as publications of the National (g) Flexibility calculations shall be based on the modulus of Bureau of Standards. elasticity E.at room temperature. 1 i (c) The cold and hot moduli of elasticity, E, and E., respec- 6tf Stresses and Reactions. (a) Using the above assumption <. tively, shall be taken from Table 8 the stresses and reactions due to expansion shall be investigated as the values shown for the at allsignificant points. ; minimum and maximum normal-operating metal temocratures, j respectively. (b) The expansion stresses shall be combined in accordance For materials not included in this table, reference ; with the following formula shall be made to authoritative source data, such as publications
- of the National Bureau of Standards. g, , gg,, 4 43,, f (d) Poisson's ratio may be taken as 0.3 for all ferrous mate- where I
rials at all temperatures. (Elsewhere in the Code there will be S. = i 3f./2 = resultant bending stress, psi found tables of values of Pois*>n's ratio for various materials S, = Jf,/22 = torsional stress, psi i which tables are given for general information.) 31. = resultant bending moment,Ib/in. $ (e) The S valuca, S, and S. at the mjuimum and maximum 31, = torsional moment, Ib/in. j operating metal temperatures, respectively, to be used for de. 2 = section modulus of pipe,in.8 termining the allowable expansion-strm range Sa shall be taken i = stress-intensification factor for the type of p,ipmg system involved from the applicable tables g g f, in the respective sections of the Code. in the case of welded pipe, exceed the allowable stress. Sa, where the longitudinal-joint etliciency may be disregstded. 619 Cencral. (a) Piping systems shall be designed to have Sa = f (1.25 S, + 0.5 S.) i sufficient flexibility to prevent thermal expansion from causing subject to the limitations of paragraph 632(6) I 1-failure from overstress of the piping material or anchors, 2- where leakage at joints, or 3 letrimental distortion of connected S = allowable stress (S-value)in the cold condition equipment resulting from excecive thruiti and moments. S. = allowable strm (N-value)in the hot condition ! (6) Fh sil.ility shall be providad t>y changes of direction in the S, and S. are to be taken from tables in the applicable sections piping threugh the uae of bends, loops, and otT-sets: or provinion of the Code. i shall be made to absorb thermal strains by expan= ion joints of i i f = stress-range reduction factor for cyclic conditions to be the slip joint or bellows types.d If dairable, f!ctibility may he applied; in the abence of more npplicable dsta the 1 provided by creasing or corrugatine portions or all of the pipe. valuas of f sha!! be taken from the fo!!owing tabic: (c) in order to modify the etTeet af expansion and contraction, "d g),p , j,,I, f,
- l expceted life
*utes.
58 Tahia, of these properties wul be provided upon a lontion of these f In the inantime, data peh4hed in P; ping llandt=2oks or 7000 and less. . catalocs rnay be used. 14000. 1.0 20000. 0.9 8 In this caw. anchorg or tie
- nf nf&ient meneth and riedityshall 0.8 be innalled ta provide for end foten due to hid presnro and other CsWkl.
causes. 100000..... 0.7 0.6 250000 and over. . . 0.5 432 1
-we 4
, m -~~ s (d) The resetions (forces and moment *) R. and R, in the hot in the foregoing equation i i' r.nd cold conditions, rc=pectively, shall le obtained as follows D - mimin:d pipo size, in. imm the reactions R deri.ed from the llexibility calculation, 1, = resultant of rntrainni thermal expansion and net linear .
" "*' "**"""'I"'
c *R U = anchor distance (length of straight line joining anchorg), R* = \1 3 / E, ft. R,= cR R = ratio of developal pipe length to anchor distance, dimen-or sionless. S. E,} N (d) Standant as*umptions and requirements are given in para-N* * (I S , g,/ graphs (f) to (i). (e) In calculating the flesibility of a piping system between whichever is greater and with the further conditions that anchor points, the system shall be treated aa a whole. The signiti-(S./S 4)(E,/E.) is lew than I, cance of all parts of the line and of all restrainti such as solid where hangers or guides, shall be considered. (f) For calculations made in conformity with paragraph (a), e = cold spring factor varying from zem for no cold spring to stress-intensiticatmn and tiexibility factors may be omitted if the one for 100 per cent col.i spring piping system is not subject to more than 2000 stress cycles during Sa = maximuni computed expan< ion stress E, = modulus of clasticity in the cold condition its expected life. For linen sjabject to more than 2000 stress
'FCI"** **IC"I*Lio"* shall take into account, stress-intensification E. = modulus of clasticity in the hot condition R = range of reactions correpndi.ig to the full expansion fact rs f und to no.t in cominnents other than plam stra$
range based on E' Pi Pe. Credit may be taken for the extra 11esibility of such components. In the absence of more directly applicable data, the R,and R. repre<ent the maximum reactions estimated to occur flexibility- factors and stress-intensification factors shown in in the cold and h<>t conditions. respectively. Chart I may be used. (e) The reactions so computed shall not excml limits which (g) For thermal-expan-ion analysis, dimen<ional properties of the attached equipment can safely sustain. pipe and fittings shall be ba3rd on nominal dimensions. 633 Supports. (a) Pipe supports and restraints not expressly (h) The total expanaion range from the minimum to the maxi-considerniin flexibility calculations shIdl he designed to minimize mum normal operating temperature shall ha u ed in all calcula-interference with the thermal expansion of the line. tions, whether piping is cold sprung or not. Et only the expan-(6) The design and spacing of supports shall be checked to sion of the line itself, but also linear and angular movements of assure that the sum of the longitu linal stresses due to weight and the tquipment to which it is attached, shall be considered. pressure does not excml S.. Where this sum neceds % S. but (i) Flexibility calculations shall be based on the modulus of does not excent S., the amount in excess of % S. sha!! be sub- elastkity E,at room temperature. tracted from S4. 