Cost minimization of a ring-stiffened conical shell loaded by external pressure

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1 Please refer o he followg: Farkas J, Járma, Orbá F Cos mmzao of a rg-sffeed cocal shell loaded by exeral pressure WEDING IN THE WORD 5:(5-6) pp (008) Cos mmzao of a rg-sffeed cocal shell loaded by exeral pressure J. Farkas,. Járma, F. Orbá 3 Professor emerus, Uversy of Mskolc, Professor, Uversy of Mskolc, 3 Professor, Mhály Pollack Egeerg College, Uversy of Pécs, Hugary Absrac A rg-sffeed slghly cocal shell s opmzed for exeral pressure accordg o he desg rules of De Norske Veras. The whole legh ad he dffere wo ed rad of he shell are gve. The shell s dvded o equdsa segmes wh oe sffeer each segme. Each segme has dffere shell hckess deermed usg a bucklg cosra ad each rg-sffeer of welded square box seco s desged by meas of he requred mome of era. The opmal umber of shell segmes (op) s deermed by meas of coss calculaed for a seres of. The cos fuco cludes he maeral, fabrcao ad pag coss. The shell membrae sresses are deermed also by fe eleme mehod. ey words: cocal shell, shell bucklg, fabrcao cos, mmum cos desg, ecoomy of welded srucures. Iroduco Cocal shells are appled umerous srucures e.g. submare ad offshore srucures, arcraf, ubular srucures, owers, aks, ec. Ther srucural characerscs are as follows. - Maeral: seels, Al-alloys, fbre-reforced plascs, - Geomery: slghly cocal (raso pars bewee wo crcular shells), srogly cocal (sorage ak roofs), rucaed, - Sffeg: rg-sffeers, srgers, combed, equdsa, o-equdsa, - Sffeer profle: fla, box, T-, -,Z-shape, - oads: exeral pressure, axal compresso, bedg, orso, combed, - Fabrcao echology: weldg, rveg, bolg, glug.

2 löppel ad Mozel [] have carred ou bucklg expermes wh rucaed usffeed ad rg-sffeed seel cocal shell specmes ad proposed smple formulae for crcal bucklg sress. Rao ad Reddy [] have worked ou a opmzao procedure for mmum wegh of axally loaded, smply suppored, sffeed rucaed cocal shells. Recagular rgsffeers ad srgers are used ad cosras o shell bucklg as well as o aural frequecy are cosdered. I he book wre by Ellas e al. [3] expermeal resuls ad desg of sffeed cocal shells are reaed cosderg several load cases. Spagol has wre a PhD hess o bucklg behavour ad desg of sffeed cocal shells uder axal compresso [4]. Recagular srgers are cosdered. aer Spagol also wh co-auhors [5,6,7] has publshed oher arcles hs feld. Chryssahopoulos e al. [8] have used fe eleme mehod for bucklg aalyss of srger-sffeed cocal shells compresso. Sger e al. [9] have gve a dealed descrpo of expermes carred ou wh sffeed cocal shell models. Mmum cos desg has bee worked ou for rg-sffeed crcular cyldrcal shell, subjec o exeral pressure our sudy [0,]. I he prese sudy we selec he followg srucural characerscs: seel, slghly cocal shell, rg-sffeers of welded square box seco o avod rppg, equdsa sffeg, exeral pressure, weldg. Desg rules of De Norske Veras [,3] are appled for shell ad sffeer bucklg cosras. The varables o be opmzed are as follows: umber of shell segmes () (Fg.), shell hckesses (), dmesos of rg-sffeers (h, r). The umber of sffeers s +, sce sffeers should be used a he eds of he shell, hus, wo sffeers are used he frs shell segme. The rg sffeers are placed a small dsace from he crcumfereal welds coecg wo segmes o allow he speco of welds, hs s marked Fgure by doed les. The cos fuco cludes he cos of maeral, assembly, weldg ad pag ad s formulaed accordg o he fabrcao sequece. The opmzao process has he followg pars: (a) desg of hckesses for each shell segme gve by wo rad (R ad R+) usg he shell bucklg cosra, (b) desg of rg-sffeers for each shell segme usg he sffeer bucklg cosra, (c) cos calculao for each shell segme ad for he whole shell srucure.

