INFLUENCE OF PRESSURE IN PIPELINE DESIGN EFFECTIVE AXIAL FORCE

Transcription

1 Procdng of OM005 Inrnaonal Confrnc on Offor Mcanc and rcc ngnrng (OM 005) Jun -7, 005, Halkdk, Grc OM ILUC O PRUR I PIPLI IG CTIV XIL ORC Olav yrlv and Lf Collbrg ork Vra, Vravn, -3 Høvk, orway BTRCT T ar dcu u of ffcv axal forc conc n offor ln dgn n gnral and n V cod n arcular. T conc of ffcv axal forc or ffcv non a bn known and ud n ln and rr ndury for om dcad. Howvr, rcnly a dcuon abou wa nad and doub on ow o ra nrnal rur rad. Hofully ar wll conrbu o xlan u of conc and rmov doub n ndury, f x a all. T conc of ffcv axal forc allow calculaon of global bavour wou condrng ffc of nrnal and/or xrnal rur n dal. In arcular, global bucklng, o-calld ulr bucklng, can b calculad a n ar by alyng conc of ffcv axal forc. T ffcv axal forc alo ud n V-RP-05 r annng ln o adju naural frqunc of fr an du o cang n gomrcal ffn caud by axal forc and rur ffc. rcn ar clamd, owvr, a ffc wa oo of on gvn n V-RP-05 and may cau confuon abou wa arora way of andlng rur ffc. I gnrally accd a global bucklng of ln govrnd by ffcv axal forc. Howvr, n V Pln andard V-O-0, alo local bucklng crron xrd by u of ffcv axal forc conc wc aly could b mundrood. Local bucklng, of cour, govrnd by local r, ru r, n l wall. Tu, m unraonabl o nclud ffcv axal forc and no ru axal forc a ud n formr V Pln andard V 96. T raon for xland n dal n ar. T ar gv an nroducon o conc of ffcv axal forc. urr xlan ow conc ald n modrn offor ln dgn. nally background for ung ffcv axal forc n om of V ln cod gvn. Kyword: Pln, ffcv axal forc, Prur ffc, ln cod. ITROUCTIO T ffcv axal forc ofn condrd a a vrual forc n conra o o-calld ru axal forc gvn by ngral of r ovr l cro-con. I, owvr, a conc ud o avod ngraon of rur ffc ovr doubl-curv urfac lk a dformd by bndng. T man roblm w nrnal and xrnal rur a ffc of ofn oo of wa on nananouly nk corrc. Trfor ffc av bn ourc o mundrandng and wrong dgn. On xaml, a gvn by Palmr and Baldry (97), a rag ln rrand by rgd ancor block n ac nd. Wn xod o nrnal rur, a nl r dvlo n oo drcon. u o Poon ffc, oo r wll nd o orn. nc ornng rvnd by ancor block, r n nl drcon alo bcom ov. of ln wll buckl wn rur rac a cran crcal lvl a own n xrmn conducd by auor. T xlanaon of conradcon of cour ffcv axal forc wc bcom ngav a rur buld u. T como acon of flud/ga rur and l axal forc wll cau bucklng. Coyrg 005 by M

2 wll b own lar, ffcv axal forc govrn rucural ron of ln n an ovrall rcv, nfluncng on laral bucklng, uaval bucklng, ancor forc, nd xanon and naural frqunc of fr an. or raon of oumo moranc o undrand ffc and b abl o ma accuraly n ordr o nd u w a af and rlabl dgn. Wn com o local ffc lk local bucklng, l r and yldng, ru axal forc govrn. Howvr, a n lar n ar, ffcv axal forc may ll b ud o mlfy dgn crron. vn oug ffcv axal forc a bn ud n ln cod for vral dcad, for xaml V 76 (976), ll mundrood and mnrrd wn com o ffc of rur. T ffc of nrnal rur rad by for xaml Palmr and Baldry (97) and ark (983, 98), wo md o nroduc rm ffcv axal forc. Qu rcnly Galgoul al (00) and Carr al. (003) clamd