6M Stresses and Reactions. (c) The maximum combined pres-sure and expansion stress shall not exceed 015 times the rated ultimate tensile strength of the annealed material at room tem-Appendix 2 perature. The maximum computed expansion stress S, shall not exceed the following allowable value At.tERxArr Ct.At ses roR CHAPTER 3 or SEcTrov 6 or Coos PoR PREssrRE PirtNG A4 PROPOSED By Tuc 31. W. Kct.t.oc.o Sa = f (1.25 S, + 0.25 S ) COMPANY where 630 Ranic .bsumptiens and Requirements. (a) Formal analysis S, = allowable strea (S-v,lue) in the cold condition or model tests shall be required for pipe lines which simultaneously Si" 2110wable stress (S-value) in the hot condition sati*fy t he fullowing conditions: (S, and S. are to be taken from the tables in the applicable 3faximum normal operating metal temperature over 500 F. sections of the Code.) Lminal pipe diameter over 6 in. f = stress-rnhtetion factor to be applied for cyclic service; Rated nrvice pn,*ure over 15 p<i. in the absence of more applicable data the values of f The method of investigati.m shall be appropriately selected to shall be taken from the following table: conform with the condition of the pmblem under examination. Total no. of full 8tre3 -reduction (6) The requirement 4 for analysis shall be considerni satistini temp cycles over factor, for duplicate unita of successfully operating inatallations or for espected life f replacements nf piping systems with a reconi of sati3 factory nuio and Ic% t.0 140no. 0.9 service. (c) It is recogniicd that for operating conditions not satisfying h"3NMg 0 0 }9 concurrently the provisions of paracraph (a), nn analysis for each t (moo . . . . . . 06 piping system is economically impractical. An an:dysis i*, there. 250000and over. . 0.5 fore. mandatory only if t he following approsimate criterion is not If the sum of longitudin.d pre **ure and weight tresaen is less satis 6cd than S.. the diTerence twtween & and the sum of these stressen Dr , may be addnl to N.. fi'(R - 1.0*>)* * * ~ 822 SdP!wis. (4 The de-ica and sparing of supports shall be checked to assure that the sum of the longitudinal stresses due Tho constants 1.05 and 0.03, as nett as the esp. ment of %, to weight and prewin d - t.ot an ni 6 The analysis for represent only appnnimate valuen, wuch will be pulvet to fur- prmure strecen shall be baani on the crodnl dimensions of the ther investigation and correction as needed. pipe, t 433
k D w CnaRT 1
- s. Forxtaittry aNo Srnssa-INTsNasrtcar:ON FACTORe rOR PartNo Conf rONENTS CHART la Poor or Ftextarttry aNo Simras-INTEN83rtCATION FACTOR 5 Mesibility if)O -
Description Stress Inte Flexibility 80 f actor k Factor i Character $stia h Sketch 3
- 60 N 3 -
_h Flealt ility Factor for gio. k = 1.sS/h Welding Elbow. ,,.a 4 \ / g er Fspe send Flexitulity factor for 65 41 9 .b jiW g= 3c Mifers; k = 1 S2,h% h r*_. .r - Bjb ndrodiue It 2o \ cl eely spaced kitre send, a,4,a
' ta -g stress intensification ee r (1 + tan s) .l.52 v V T. rector: i = 0.s/h's 9 g, , f _ _ , ]
h '* D'/s h ylp_ 2 rg
' ' Ir ~ lo \' f g
.g, ma p8 -A 3
,q---- +7 i
saaely spaced kitre Bond a,a,* _ ____ - - _ - _ * - g e -
**r D * "a") I52 O9 , , ~
)
W h% l e tot e
~~ 2-~.l_ r i gg,2 M
r 4 g3 __ __ __ i s.14ts ree 8.* I i per ASA B16.9 o3 *t
- 2 - --- - -- ' hg i-l kh ' _
6_ =_}*.r g _ s os y ,
'~~ g ._
Reinforced Fabricated Tee, 5,a vita pad or enddle j Qg ~(g ,34T)b o2 0304 0608Jo as 2 .3 .4 .6 .8 to ts 2
,p _
--.f.I'g* t i chorocternette h j
unretarorded pod j- saddle _ .o .rs - s # py-rabricated Tee 8,* l O9 _t' ^r 8 '5 '
- i p
/s r
-- -- '11
- w g375 O
p ' ' lC ~ f and il nged: C= h'4 Butt Welded Joint, Raducer, 25 ~2 ands fionge(C=h% or Woloing back Flange l l,Q Leutle4elded Slip on of the same normnal weigt t or schedede as the p* The denibihty facte.ra 4 and strtas er Socket Weld Flange l l,2 be taken less tlan us.ity. They appry over the e e used ir. the myntem and Wil in no case ertive are length (st.oa n by heavy center
' ~~ "" ~
heen ia the sketche.) for curved and mitre elbows, and to the interse intie A compute,1 from the formulas sisen where: Fillet welded Joint, or ft - t,end radius of welding clbow or pipe bend Single *elded socket weld F1ance r - mean ridsus of matchinst t ipe l l*3 8 " **Il h *k "*'c h RD
- _ a - eme h'a'l a"'gle n '* *I between a'"djac'D*
ent mitre sure i __ __. _ _ _ . s - rostre sics. ine et c rater T - pad or and<lic tha kn ,1.ne th 3 9 lap joint stub) j l,6 a Whne'flanges ' ' 'are attache <l to one or both ends, the values of & and e in the Table I,;Il's w tCtl One end flanged: 4 t ' =. Both ende fianged: ABD. Screwed Pipe Joint,
- Alm includes single.mitto joa'nt.
er3.-ed nance 1 2.3 Carrugated straight F1;o, or ce,r. ated or crea.ed send 5 2.5 _ ,. .g f I C,I
.. . _ . . . . k- f kg , 9
- y person:' as raaibie. mith futi and symnathe'ie tudy bein< ziven Appendix 3 to all minority viewpoints, and with artive solicitation of all kinds Ft1xiarun Fwrons ron Craven P:PE of critici<m. A s[wial word of praise ig due to the author of t his "IIhough the Tek Forre Iteport reprnents a joint In the following. the three surec*<ive approximations of von P*I*it.I".'
dort. u evident that at least m the preparation of this evel-Kirmin's flexibility fattor are shown both in the form in which lent paper, the author has gone far beyond the call of duty. they are usually found in literature (117) and in a reformulation The writer's further comments will be given under the headings by the author which makes them easier to compare of the ection titles to w hich they pertain. Flexibdity Factors awl .strrss-Intenstfimtwn Factors. The prac. ' I' " 12h' + 10 1248 + 1 tical piping engineer is not in a peition to select from all the theoretical and experimental data which have appeared on the 9 subject of ticxibility factors and stress-intensification factors in
- 1 + 12h* + 1 piping components. The selection represented by the simplified
}* Formulas [2l through [6] in the text of the paper and in Chart 1 g ,105 + 4130h8 + 4S00h' of the Report will be of great convenienre. While it is not un. l likely that further research in years to come may suggest modinea-
~
3 + 536h8 + 4800h' ti n I s me f these formulas, it may be fairly stated that thev 9 + 0.255000/h, represent as good a selection as may presently be made and
; - 1 + 12h' + 1.3400 + 0.007500/h' they are a great improvement over previous formulas in sim.