3 3 These desg seps should be carred ou for a seres of segme-umbers. O he bass of calculaed coss he opmum soluo correspodg o he mmum cos ca be deermed. Desg of shell hckesses Accordg o DNV rules [3], for shell segmes bewee wo rg-sffeers of rad R ad R+ he bucklg cosra vald for crcular cyldrcal shells wh equvale radus e R R, cos cos R () a R R 0 a, R a R, () ad equvale hckess 0 e cos (3) The ormal sress due o exeral pressure a shell segme should be smaller ha he crcal bucklg sress where pr b y cr, 4 e E f f y (4) C E e, e (5) e cos 0.6 C 4, Z, E e Z (6) Ree R + R 0 =

4 4 R + h R ef h E r x R R E h r Fgure. The ma dmesos of he cocal shell a shell segme wh he rg-sffeer of welded square box seco Usg Eqs (5), Eq (6) ca be wre he form of C e (7) R e e From he shell bucklg cosra Eq (4) he ukow ca be calculaed usg a Mahcad algorhm. 3 Desg of a rg-sffeer for each shell segme For rg-sffeers a square box seco welded from 3 pars s seleced o avod rppg, whch s dagerous falure mode for ope-seco sffeers (Fg.). The cosra o local bucklg of he compressed sffeer flage accordg o Eurocode 3 [4] s expressed by h, / 4, 35/ f (8) r y for fy = 355 MPa /δ = 34. Calculag wh Eq (8) as equaly, he oly ukow for a square rg-sffeer s he hegh h. Ths dmeso ca be deermed from he sffeer bucklg cosra relag o he requred mome of era of a sffeer seco abou he axs x of he po E, whch s he gravy ceer of he cross-seco cludg he 3 sffeer pars ad he effecve par of he shell (Fg.)

5 5 where I I y x x I req h 6 4 b pr R E 3h h ef E 3h E ef 3Ey RE f E 3 y h / 3h ef ef h 3 ef, ef 0, ef. R 0.005R / 3 ef (9), (0) ef m 0 56 () h RE R h ye (3) The requred h ca be calculaed from Eq (9). We do o cosdered a sgfca dfferece ed resras for he wo ed segmes. 4 The cos fuco The cos fuco s formulaed accordg o he fabrcao sequece as follows []. () Formg of 3 plae elemes for shell segmes o slghly cocal shape (F0). () Weldg 3 curved shell elemes o a shell segme wh GMAW-C (gas meal arc weldg wh CO) bu welds (F). (3) Weldg of + rg-sffeers each from 3 elemes wh GMAW-C flle welds (F). (4) Weldg of a rg-sffeer o each shell segme wh GMAW-C flle welds (F3). (5) Assembly of he whole sffeed shell srucure from shell segmes (F4A). (6) Weldg of shell segmes o form he whole shell srucure wh - crcumfereal GMAW-C bu welds (F4W). (7) Pag of he whole shell srucure from sde ad ousde (P). The oal cos cludes he cos of maeral, assembly, weldg ad pag M F0 F F F3 F 4 P (3) M km V, km.0$ / kg (4) () The volume of he whole srucure cludes he volume of shell segmes (V) ad rgsffeers (Vr) V V V (5) r 0. 5 F0 kf f e, R 5, e

6 6 F 0 F 0 (6) where he facor of fabrcao dffculy s ake as f 3 ad he seel desy s ρ = 7.85x0-6 kg/mm 3, kf =.0 $/m. where F kf 3 V.3x0.5x0 x e, F F (7) e e (8) 3 V R 3 F k F 3Vr.3x0.3394x0 awx4 R h (9) R h / h R h Vr 4 rh r he dffculy parameer s 3. A dffere pars hs parameer ca be also dffere, for smple plaar srucures s ca be, for more complcaed spaal srucures ca be 4. he flle weld sze aw = 0.7δh. F F (9a) 3 F 3 k F V3.3x0.3394x0 a w x4r, V V Vr 3 (0) F 3 F 3 (0a) F 4 F4A F4W,F4A kf V, F 4 W F 4W () F 4W P P 3.3k x0.5x0 xr () F.9358 Rmax R P P, P kp 4 0 (3) k h R h / (4) P 4 kp = x4.4x0-6 $/mm. We could cosder also he mmum wase of plae cug process, bu hs case we cosdered oly he mmum cos of he srucure. Mmum wase ca be cosdered, whe more dffere srucures are made smulaeously. 5 Numercal daa (Fgure ) Toal shell legh = 5000, sde rad Rm = R = 850 ad Rmax = R+ = 850 mm, yeld sress of seel fy = 355 MPa, wh a safey facor for yeld sress fy = fy/., exeral pressure esy p = 0.5 MPa, safey facor for loadg γb =.5, Posso rao ν = 0.3, elasc modulus E =.x0 5 MPa.