a xron for ffcv axal forc and way ald n om V cod lk V-O-0 and V-RP-05 wrong. T no ca a own n followng. T ar wll no com u w any nw xron or alcaon for ffcv axal forc. T nnon olly o ry o gv background for conc and alcaon n ln cod. By dong o, o a dgn crra bcom ar o undrand and a wll no b mnrrd n fuur. CTIV XIL ORC COCPT T conc of ffcv axal forc mlf calculaon of ow nrnal and xrnal rur nflunc bavour of a ln. Trfor vry moran for ln dgnr o fully undrand conc. of, xrnc of auor a ffcv axal forc qu ofn mundrood and ald wrongly. T ffcv axal forc xland n dal n many ar,.g. ark (983). Howvr, a or dcron ncludd rn for ak of comln. T ffc of xrnal rur mo aly undrood by condrng law of rcmd: T ffc of war rur on a ubmrgd body an uward drcd forc qual n z o wg of war dlacd by body. rcmd law bad on aumon a rur ac ovr a clod urfac. Pycally, rcmd law can b rovd by condrng an arbrary volum nd a largr lqud wou any nrnal flow du o mraur /dny dffrnc. nc ffc of rur ovr urfac of arbrary volum an uward forc qual o wg of lqud, arbrary volum wll b n qulbrum and wll nr mov u, down nor o any d. Of cour am concluon racd by mamacally ngrang xrnal rur ovr urfac of volum. ow, condr a con of a ln xod o xrnal rur a llurad n fg.. T only conal forc ncludd axal forc,, o-calld ru wall forc found by ngrang l r ovr l cro-con ara. Or conal forc lk bndng momn and ar forc ar omd for clary a y wll no nr calculaon of ffcv axal forc and ffc of rur. gur - quvaln ycal ym xrnal rur n, con w an axal forc,, and xrnal rur,, (lf fgur) can b rlacd by a con wr xrnal rur ac ovr a clod urfac and gv rulng forc qual o wg of dlacd war, buoyancy of con (mddl fgur), and an axal forc qual o. Condrng ffc of xrnal rur n way a own n fg. do no cang yc or add any forc o con. Howvr, gnfcanly mlf calculaon. T alrnav would b o ngra rur ovr doubl curvd urfac. o alo a varyng rur du o varyng war d ovr urfac nd o b accound for n ordr o g ffc of dlacd war, buoyancy. mlar condraon, a for xrnal rur, may b don for nrnal rur. Howvr, a n from fg. wn condrng a con of a ln w nrnal rur, xrnal forc acng on con axal forc,, and nd ca forc,. gan or conal forc lk bndng momn and ar forc ar omd for clary. rur ac n all drcon n vry on n lqud, nrnal rur wll alway ac on a clod urfac. urr, rur a cu away con nd wll ac a an xrnal axal load n comron. rom condraon of xrnal and nrnal rur acng on a ln con bcom clar a ffc of may b accound for by o-calld ffcv axal forc: () In addon ngrad ffc of rur ovr clod urfac gv: Buoyancy (xrnal rur) Wg of nrnal lqud (nrnal rur) Coyrg 005 by M

3 rom can clarly b ad a ffcv axal forc a ral forc a can b maurd and a av a ycal nrraon. PPLICTIO O CTIV XIL ORC L u ak a look a a fw xaml wr ffcv axal forc conc may b ud o mlfy calculaon of ln ron. On xaml alrady mnond n rvou con; xrnal forc o b ald o lock ln axally or rvn any nd xanon c, fg 3. Tn any ranfr of ar forc a bnd nglcd. gur - quvaln ycal ym nrnal rur CTIV XIL ORC RL ORC? om of confuon among ln dgnr rgardng ffcv axal forc may b du o u of rm ru forc for l wall forc,, and rcon of ffcv axal forc a a