252 + 73.912h* + 2.446.176h' + 2.S22.1004 plicity and convenience, it is particularly striking that, with
~ pr per interpretation of the quantities involved, Formula [5]
3 + 3280h' + 329,3764* + 2E22.10048 is valid for so many ditierent pipmg components, and the author 9 + 0.300306/h' + 0.0010.W7/h* is to ne thanked for having introduced this formula in his paper,
= 1 + 12h' + 1.400% + 0.0139 4G/h* + 0.00001276/h' reference (114)."
The author mentions that the bend-dexibi!ity factor given by In discussing Shipman's paper (17), Jenks gave the following Formula [1] or [2] or other similar formulas was used only for i formulation as reflecting the nth approximation of the von "in-plane" bending before Vigness (70) showed that it also K&rmin flexibility constant should be used for "out-of-plane" bendinc l'nfortunately, the appearance of the Vigness paper was not sufficient to chance a 9 rather firmly established practice. The Task Force Report does
- k. = 12h' 1248 + + 10 1-j - j = 1 + 1248 + 1-J. not emphasize the applicability of this factor to both types of I where f is a complex function of h which has the following values: bending, and many analysts continue to ignore the increased out-of-plane flexibility. In the writer's opinion, the Report A 0 0 os 0.1 o2 0.3 04 0.5 0 75 1.00 eliould forcibly direct the reader's attention to this development.
j I 0.7625 o.5684 0.3074 01764 0.1107 0.074&d 0.03526 o.02026 One other remark is in order concerning stress-intensitication The flexibility factors obtamed from the preceding four formu- factors. The second paragraph of the section headed Stress-
!as are compared with those obtained from Equation 12] Intensification Factors adequately defines these factors for the 1.65 purposes of the paper. However, there are other types of stress-intensification factors applying to pipe loadings other than those km " 7 . A I of interent in piping-tlexibility analysis. For example, the factor for four values of h covering the normal uaeful range. It will be observed that this simple approximation gives values closely com- i ,, 4Nh'*d - O **
l 4Rw=d - 20 9 a-paring with the more preci o of the other formulations: l Membility c maracteristie A = 0.05 0.t 0.5 1 gises the intensification of hoop stress due to internal pressure l l v5 N 2!lI$n'8"a'nS"NaIoI Al = N !@ j $ [ w hich takes place at the throat of a pipe 1+nd or elbow (llSL l'rimarti .inalysis. The author's exposition is the first, of von Kermin third appronmanon. As = 34.o 17 3 32'i t.69 Jenu nth acernumanon. 4. - 34.6 17.3 3.29 1 69 which the w riter is aware, that lists the sources of inaccuracy in Approumauon 4,awd on Denin 43 = 33.0 16.5 3.30 1.65 analytical evaluations of what he calls " shape factors." It is vitally important that these sources of error be recognized, for
! DisctissiOn otherwi<c the analyst and those to whom the analysisis submitted Joux E. Ilaocx." Tids is one of the most important papers cannot have a meeting of minds. That is definitely not to say, however, that the corresponding errors should be eliminated or which has ever been written on the subject of piping. The entire
- industry is indebted to the members of the Task Force and of the outlanc 1; a good anaiyst is on the lookout for approximations nhich a'Tord a considerable saving in etTort at theexpenseof but a working group for the study and inventive etTort that is repre.
= mall and tolcrable loss in accuracy. However, the apprmima-sented by the May 4,1953, Report, and the present paper goe, tion should not be bidden or denied; instead,it shouhi be deline-beyond this in presenting not only the results but alm the ated fully and its etTrets on the final results should be evaluated.
rationale. Further, it should be remarked that the manner of Sub-titution of spute corners for curved members is only one presenting not only this paper but al-o the Tuk Force Report i, of the many wavs that an actual piping rontiguration may be in keeping with the ewellent tradition c<tablished in connee. l " idealized" preliminary to the actual mathematical or model e tion with the development of the ASill: lloiler and Pres-ure 1 Vessel Code and carried on ia the ASilE <pon<ored American analysis. Frequentiv it is justitled to neglect relatively sheht changes m direction small otiets. and so on, in ord r to simphry l Standard Code for Pressure Piping-a tradition of ordaly de. 4 the conlicursten actually subjected to analysis; however, the velopment incorporating contribution < by as many inten -red' A event of such "i irali. ation" should be made clear.
= Director of itewearch. Alidnest Piping Company. St. Louis. Alo. ^k/j Mem. AMIE.
8 Numbers in parentheses refer to the author's bibliography. r 435 l 4 g I t e
h.e
-U The " square. corner approximatinn" which is wi.lely u+d still :
2 has never been evahtated fully. Life (* short and pniblems are tangents, however, the increaani flexibility of the hcnd gov.rn. nn.1 the reactions are overestimate.1 in the septarc-corncr approu. difficult no that this i.lentization mill continue to be uwd. but it la I to be hoped that further developm. nts will enable u to nuake mation. Of courne the etTert del = nds upon the value of the ben,1-flexibility factor, k. , reliable estimates of its cifnts on c:dcolate.1 re,ults and Ihat seill other developments will provide a 1nely imple motheul of corrcet- Another point should la raised concerning the nature of Ihe appnesimation* implicit in certain atedy1ical solutions. In } ing a to known squ in-corner br within tolerable analysis so a4 toThe limiN of accuracy. obtam n 3 nits dehnitely strictly tumlimen*ional ca es, there i* such uiter is not particularly hopciul that these dev .opments will be forth- axis" and the n~ultant force svetem can le re.luced to a siner coming in a mat ter of just a few years though. force pawing througli the " clastic erntniid" of the configurata..n One indication of how dm ptive this area may le, may he seen and hing along the neutral axis. In symmetrical caws the e from the .uithorbi statement that the square-corner approxirna- neutral axis does indml parallel the line-connecting anchor , tion " . lead
- ta att overestimate of reactions. " This was un bu t at the author ii ,licate=, errorn result from making this assunp tion in nonsym:r.' trical cases. In gener:d three dimen-ion:d opinion which the a riter shared until he wv brought up short by ;
cases, Ihere i* no sch thing as a neutral axis. The resultant force a statement of Dr.10. G. Ihker: "A wrious ol@ction (to the square. corner appr nimation) has leen that square-corner errors system consi*ts of tbree moment components and three force ron: are usually on the w rong side, that, is, ticxibility is over-ewti- ponents nll of wht, h can be repreecntnl in various ways, naruch. ; mated."88 An attempt to reconcile the difference leads the writera as a wrench, a* a motor, as a combination of a line vector an,i free vector, and *o on. 1 to the conchision that both statements are corn et-if applied to I the proper type of con 6euratian. The writer's experience, and Only in verv =preial cases does the arench or motor breome k presumably n!so that of the author, have been mainly with sta- singular, reducing to a line vector of force with the free-moment . tionary insta!!ations whereas that of I)r. Raker is with marine vector vanishing, and only in these cae ia it possible to speak of installations. A bend or clhow, as compared to a square corner, a neutral axis. A t tempts to repre=ent a three-dimensional , has two opposing effects on flexibility- problem in terma of a neutral asia imply doing some violence On the one hand, the Kdrmaa-flovgaard-Vigness-Reskin, etc., to the fundamental principles of mechanics. Again, this is not - flexibility factor causes the bend to be more flexible than the to say that the attempts are not warranted if they succeed in ' corner; on the other hand, the hend or clhow "short-cuts" affonling a great simplification with but litt!c loss in accuracy, , the corner and geometrically offers a stifier path. In stationary but it doe = not appear that the question of how much the ac.