7 7 6 Resuls of he opmzao The dealed calculaos are carred ou for umbers of shell segmes = 3-5. The correspodg maeral ad oal coss are summarzed Table. Table. The maeral ad oal coss $ for vesgaed umbers of shell segmes. The opma are marked by bold leers M I ca be see ha he opmum umber of shell segmes for maeral cos s Mop = ad for oal cos op = 6. Ths dfferece s caused by he fac ha he fabrcao (assembly, weldg ad pag) cos represes a large amou of oal cos. The cos daa show ha, he fabrcao cos, he formg of plae elemes o shell shape, weldg ad pag have a sgfca par. I order o characerze he dmesos of he opmum srucure, he ma daa are gve Table. Table. Ma dmesos ( mm) of he opmum shell srucure ( = 6) R h r The fabrcao ad pag cos compoes for he opmum srucure are gve Table 3. Table 3. Fabrcao ad pag cos compoes $ for he opmum srucure of = 6 F0 F F F3 F4A F4W P ΣP

8 8 Fgure. Fe eleme resuls of he cocal shell sresses The membrae sresses shell segmes have bee calculaed also by fe eleme mehod (FEM). The COSMOSM.8 (verso 56 ) program wh fe elemes SHE4 has bee used. Number of elemes was 466, ad umber of odes was 43. The maeral was lear elasc ad he Gauss egral has bee used. For = 0 he sresses are MPa, whle hose opmzao process are 0-4 MPa, hus, a good agreeme s amog hese values. Fgure shows he membrae sress values obaed by FEM. Accordg o he FEM lear bucklg aalyss, whch does o cosder he effec of al mperfecos ad resdual weldg sresses, he crcal exeral pressure s.85 MPa, so he opmzed srucure s safe eough agas bucklg. 7 Coclusos The opmum desg problem s solved for a slghly cocal shell loaded exeral pressure wh equdsa rg-sffeers of welded square box seco. The opmum umber of shell segmes s foud, whch mmzes he cos fuco ad fulfls he desg cosras. The hckess of each shell segme s calculaed from he shell bucklg cosra. Ths cosra s smlar o ha for crcular cyldrcal shells, bu equvale hckess ad segme legh s used accordg o he DNV desg rules [3]. The dmesos of rg-sffeers for each shell segme are deermed o he bass of he rg bucklg cosra. Ths cosra s expressed by he requred mome of era of he rg-sffeer cross-seco. The cos fuco cludes he cos of maeral, formg of plae elemes o shell shape, assembly, weldg ad pag. The fabrcao cos fuco s formulaed accordg o he fabrcao sequece. The formg, weldg ad pag coss play a mpora role he oal cos.

9 9 The cos dfferece bewee he maxmum ad mmum cos he vesgaed rage of shell segme umber ( = 3 5) s ( )/9588x00 = 7%, hus, a sgfca cos savgs ca be acheved by opmzao. The rg-sffeg s very effecve, sce he usffeed shell eeds a hckess of 4 mm, whch s urealsc for fabrcao. Ackowledgeme The research work was suppored by he József Öveges scholarshp OMFB 0385/006, gve by he Naoal Offce of Research ad Techology (NTH) ad he Agecy for Research Fud Maageme ad Research Exploao (PI). Refereces. löppel,. & Mozel,E. (976) Traglasversuche a sählere, uversefe ud rgversefe egelsumpfschale. Tel. Versuchsberch. Sahlbau 45, No Rao,S.S. & Reddy,E.S. (98) Opmum desg of sffeed cocal shells wh aural frequecy cosras. Compuers & Srucures 4, No.-, Ellas,C.P., Supple,W.J. & Walker,A.C. (984) Bucklg of offshore srucures. odo, ec. Graada Publ. 4. Spagol,A. (997) Bucklg behavour ad desg of sffeed cocal shells uder axal compresso. PhD hess, Uversy of odo, odo. 5. Spagol,A. & Chryssahopoulos,M.. (999a) Bucklg desg of srger-sffeed cocal shells compresso. J. Sruc. Eg. ASCE 5, No Spagol,A. & Chryssahopoulos,M.. (999b) Elasc bucklg ad posbucklg behavour of wdely-sffeed cocal shells uder axal compresso. Eg. Sruc., No Spagol,A. (00) Dffere bucklg modes axally sffeed cocal shells. Eg. Sruc. 3, No Chryssahopoulos,M.., Pogg,C. & Spagol,A. (998) Bucklg desg of cocal shells based o valdaed umercal models. Th-walled Sruc. 3, No.-3, Sger,J., Arbocz,J. & Weller,T. (00) Bucklg expermes: expermeal mehods bucklg of h-walled srucures. Vol.. Shells, bul-up srucures, composes ad addoal opcs. New York, Wley & Sos. 0. Farkas,J., Járma,., Syma,J.A. & Godos,Gy. (00) Mmum cos desg of rgsffeed welded seel cyldrcal shells subjec o exeral pressure. Proc. 3rd Europea Cof. Seel Srucures, Combra, 00, eds. amas,a. ad Smoes da Slva,. Uversdade de Combra, Farkas,J. & Járma,. (003) Ecoomc desg of meal srucures. Roerdam, Mllpress.. De Norske Veras (DNV) (995) Bucklg sregh aalyss. Classfcao Noes No.30.. Høvk, Norway. 3. De Norske Veras (00) Bucklg sregh of shells. Recommeded Pracce DNV-RP- C0. Høvk, Norway. 4. Eurocode 3 (00) Desg of seel srucures. Par -: Geeral srucural rules. Brussels, CEN.