fcou, non-ycal forc. T alo clamd by Galgoul al. (00) ang a rm a laral forc and no an axal on. T quon o b anwrd rally; I only forc caung r n wall ral forc? L u condr am xaml a ark (983), a rnforcd concr bam. nc concr only r ngnfcan nl r, load-barng caacy of concr lmn may b mrovd by ung r-rd (nl) rnforcmn. Wou any xrnal load, concr wll b n comron and rnforcmn n non. Bu wa ral axal forc n bam? I n comron du o concr r? I obvou a an ngraon ovr oal cro-con, ncludng bo concr and rnforcmn r gv an axal forc qual o zro. T como axal forc a clar mlar o ffcv axal forc conc. Tu anwr from a ffcv axal forc a ral forc. Bu ow could b nrrd or maurd? If ran gaug ar mound o ln, l ran and u, l r and rby l wall forc or ru axal forc may b dducd. L u, owvr, condr a ln rmnad w a blnd flang wc could b ca durng rur of ln ym. If nd fr o mov, no xrnal load ac on (aumng no xrnal rur,.. abov a war). Wn ln rurd wa wll axal forc bcom? rom ml qulbrum calculaon obvou a ru, l wall forc wll b qual o (n non) and ffcv axal forc wll b ff - 0. T man a ffcv axal forc forc on may maur a blnd flang. urr ffcv axal forc a mu b counracd n ca axal xanon of ln nd ar o b avodd or ln o b lockd axally w nrmn rock brm,.g. o con a o ln and nur conrolld laral bucklng. ll y of ln ancorng and nd rmnaon mu condr ffcv axal forc. gur 3 - orc o rvn any axal xanon a bnd c. g. ow ln durng nallaon ung a ycal -lay barg w ln bn ovr ngr and n ag bnd nar abd. gur Pln durng convnonal -lay nallaon. By ml condraon ung ffcv axal forc conc, axal forc n ln afr nallaon can b mad. qulbrum of orzonal forc rqur a ru axal forc,, n ln afr nalld,.. a abd, qual o barg non, l, n addon o ngrad ffc of xrnal rur. In addon orzonal comonn of rollr conac forc a ngr mu b accound for, bu ar omd r for mlcy. mnond arlr ngraon of varyng xrnal rur ovr doubl-curv comlcad. Howvr, by clong ngraon urfac, can aly b own a ffcv axal forc a boom mu b: () l ccounng for orzonal forc comonn of rollr and any or rlaxaon du o axal ldng c l 3 Coyrg 005 by M

4 lad o o-calld rdual lay non, H. T forc o b condrd a an ffcv axal forc. ow, ung H a ffcv axal forc afr nallaon, ru axal forc bcom: H (3) ln orad, ru axal forc g no comron du o rmal xanon (- α ΤΕ) and no non du o oo r and Poon ffc (ν ) f no allowd o ld axally (fully rrand). T ru forc bcom: H ν α T rom dfnon of ffcv axal forc, followng dducd: H ν H [ ν ] α T α T wc am xron a gvn n V-O-0. o a n V-O-0, rlacd by. T do no man dffrnal rur bwn our and nrnal rur, bu cang n nrnal rur from nallaon, accounng for a onal war-flld nallaon w a ydroac rur nd. V-O-0 CTIV XIL ORC n alrnav roof of ffcv axal forc for a fully rrand ln wll b gvn n followng. T bad on wo fundamnal xron; ffcv axal forc and Hook law: (6) (7) ε l [ l ν ( r )] α T wr ε l axal (longudnal) ran, l, and r ar axal, oo and radal r, ν Poon rao, α rmal xanon coffcn and T mraur dffrnc. urr, followng rlaon aly: / (8) l ( ) / (9) ) / (0) r ( wr l cro conal ara of, and ar xrnal and nrnal damr and nomnal wall ckn. L a-nalld ln condon b dnod w an ndx. T only un-known n condon longudnal ran wc gvn by Hook law a: () ε l, [ l, ν (, r, )] α T () (5) m wn ln lad down, do no rly on any forc ranfr bwn ol and, nc, ffcv axal forc qual o boom non forc, H (ffcv forc). T quaon can n b r-wrn a:,,, ε l, ν H,,,,,, ν T α, α T () wr H (ffcv) boom non. urng oraon, dnod ndx, longudnal ran wll b, mlar o abov:,, ε l,,,, ν, α T (3) nc axally rrand; ε l, ε l, and can b olvd from (ng q. () qual o q.