- install.itions, the bend radius is small compared to a representa- curacy suffers han been explored adequately. ?
tive dimension (say, the straight-line distance between end Finally, some inaccuracy is involved in neglecting secondary bending terms for hends and elbows." In almost all cases the points) that characterizes the contiguration, and consequently the increased !!cxibility is of greater influence than is the short- crror in slight and the simplification great; however, for tight cut effect. On the other hand, marine installations are likely to configurations involving short-radius thin-wall elbows, the be more confined and the bend radium is a larger fraction of the secondary terms may become of great importance. In fairnese corresponding representative dimension so that the short-cut it should be mentioned that no great dif!!culty is involved in effect predominates. taking the secondary terms into account in usirg the Piping IIandbook method of analysis.
- i Self-Spring and CoM-Spring Efects. The analyses of the Re-
} l i } i I
'I_ ,,P' ]3., port and of the paper aaume that there is a single quantity e I
,' 3 y ,.-r
- wN which characterizes the amount of cold spring in the system. In
'I -
i f,2, - i~ g certain actual design =, however, ditierent degrees of cold spring are employed in two or tllrce of the co-ordinate dimensions. It in 4 y,. ,, C : - ' not clear what computational procedure may be implied m such
, e---5 --
.x ! cascs by the rules incorporated m the 1(cport.
. g
- '" ' I ._, _ ,o! m .g The writer invites the author's further comments concerning
.- -' ,! t the factor % which appears in Formula [171. The use of this
[J EM,
/ I
! d
% war i i h _
factor tbooretically resulta in an overestimate of the initial hot reaction and this fact, coupled with the extrrme conservati<m or l W, l I i- ,C, %tus ~ o,trichlike at itude cf man.v manufacturera of rotating or recipro-
,7'f
*' .ou.~,..--....-...,.~ cating equipment, mav rc* ult in the rejection of some designs
".* W::*.Z' :'.! L7.:7:'*.*:f'" ';:*:T*.M. d*,*;;:".:J" "
. uhich actually are adequate. It in recognized that the % limita.
tion on tite amount of col.1 *pring that can be counted for certain ('
' '. t .. h c. .. .h . . .
j lh h ll hI h c mputational purposes han been a part of the Code for several
*"* *' ** ~" " .h h ., ,. .
years. Dace the Tek Force have parti-ular reason for reaffirming Fro.7 Coverarsaw or SocramConxrn Arrnotnrstrov 4so Exact thi.e attitude
- Doc 4 the % limitation reticct recognition of tha Socorrox ros Cocu. Leo I-Denn fact h all com.mfiw and analyscs are but imperfect wars of predict.mg physical behavior, and that no matterhowcarefully That the square-corner approximation can give values of reac- e ldspringing is c.dculateil an.1 performed, actual reactions are not tive forces and momenta which are sometimes too hich and simie.
""* #y to reduce 1 to lone than one tbird their calculated times too low mar be seen from Fig. 7 of this di<eunion, whom ""'""" "PN"" " " ' ' **#'" " "#
the simpic*t pmble ca<e is analvml-that of an equai leg L- that the formula for R. hecome + ! bend. (In preparine Fig. 7, valuc4 were calculated on!v for L/R
~ 0,1, 4,9, and intinity.) If the tane nts arc short rehtive to .,
p R. = I ~c t i the bend r*lius, the short-cut etTect governs and the square- 3 E, R corner approximation undere timat.s reactions. For longer or
" Private communication. April 29,1953. i*
ss Author *a reference US), p. Sol, [ l
g6- i- ie a a e - _ - m , _ - - - i t-t
- E.R The first strens cycle indicatcp that the stress exceeded the In " K elastic limit in one or more areas and must have produced local.
ized deformation that later eihom,I up as self-spring and atress (nhichewr is larger) so that cold spring in excess of 100 gwr cent when the line was allowed to become cold. Thi.s overstrcos is not might net be employed to reduce the theoretical value of Ra desirabh and neither is the change of grain structure that will below what is reasonable. take place in these deformed areas. This changed grain structure The statement ". .wrvice failures are associated with cyclie, will have a higher en en rate from the nwt of the pipe where the rather than static stren application. " ap! wars in support of Ihe grain strueture was not raitically altered by overstress.u,25 In stress-range roncept. One may remark in pas-ing that the service other wonia, any piping sptem that shows a rapid relaxation failures to which reference is made are clearly thow in pipingand - (other than the nornni creep characteristic for the designed connections and not in rotating or reciprocating mechanical equi P - streu) ha3 tren weakened in some area or areas and its strength ment where a mal or noniunction is more usually the result of is no longer certain. This, the writer 8ubmits, is not a good static overload. Ilowever, there are practical caws where static approach to the design of high-temperature pipine. stress rather than stress range governs the mtegrity of the piping The writer believes that it has twen fairly well ntablished that itself. In very "ti;:ht" configurations compor<,1 of very thin-wall this localizn! deformation ilocs not take place in the cantilever piping and componen% local crippling may govern. The phe- portions of the piping system (except gnwibly for a very small nomenon is one of instability rather than of strength and it is di3tance adjacent to bends and elbows when these contain over. recognized that the Code cannot incluile rules for such exceptional strew). and that this relaxing deformation occurs in the bends cases, and cibows of the piping system with the present approach to Allouwbfe Stress Range. The writer believes that the stress- design. range concept is useful and generally valid and is pleawd to see For most load-resisting members any permanent deformation it recognized by the propo*d rules of the Task Force Report. or set that accompanies stresses below the yield point of the However, he Icels that there shouhl be leeway for designer and material does not damage the members seriously. It is the per-user, if conditions call for it, to agree upon other criteria appro- manent deformation that occurs at the yield point that is dan-priate to the particular situation involved. gerous.