(3)): H,,,,,,,, ν T α,,,, ν α T () urr, xrnal rur am,..,, and dffrnal mraur from rfrnc (.. T - T ) can b dnod a T and quaon can b mlfd a: H,, ν, ν,,, α T (5) Inroducng a nrnal rur dffrnc from layng (.., -, ) quaon rad: H 0 ν α T H ν α T (6) (7) Coyrg 005 by M

5 T xrnal rur wll no affc ffcv axal forc n oraonal condon. T H T H α ν α ν 3 (8) Bo Palmr and Baldry (97) and Hobb (98) ar corrc and accordng o V formula wn com o nrnal rur. V-O-0 LOCL BUCKLIG T local bucklng crron n V 96 for nrnal ovr rur bad on a ur von M calculaon, condrng wo dmnonal r ag n wall. In gnral rm bcom: 3 3 Co f M M M c () To on, only mlfcaon a radal r aumd conan acro wall ckn. Howvr, abov quaon can b aroxmad w: [ ] T H α ν (9) T ordr of rror nroducd (of rur conrbuon) by mlfcaon : ν ν 3 (0) Concnrang on brack n nomnaor of Con rm, a bn l u no funconal and nvronmnal load n V 96 a: () and lod n fg 5. T rror of mlfcaon l an % for / largr an 5!. o a rror vald for nrnal rur rm only and rally nglgbl. I alo wor o mnon a n mo HTHP ca, rmal xanon rm a domna ffcv axal forc. T can b r-wrn by ncludng dfnon of ffcv forc, dfnd a: (3) l no funconal and nvronmnal ar bcom () w / Rlav rror 0 Includng dfnon no nnr brack of con rm, bcom: ( ) (5) umng n walld can b r-wrn a ( ) ( )... ( ) (6) gur 5 - ma of rror du o mlfcaon of axally rrand r formula T concluon from dducon ar: T gvn formula, q. 5. n V-O-0 corrc f can b condrd a a n walld - rror du o mlfcaon can b n n gur 5. Hnc, brack n nomnaor can b mlfd by ung ffcv forc. T local bucklng formulaon a 5 Coyrg 005 by M

6 bn furr dvlod by Taylor xanon, ncludng ran ardnng and or mnor adjumn o f w analy n V-O-0 bad on am rncl a xland abov. Hnc, local bucklng formula a bn drvd a by u of ru wall forc. Howvr, rul urn ou o b mlr f convrd o ffcv forc. T followng commn aly: T nw forma mlr o u and undrand. I wll ud for rformng dgn cck (g(x)<) n conncon w global analy. Comard o orgnal formulaon, ulaon unalrd for bndng domnan ca. T lm a now alcabl alo n ca of axal forc and rur only. T forma and axal forc ulaon conn w radonal r-bad von M crra. o a rur rm ar no facord. xrm rur ca ar andld n (ym) bur cck. V-RP-05 R P RPO T mo moran aramr wn com o rucural ron of fr an naural frquncy. T aramr nr rducd vlocy and rby govrn wr vorx nducd vbraon wll occur or no, gvn our damr and flow vlocy normal o an. By cangng naural frquncy,.g. by nroducng addonal an uor or rducng an lng, VIV ron may b mgad. rom xbook lk Cloug and Pnzn (975), obvou ow axal forc nflunc on dynamc and frqunc of a fr annng ln. Howvr, r av bn a lo of mak wn com o ffc of nrnal rur n varou ar and ror. T la xaml ar by Galgoul al. (00) wr clamd a nrnal rur wll