; Thelast paragraph of this section of the paper should not escape The problem shouhl be tackled at its source, bends, and elbow s, ' attention and the Code rules themselves should contain an and something should be done at these points. The writer also admonitory remark concerning the erTect of corrosion. believes it to be incurrect for the proposed Code section to accept Allarable Reactions. The writer would like to commend the local overstress in any part of a piping system. Reinforcement author's evaluation of the lack of rea ism redected in the limita- would be adited in any other place where it was known that high tions on allowable pipine reactions presently established by manu- local atrus was prnent. Why not at bends and elbows? It facturers of the equipment to which the piping attaches and of appears that the stress-intensification factor for bends and ellmws the economies which wouhl result from an upward revision of requires serious re-evaluation and revision upward.
such limitations. The writer understands that this is a question It is felt that the pmposed Code section should r1guirc hia;her under consideration by a group of users of major rotating equip- schedule thickness for bends and elbows (al.o possibly tees) than ment. the required pipe thickness so as to eliminate Or minimize local What Systems Require Analysisf It would be most helpfulif deformation caused by exceeding the elastic limit. the proponents of Formula [23] would present an evaluation of Fuch a requirement also will aid the more economical design of the applicability and accuracy of this formula and if others were piping systems. At prese it too high a price is being paid for the to contribute to the subject. Formulas like this constitute, in false tievibility of bends and elbows by a stress-intensification ' effect, greatly simplified methods of analysis which,if their range factor that not only cancels out any apparent gain but causes an of validity could be assened, would be very usciul for targing oventesign of the whole piping system in onter to prevent the shots and highly approximate analysis. Ilowever, the writer streu-intensification factor from carrying the stress in the elbows sides with the majority opinion of the Task Force in not wishing over the allowable strem limit. Thickenine the elbows will tend to raise this or a similar approximate formula to the dignity of a to eliminate what is generaliy a minor source of fl'exibility of the criterion for mandatory requirement for analysis, piping system, but will bring the stn a characteristic into line Conclusion. The writer has submitted comments on the Atay with the rest of the pipingdesign. Relaxation,ifit should occur, 4,1953, Report directly to the Ta k Force (and it shouhl tw hoped should be through slow creep and uniformly relative through the that all persons having an interest in the problem of piping flexi- various stressed portions of the piping system. bility willsimilarly contribute their ecmments). One point which was developed in thew comments deserves mention here. The II. C.10. Mrmn." To the author should go the thanks of the Code should definitely provide for alternate procedures of inter- Society and industry in general for his most execilent paper, pretation in certain exceptional cases where all interested parties Many years ago the writer discovered that when he became can agree upon an anner based upon sound engineering principles involved in the subject of Stremes in pipinat as the result of thermal even if this implies deviating from a strict and literal application expansion he was entering a labyrinth from w hich he has not been of the Code rules. Otherwise, legil or contract technicalities. able to extricate himscif to thi< day. enforced by in<iectnre powericss to make execptions, may require That the subject is a most complex one is attested by the long uneconomical design. Bibliography accompanving the paper. and some of the names that appear in this liibliography are one8 that w illlong he remem. F. M. Lanex.u Referring to the Preamble 617 of the Pr* bered. Such men as Prnf. Wi!!iam I!oveaani. Mr. Sabin Crocker, posed Rules for Chapter 3. Section G. of the Code for Prenure W R H. IWeim. Mr. A. R. C. Markt, and m iny, many others Piping, and also to the fourth and fifth paragraphs under Sc!'- Spring and Cold-Spring EEccts of the present paper, dealing a "Analy,is of Basic Probi.ms of Ilich Temperature Creep." by with the relstation of the first hot cycle of a pipinir syatem, the O. D. Sherhv and 111 Nrn. following commenta arc otTered: ""MetalNnncal Aspects of Strength at IUch Temperature " by G. V. Smith.
" Staf Engineer. Bttns and Roe.'Inc.. New York. N. Y.
" Gibbs & Cot. Inc.. New York. N. Y.
437
havs done much to throw light on the subject and provi le means Thus the u*e of cold spring in so far as stress is concerned be-to calculate the straw. and reactions which may be encounterni comes of little importance, but is of importance where the rene-
, in service a* a result uf the expansion of piping, tions and moments at attachments to equipment are concern.,h The mere disliculties involvnt in computing the phpical char- The proposed revision to the Code includes the accessary 4
acteristic, of claborate piping systems are in themwives enor- formulas for dealing with these reactions. mous, and we owe an everlasting debt of gratitude to Profeasor In conti.lcring this complex subject, the committee has kept Hovgaard for the ba ic equations he .leveloped. strongly in mind three fundamental principles: On the surface it would appear that once we had methods for (a) Any remiirements in a Code must be kept as simple a4 determining the stresses, all that would be necessary wonld be swible, since a C.nle i< not a textbook, but an attempt to estab-to set satisfactory limits on such trese for various conditions, lish sienp wts as to when danger might esist. and that would be the end of the matter. Ilowever, in a paper (6) The greatret cur + of regulations is that they regulate by Mr. D. II. Ros*heim and Mr. A. R. C. Markt in July,1140, too much and, by so doing. cramp the free him of the designer, the conerption of a stress range came into prominence. and sometimes even reault in freak designs being developed to When the writer was first asked to accept membership on the circumvent unreasonable regulations. Subcommittee on Flexibility, he was still very much'of the opinion (c) Since the u hole subject is exceedingly complex, the deter-that, by determining the stresses ca accurately as practicable and mination, as to the methad to be used for making analyses and as establishing limits for these stresses, all would be well, as this to when ruch computations are required, should be left in the method had given satidactory results in the reany Naval ves<eis hands of the designers w ho, on the other hand, should be prepared where they were applied. to provide necessary data, if and when a serious need for same is But then the stress-range concept begin to enter the picture indicated, tnd, while it took the writer some time to get even a hazy view In conclusion, the writer wishes to thank the author and all the af the importance of this conception,it became a part of the pro- members of the committee for what they have accomplished and posed revision to the Code as the result of two very fortuitous state that it is his belief that the sooner this proposed Code can circumstances. be adopted, the better it will be for industry. The writer was required to spend considerable time in Turope a There are many comments that still have to be digested but it year ago, but before leaving asked a small group to work on a is hoped that before long the co:nmittee can meet again and clean draft of the proposed revision. This group consisted of Messrs. up the loose ends. Markl, Spielvogel, Illair, and Wallstrom, and the writer cannot refrain from stating once more his appreciation to these men for L. PAcu." The author's paper and the reports of the Task the wonderful work ther did in coming up with a proposed draft, Force are valuable contributions to a better understanding and which, after the committee as a whole met, was submitted to the clarification of the many prob! cms involved in the growing field Executive Committee as a report, and has been circulated to of pipe.* tress analysis. the membership. This discussion is concerned only with the brief statements The second fortuitous circumstance is that for the past year the given by the tuthor on approximate assumptions. Sincedetailed, writer has been somew hat "under the weat her" which perhaps has correct pipe-stress calculations are very time-consuming, a large m given him more time to think, and as a reault has come to accept volume of woric is done by usis g approximate assumptions. the concept of tha stress range not merely with some reluctance Therefore a more detailed commeat on some of these assump-but enthusiastically as a stroke of genius. tions seems worth while. In order to come to this conclusion, he had to develop a certain While the author's statements hold for the majority of pipe-few mentalimages ahich would make it clear what was involved stress problems, some exceptions r iay occur. Regarding the sub-in using the stress-range concept, stitution of square corners for curved memters, there are pipe The first point was that in Professor IIovgaard's work he states bends having large radii (R = SD, or larger), and heavy wall that where a pipe is increased in length between two anchorage thicknesses, whose virtual lengths are smaller than those of the points as the result of temperature, the stresses are substantially substituting square corners. This willbe the case when the virtual the same as would occur if the anchorage points were moved bend length, L' - 1.571 KR ieless than the length of the square mechanically by an external force which produced a displacement corner, L = 2R or for all bends, whose flexibility factors arc less equal to the increase in length due to temperature, except for dif- than firences due to changes in moduli of cleticity. 2 The second point was that based on the foregoing statement: K= g g , = 1.273 . if we were to erect a piping system cold with 100 per cent cold spring in all directions, we could compute the streues in the While t here are (cw bends u it h such low K-values, their existence, cold condition and when this system was heated up to the full nevertheless, should be noted. Substitution of square corners for temperature, the stress in the hot condition would be zero, such bends will tend to " loos <n up rather than " tighten" the , On the other hand, if the system were erected with zero cohl pipe. rpring, the strews would be equal to those occurring in the Whether the substitution of square corners for bends and elbows cold condition with im per cent cold spring except that they will result in an over or un.lerestimate of the streases is difficult would be opposite in sien anil that they would be somewhat less to predict. Ibiiles the fleubility factor and stnw-intensification because of the di;Terences in mailuli of clastivity, factor, the prolmrtion of curvni memler lengths to total pipe Next, when establi<hing limits of stress for the strenes as com. length, and the location of the curved members with respect to puted for the cohl con lition with im lwr cent cold sprine, the the neutral asis (tbru<t line) will also atiert the end results. The strens which can occur under any future conditions is limited, neutral axis itscif may shif t censiilerably when the square-corner whether cold spring is used or not, sub*titution is made, thus changing the moment arms as well as We have the phenomena of self-sprine and relaxation to con. the forces. A chift of the Imint of maximum stress for the two sider, and while tice factors will not attert the stress range to as<umption* aim mar result, which the pipe will le ,ubjected, they will tend to relieve the msximum stremes in either the hot or cold condition. n GI R&cw Dicidon. Artimr G. SteKee and Co.. C!mland. Ohio. Assoc. Mem. ASME. I i va , I i
cm . i p Regarding the assumption that the neutral axis parallels the The Task Force reported that the amount of relaxation is un- , line counwting the anchors, this holds only for synunetry with known and cannot le judged reliably. If this were completely ;' respect to a line. For pipes ahirh are symmetrical with re* lect so, the writer would point out that thi. uncertainty would con- ; to a point (such na a nymmetrical hhape), this nssumption stitute a very good reason for taking steps to assure complete [ would place the neutral axis as owing through the anchors. freedom from s. tress in the hot condition in onler to minimiec But such a position of the neutral axis would result in zero- local creep due to relaxation. llouever, the writer would point bending moments and zerodiending stress at the anchors, which out that either the relaxation properties of piping materials are obviously is incorrect, well known or may be readily determined by well.known relaxa-tion creep tests. If the protwed new wetion is to make no pro-C. S. L. Rosissox." The stress range with emphasis on the vision for estimating numerically the relaxation characteri< tics anticipated cycling is certainly of greater phyeical significance of a piping system, the writer recommends that it ought to give than the maximum cembined stress. It is better not to combine definite encouragement to the elimination of all need for relaxa-(as we have teen doing) stress components like the pressure tion during the carly periods of operation by requiring installation longitu linal stress and the weight-load stress with the thermali to be such as will assure it to be free from stress when hot. expansion strtss which may be relieved by yielding or by cold spring. The preuure longitudinal stress may be considered fully D. B. Rossustu8i Axo E. F. Sucmta.88 The author is to be by conservative selection of pipe-wall thickness to accommodate congratulated for the broadly comprehensive discussion he has the pressure circumferential stress. With shipboard piping the presented, which more than fulfills the purpose of the paper in weight-load strenes are negligible because numerous supports are explaining the background of the Task Force Report. In this used tolimit sway and vibration. paper the author has documented carefully the accepted facts, It also may be puinted out that the stress-rance concept is uw- and his well-thought-out conclusons are largely incontestable ful where the movement is not entirely thermal. Such an exam- within the contines of presentalay knowledge. Therefore this ple occursin shiphoard piping. If a pipe extends over a considera- discussion will attempt to do no more than ca!! attention to a few ble length of the vessel,its flexibility may be increamt to accom- points on which we feel further progress is mostly to be desired. modate hull strains. Both this hull-movement stress and the We note that in describing the General Process of Solution. thermal-expansion stress will be reduced by any plastic strain in wherein the author has listed significant physical properties of the the piping, and what are most serious about these stresses are pipe material, he has omitted such properties as tensile strength their periodicities. and various measures of ductility, as well as impact values and However, it is undesirable to state: " Formal calculations or transition temperature. While we do not have any specific pro-model tests shall be required only where reasonable doubt exists posals to otter at this time we should hke to suggest that fracture as to the adequate flexibility of a system." This statement im- in pipe materials often may be dependent upon properties which plies that the approximate thermal-expansion stresses are readily at present are largely unassessed, and that a fully dependable observable. Such is frequently not so. Furthermore, with higher design basis awaits further fundamental research in the mechs-temperatures (above, say,800 F) detailed thermal-stress estiroates nism of fracture made under the co-operation of engineers and are profitable not only because of the larger thermal movements physical metallurgists, but also because of the greater cost of the alloy piping and of its Under the subject Flexibility Factor, we should like to call fabrication. With the current lesseningof business activity more, attention to what we believe is a noteworthy omission in not and not less, attention could be directed to thermal-stress details. discussir.g the work of Clark and Reissner (author's reference Our ASA Code may be too conservative but this should be cor- 107), who succeeded in obtaining an asymptotic solution of the rected by increasing the allowable stress or stress-range values, differential equations leading to the simple expression: Eaxr.st L. Romxsox.# The writer wishes to emphasize the 3 (1 - pry k-importance of recognizing and trying to evaluate and limit the 1 A maximum accumulated total strain in any worst location. where The paper is an excellent exposition of the proposed new section on flexibility of the Code for Pressure Piping. Certainly it is k = flexibility factor highly de*irable to take cognizance of the stress ranee an.1 pre- y = Poisson's ratio orribe a limitation for it. Certainly the initial streu does relas A = ticxibility characteristic and tend.4 to anneal away. But, by this very proccu, it does add Using a value of r = 0.23 the flexibility factoris found to be to accumulated creep. Creep is not uniform but it tends to be concentrated in the k = 1.65 most highly strened elbows or rims of pipe while t he lower st ressed lengths provide follow-up clasticity to multiply creep in critical regions. It would be desirable to try to evaluate the situation in thus confirming by rigornus analysis the fleskin approximation given as the author's Fornmla 121 these places and prescribe suitable limit <. The writer is somewhat teu than a itiatied with the comparison, On the subject 8tren-Intensitication Factors, it might be embodied in the alcebr,ic formulations given in the Appen.lix to well to point out that there is some inconsi. trncy in attemptme the report of the Task Force. The=e formulation.< represent only carefully to evaluate local st resses and cyclic etiects under thermal one set of conilitions whereas it would seem appropriate to give expansion of piping while ignoring them in other forms of loading. cognizance to at lea.: four sets of conditions: (a) hot condition; In both piping and veuct codes at p esent, local effects gener,lly are taken e,re of hv a margin in the allowable stremes, and deti-(b) cohl condition; (c) range of
- tress or straint (J) maximum nitely cyclic service i< lef t to the respon<ibility of the de=igners.