ncra frquncy. nc dcuon abou ow rur ffc nflunc on frqunc or mor rcly f nrnal rur nd o ncra or dcra frqunc, of oumo moranc o g gn rg, condrng govrnng quaon of dynamc for bam. v P M Q q R MdM QdQ gur 6 orc acng on an nfnmal lng of a bam. dx P x By condrng qulbrum of laral forc and bndng momn acng on bam con own n fg. 6, dynamc quaon of moon for bam con xod o an axal nl forc, P, and a drbud laral forc, q, rad: v v v (7) I P m q( x, ) wr v laral dlacmn, x axal co-ordna, m and I and m bndng ffn and dynamc ma r un lng, rcvly. T clacal oluon o dffrnal quaon wou any laral forc (fr vbraon) gv followng fundamnal vbraon frquncy: I P f 0 C ml Pcr (8) wr L an lng and P cr crcal bucklng axal forc wr an buckl. o a P and P cr ar ov n non, and a P cr and a conan C dnd on boundary condon of an, for mor cfc gudanc V-RP-05 or yrlv and Mørk (00). T P cr rm may b rlacd by ulr bucklng forc for a nnd-nnd an, P I/L (ov n comron) and a cond boundary condon conan, C : I C f 0 C ml P P (9) Wa an wn bam or u n war and ubjcd o xrnal and nrnal rur n addon o axal forc? Lookng a govrnng dffrnal quaon obvou a mo of rm rman am; ffc of bndng and axal forc do no cang. o a axal forc, P, rcly akng o-calld ru axal forc,, gvn n V-O-0 and V-RP-05. T forc ngrad axal r ovr l cro-con and conan rm from rdual lay non, mraur xanon ffc, Poon ffc from oo r and any axal xanon/ldng ffc. or ca w n war and xod o nrnal and xrnal rur, vbrang ma wll alo nvolv ma of conn and ydrodynamc addd ma ( ffc of movng roug war and crang rur ffc around crcumfrnc). v v v (30) I m q( x, ) ff mnond, xrnal and nrnal rur wll av an ndrc ffc on quaon roug oo r and Poon ffc on ru axal forc. Howvr, a own by Galgoul al. (00), ffc of nrnal rur can b n a a laral forc, q. Condr nfnmal lng of a own n fg. 6 wc dformd w a radu R v/. u o dformaon, fbr a comron d bcom orr an 6 Coyrg 005 by M

7 on a nl d. T rlav ornng bcom (Rr nφ)/r wr φ dfnd n fg. 7. gur 7 formd cro con w nrnal rur and w a bndng radu R. T n ffc of nrnal rur wll b mlar o a drbud load, q. T ngrad ffc bcom: R r n φ v (3) r n φd / R R 0 x q φ wr r dno nrnal radu. T govrnng quaon of moon now bcom: v ( v v I ) 0 m ff and fundamnal frquncy: f I C 0 C m L ( ) P (3) (33) In am way ffc of xrnal rur can b ncororad. I n a by ung dfnon of ffcv axal forc: (3) R/d v/dx bo govrnng dffrnal quaon and xron for frquncy ar mlfd. Of cour am xron would av bn dducd f conc of ffcv axal forc a bn ald n ad q φ of axal forc, P, from bgnnng. Tn cumbrom ngraon of doubl-curv urfac would av bn avodd. L u condr q. (7) wou dynamc rm (nra rm). Havng no xrnal drbud load bu ncludng xrnal and nrnal rur wll lad o an quaon mlar o q. (3) bu wou nra rm: v I v ) 0 ( (35) olvng quaon gv followng crcal load, bucklng load, for a nnd-nnd boundary condon: cr cr I L (36) T ow a r a clar rlaon bwn ow nrnal (and xrnal) rur affc bo global bucklng and naural frqunc of a an. I alo qu obvou a naural frquncy wll dcra a nrnal rur ncra. nally, a ffcv axal forc aroac crcal bucklng load, frquncy aroac zro, 0. Howvr, occur for orcal ca w nnd-nnd uor condon. In raly, a ln an wll xrnc a gradual dflcon or aggng a wll gv ra o non-lnar ffc no accound for n xron abov. By raon, naural frquncy of fr an ould b mad by u of or ool,.g. non-lnar analy, wn ffcv axal forc rac a cran valu and non-lnar ffc bcom gnfcan, a rcommndd n V-RP-05. nor commn o b gvn o q. (36) a xron gv crcal bucklng forc for a nnd-nnd an. or mor ralc boundary condon, V-RP-05 gv om advc for a ngl an uord on ol (flxbl an ouldr). In ca, a C coffcn qual o 0.5 ud n combnaon w an ffcv lng of an longr an aarng an lng. Howvr, nnon of xron for rucural ron gvn n V-RP- 05 o uor calculaon of VIV and fagu and no o gv xac gudanc on an bucklng. or mo ral an, an dflcon wll gradually ncra a ffcv axal forc nd oward crcal bucklng valu a corrcly ad by Palmr and Kay (99) and Galgoul al (00). T dflcon wll rla om of axal forc and may alo cau an o van a an g lmd. nyway, a ffcv axal forc ncra n comron and aroac orcal bucklng lm, ln ron bcom comlcad and gly non-lnar. Trfor, xron bad on lnar bam ory can no b ald and mu b rlacd by for xaml non-lnar analy. u o, rang of alcably for xron bad on bam ory n V RP-05 lmd o or and modra an lng L/ < 0, modra dflcon δ/ <.5 and modra gomrcal ffn ffc C ff /P < 0.5- T xland n mor dal n ar by yrlv and Mørk, Coyrg 005 by M

8 COCLUIV UMMRY T followng commn can b ud o ummar dcuon wn ar: ffcv axal forc a vry ml and ffcn conc o accoun for rur ffc. T xron for ffcv axal forc n V cod corrc aloug om mlfcaon av bn mad. T local bucklng nfluncd by ru l wall forc and oo r. T V-O-0 local bucklng crron bad on ffcv axal forc. In way crron mlfd comard o alrnav ung ru axal forc. T naural frquncy wll dro a nrnal rur ncra. T rur ffc on frquncy of a an accound for by ffcv axal forc conc. RRC Carr, M., Bruon,. and Ll,.., Laral Bucklng and Pln Walkng, a Callng for Ho Pln, OPT003, Offor Pln Tcnology confrnc, mrdam, T rland, 003. Bruc, R., nazz, M., Val, L. nd Vrly, R., Laral nakng of Ho Prurzd Pln Mgaon for Troll Ol Pln, Procdng of OM996, 996. V 76, Rul for gn, Conrucon and Incon of ubmarn Pln and Pln Rr, ork Vra January 976. V 96, Rul for ubmarn Pln ym, ork Vra, cmbr 996. V-O-0, V Offor andard ubmarn Pln ym, ork Vra, January 003. V-RP-05, V Rcommndd Pracc, r annng Pln, ork Vra, Marc 00. yrlv, O. and Mørk, K., rucural Ron of Pln r an bad on Bam Tory, Procdng of OM00, Olo, orway, 00. Galgoul,.., d Barro, J.C.P. and rrra, R.P., T Inracon of r an and Laral Bucklng Problm, Procdng of IPC 00, Calgary, Canada, 00. Galgoul,.., Maa,.L.L. and Claro, C.., cuon on How Inrnal Prur Trad n Offor Pln gn, Procdng of IPC 00, Calgary, Canada, 00. Hobb, R..., In-rvc Bucklng of Had Pln, Journal of Tranoraon ngnrng, vol. 0, o, Marc 98. Palmr,.C. and Baldry, J..., In-rvc Bucklng of Had Pln, Journal of Prolum Tcnology,. 83-8, ovmbr 97. Palmr,.C. and Kay,., Raonal mn Crra for Pln an, OPT, Offor Pln Tcnology confrnc, 99. ark, C.P., T Influnc of Tnon, Prur and Wg on P and Rr formaon and r, Procdng of OM, 983. ark, C.P., T Influnc of Tnon, Prur and Wg on P and Rr formaon and r, M ranacon vol 06,. 6-5, Coyrg 005 by M