total local creep. With piping calculations, stress intensifications at least have of ten
l'ncincer. Central Technical Detri-tment shipbuiblime Divi ion.
Bethichem s.vl company, tNincy. Atu*. \ tem. M\f 1:. s' t'hief \lechanical lineincer. The it. W. Kelloeg Company. New
" Structural 1:ntineer. Turbine Dni ion. t'encral l'lectric Com-
. York. N. Y. .\lem. M.\t t!.
pany, Schenectady. N. Y. Fellow A811!!. at Stechanical En.cineer. The M. %'. Kellogg Company. 430
- 7 a
f v Sone unaam sned; thus past, experience would not sprear ta sup-port an extreme need for the detailed recognition of them which At nome length the author hu discusaed What Systems it... m is proposed. Further supporting this conte ntion it is also recalla! quire Analysia. We concur with the author and others on th
?
that the author points out cl where that a safety factor of about Task Force regarding the impowbility of formulating =imp I 2 is available at the proposed allowable strean levels, even 7000 cycles. system. up to rules which will predict accurately the stresses in an We further agree that the vague guidance which thr ii Regstding the author's Formula [s!, expreeing a relation be- Task Force felt more or less compelled to retain is qtute mth. ! tween failure stress and number of cycles, there appearn to be a cient for a Standard of Good l'ractice. The salient point. how ever, is that the l'iping Code may be considered no longer auch a ! good powibility that the component 0.2 may vary cemsiderably . depending on the material and po+ibly up m its condition (i.e., standard since it is rapidly being adopted as a Safety rode, it. cold-worked or heat-treated). Evidence of this appeared in rules becoming mandatory and enforecable by law. Thu4 the t{ cyclic tests of IS-8 corrugated expansion joints where an exponent propo<rd wording leaves the designer in a legally indefensible *~ of about 0.33 was indicated. Further data relating to this ques- position unless he takes on a full burden of calculation *. Fur-1 tion have been presented by L. F. Coffin, thermore, nll p tmissible wording op rates to the detriment of the - Attention is again directed to the etforts of Clark and Reissner responsible manufacturer who would be obliged to live up to thr from which a theoretical outer surface circumferential atress. most stringent interpretation, whereas those who have no reputa. 1 intensi6 cation factor of tion to maintain would not hesitate to use the loophole afforded and prepare no calculations whatsoever. ~, 0.8138 Y12 (I --o') ,,h80 The solution of Alt. Par. 610 proposed to the Task Force bv our h% h% representative, Mr. Wall 3tmm, is adndttedly not beyond im. provement. Besides changes to the values given, additional cri. may be obtained for pipe bends subjected to in-plane bending if teria might incorporate such con 3iderat Poisson's ratio is taken as 021 If the streas-intensification factor is related to the fatigue properties of straight pipe. following the or hazard to personnel. Regardless we are convinced that it is a step in the rn;ht direction to set up author's dc6nition, the foregoing relation should be divided by definite requirements stipulating that eertam piping be calculated. a factor of 2, representing the stress-m. . m herent The fact that a preci<e detection of every rase of overstress can-tensification factor. to plain pipe as compared to polished bsrs. The operation yields N
, 0,9 Mh MbMW MM MMim d gi% mi4 m of ed lim 8"
p7. analysis at all Even the most experienced piping-stress analy=ts ' often do not anticipate correctly the results of their calculations. which offers partial substantiation of the author's Formula (51, Hence we conclude that if a criterion esists which for the a Regsrding the section Self-Spring and Cold-Spring Diects, user of the Code will even moderately reduce the guesswork in we believe that designers should be warned of certain practical this matter, such a criterion still muat besdjudged a worth-while aspects of applying cold spring. If the operation is to be fully tool with which to encourage sounder engineering, effective, it is not usually sufficient to cut the pipe short and J simply pull the ends together for the closing wald: counter- At rnon's Cimt:as
- y moments also should be applied when the last joint is made to The voluminous discussion of this paper is an encouraging arrest angular displacements of the adjoining parts (as would be token of the wide interest commanded by its subject.The required on the bend presented in Fig. 2. in addition to eimply author, the Task Force. and piping engineers at large owe a lar pulling the ends together through a distance ELL For the cold- debt of gratitude to the di.<cussers who have given freelv of their springing or high-pressure turbine leads in space configurations, knowledge and experience, either to highlight the improve the writers' company han found it expedient to apply such counter- made in the code formulation or direct attention to remaining moments by suitably located force =, the hication and magnitude shortcomings-the latter mostly the rceult of oversimplification of which are carefully cah ulated. in the interest of providing rules which could be followed by the average engineer. .
The author's remarks regarding the so-called relaxation limit invite some comments. At a temperature w here viscous creep is In order not to add unduly to the length of this paper, the I , signi6 cant, it would seem that the asymptotic value of residual author's clo ing remarks u ill be confined primarily to those phases ' stress would be zero. At lower temperaturca, the process taking about which quc<tions have been raisent. It is gratifying to n place consists of local yielding accompanied by the usual strain that the general approach has met with unanimous approval and hardening. - This leads eventually to a fully clastic action, and dissenting comments are largely of a cautionary nature, intended . the whole operation would seem to be dependent more upon the to warn against too implicit a reliance on the rules to the exclu-shape of the part than the material of which it is made. We sion of good judgment. The $ should be interested to have the author point out any evidence suggi~ted ticxibility and stress-intensiScation factors he has found to support the existence of the relaxation limit an a have been accepted cencrally as reticetink the best available in. I bons tide material property. formation. , In fact. Meurs. D 11. Ro*heim and E. F. Sheaffer , , In his di4cus* ion of Allowable Reactiona. the author have posed gone further by demonstrating in ih tail how wall the pro. directs value4 attention to a problem which has in en the ource of a con-idera- fnr curved members are confirmed by Clark and ble waste of pipe material. We refer particularly to the case of lleis.-ner% an.4 -i<. Mr. J. Ik Ilrork'* euggestion, that equal pumps, turbinen, and other equipment for which the manufac- applicabihty of the<c factor
- to out.of. plane hending be crapha-turers havr been known to make it a condition of their warranty sired in the l' rop.ml Itule<. Las since been acted upon by that no pipine reactiens he impoel w hatsoever. As the author chaner in Lte I to Chart I shown in the last, April 1,1%4. .
points out, such a requirement is quite impractical since the draftpip-of theTek Force !!cport. i ing must u<ually absorb etpansion of the equipment a* well as Mr. F. M. Kamarck i4 alone in questioning ihe ticxibility of its own exp.msion. It is hnprd that enntinued empha i< nf thia elbows and bend.< nnd suggesting upward revision of the strc44-point will in. luce equipment mannfsturera intensification factor *: the author contb-e4 to dit!iculty in fol-j to inte-tieate and lowine his motivatmn. provide for re.sonable limit of allowable piping reactions. to incline to the oppo.,ite view;Mr+.rs. llocheim and SheatTer i while accepting the values sug-D 440 e
~
1
------w - . - -
geated for the stresa-intensification factors as proprr, they ques- ultimate condition), and finally the total strain. Ilowever, even tion w hether it is really necessary to include t hem in calculations, if the knowle.lge and eyerience were available to set limits for referring to preuure-venet design practice where similar factors each of thene items, the complexity engendered would be pro-are tacitly absorbed in the safety factor. While conceding that bibitive no that every single analysia would require the attention a similar pr cedent exi ts for piping-stress analvais, the author of an espert. To reduco the problem to a practical level, the believes it unmund to submerge calculable variabica in the wafety stress range, the initial hot reaction, and the ultimate cold reae-factor, its function being to take care of re-idual uncertaintiet tion were sclerted from this array as the most significant per-If the nfety factor m>w eminalied in the rules was felt to be too formance yardsticks; and the limits for the stress range, and the high-and there are experienced piping- tress analvats who in- etress cimnoting the relaution limit (an operating constant cline to this view-it would appear more logical to correct this rather than a true physical progwrty), were relati,I to the allowa-by expanding the allowable attess range, following 5!r. C, S. L ble stresses entablished elsewhere in the Code for Pressure Piping. Robinuan'a excellent advice. No separate limitation on the total amount of creep was estab-Whether the rules are too conservative or not depends on their lished, the reasoning being that the strc<*-range limitation would future interpretation by customers and inspection authorities, at the same time serve to control the total > train, and this view is In the author's opinion, the stress range adopted is sutliciently still held by the Subgroup as applicable to the average piping
- conservative to allow the designer a remannable amount of lati. system. IIowever, Mr. E. L Itobinson's comments led to an in-tude, by which is meant that the error introduced by making vestigation of leu u<ual configurations characterited by small approximations could run to something hke 25 per cent without branches where relaxation would not be etTcetive as a re ult of causing concern. In this phase of engineering, as in others of a elastic follow-up from the larger, loacr strev<cd portion of the compics nature, hard and fast rules never abould be allomi to line nnd the long-time ductility of the grain boundary (which take precedence over sound engineering judgment; they should could be as low as I gwr cent) could be exhausted; to cover the-e be used only to develop it or to supplement it. Both 51r. II. C. E. cases a cautionary note has since been inserted in the preamble Meyer and Mr. J. E. Brock have warned against fettering the (see April 1,1951, issue of the Task Force lleporth stress analyst by too strict a regulation or too literal an inter- Mr. Kamarck, while approaching this topic from a ditierent pretation of any mies devised; the author would like to join them angle, appears to have been guided by the same fear as Mr. floh.
in a plea for enlightened enforcement, neither too strict nor too inson. Ilowever, his statement that any stressing beyond the lenient. Perhaps the body of authoritative opinion encompassed elastic limit, even though it occurs only once, constitutes a dan-in this discussion may help to bring this about. gerous weakening is not borne out by experience, in the piping While still on the subject of approximations and accuracy, the field or elsew here. It would condemn as unsafe the bulk of high-author wishes to signify his agreement with the conclusions temperature piping installed in the past 20 years which has been reached by Mr. J. E. Brock and Mr. L. Pach relative to the ef- designed to stress limits not much diderent from, often consider-fect of square corner assumptions. It might be added that much ably higher than, tho:.e established in the Proposed Rules. This greater deviations from the mathematically accurate results than includes carbim-molybdenum steel piping, which is known for its are revealed in Fig. 7 of the paper would be obtained if the low ductility under prolonged creep loading.
. complete range of flexibility factors (up to 25) for long-radius Of course, where legitimate doubt exists as to the ability of a welding elbows within the range of sizes and thicknesses of material or system to absorb creep.100 per cent cold spring re-American Standard 1136.10 were considered, mains a solution. Ilowever, as Messrs. Rossheim and Sheader
, The only remaining issue of importance concerns the effects point out, it is not as simple to cold-spring a system properly, as ! of local yielding or creep and the resultant relaxation. The author would appear at first glance. Incidentally, the % factor in the concurs with Mr. E. L Robinson that a complete analysis of a formula for the hot reaction, about which Mr. Brock has raiscel piping system under thermal expansion should consider at least questions. has been put there to allow for the uncertainty of at-several stages or factors descriptive of its stress-and-strain his- taining the designed cohl spring in actual installation; the sin-tory, and desirably should include the initial hot and cold stresses gle formula given in the Proposed Rules, however, is sufficient, and strains, the ultimate (related) hot and cold stresses and since the cohl-spring factor c by definition is limited to unity as I strains, the strees range and the incan stress (primarily for the a maximum. l l l l t l l G 441 l i I l
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