CREEP TRANSITION STRESSES OF ORTHOTROPIC THICK-WALLED CYLINDER UNDER COMBINED AXIAL LOAD UNDER INTERNAL PRESSURE UDC

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1 FACA UNIVERSIAIS Sees: Mechcl Egeeg Vol. 11, N o 1, 013, pp CREEP RANSIION SRESSES OF ORHOROPIC HICK-WALLED CYLINDER UNDER COMBINED AXIAL LOAD UNDER INERNAL PRESSURE UDC Pkj hku Deptmet of Mthemtcs, Idus Itetol Uvesty Bthu, Id Abstct. Effect of sotopy hs bee llustted gphclly. It s foud tht the sotopy of the mtel hs lttle effect o dl stess but the effect s moe pomet o the xl d tgetl stesses fo hghe to of sotopc costts log the dus. he esults dcte the mxmum stess s ot lwys o the sufce. Key Wods: Ceep, Cylde, Lod, Pessue, Stesses 1. INRODUCION A thck wlled ccul cylde s wdely d commoly used ethe s pessue vessel teded fo stoge dustl gses o s med tspotto of hgh pessuzed fluds. Ceep of the thck-wlled cylde ude tel pessue hs bee dscussed by my uthos [1-10, 1, 13, 15]. At hgh tempetue, ts thck wlled tubes subjected to tel pessue d xl lod exhbt cotuously cesg defomto wth dectos. he thck wlled cylde ceep ude tel pessue loe my be foud ltetue fo sotopc [6-9] d othotopc [10-11] mtels. At hgh tempetue, the thck-wlled tubes ude tel pessue e usully plced vetcl posto. Axl lod s thus exeted o the tube ot oly by tel pessue but lso by ts ow weght. Whe xl lod s exeted o the tube ddto to the tel pessue, the stess dstbuto s lteed. Solutos become moe complcted. It must be oted tht geel, the soluto cot be obted by combg the effects of septe lods. he poblem of the thck wlled cylde ceep ude combed xl lod d tel pessue hs bee dscussed by Fe [1], Schwcke d Sdebottom [13] the sotopc ceep the- Receved Febuy 1, 01 Ackowledgemets. he utho e gteful to the efeee fo hs ctcl commets, whch led to sgfct mpovemet of the ppe. Coespodg utho: Pkj hku Deptmet of Mthemtcs, Idus Itetol Uvesty Bthu U, Hmchl Pdesh-17301, Id E-ml: pkj_thku15@yhoo.co.

2 1 P. HAKUR oy. Rmott [6] lyzed the bove poblem by tkg to cosdeto lge st. hs utho mde the followg ssumpto: 1) he mtel s compessble.e. z 0. (1) ) Axes of sotopy cocde wth the pcpl xes of the cylde. 3) he ceep defomto s ftesml d the pessue s ssumed to be ppled slowly d held costt dug lodg. ) hs poblem s ssumed to be tht of geelzed ple st so tht z K. () I ths ppe, the dstbuto of stess d ceep te hve bee obted wth the help of dgtl compute by cosdeg the costtutve equtos of the sotopc theoy gve by Bhtg d Gupt [11].. SOLUION AND DISCUSSION OF HE PROBLEM Cosde ufom thck wlled cylde of tel d extel d d b espectvely, subjected to tel pessue p d xl lod L. Co-odtes, d z e tke dl, ccumfeetl d xl dectos of the cylde espectvely. he comptblty equto s: d. (3) d Combg equto (3) wth equto (1) d tegtg, oe gets: C K C K,, z K. () whee C s the costt of tegto. Fudmetl costtutve equtos fo sotopc theoy e gve by Bhtg d Gupt [9] s follow: [( GH) H Gz] [( H F) Fz H], z [( F G) z G F ]. (5) Stess vt s defed s: 1 1 [ ( ) ( ) ( ) ] F z G z H. (6) whee F, G, H e costts of the mtel d s the st te vt. Stedy-stte ceep te s fucto of stess oly. Assumg Noto's lw of ceep, we c wte:, (7)

3 Ceep sto Stesses of Othotopc hck-wlled Cylde ude Combed Axl Lod whee costt mesue. Substtutg equto (5) the vlue of d fom equto () d solvg fo z, we obt: K C C K ( F H) F G ( G H) z. C K ( F G) ( F G) Substtutg fom equto () d z fom equto (8), equto (5), oe gets: C K 1 ( F G) ( F G). HF FG GH Afte substtutg the vlue of stess vts d st te vts fom equto (6) d (7) equto (9) the esultg equto becomes: 1` C ( F G) 1 1 C K K F G F G F G H 1 HF FG GH ( ) ( ) ( ). (10) C K ( ) F G he equto of equlbum e gve by: d. (11) d Itegtg equto (11) fte substtutg vlue of ( ) fom equto (10) d setg boudy codto = 0 t = b leds to: C ( F G C ) 1 ( F G ) 1 K ( F G H) d, 1 HF FGGH K b (1) ( F G) C ( ) K F G he tgetl stess s gve by: d. (13) d he xl stess blces the sum of extel xl lod L d tel pessue p.e. b zd p L. 1` (8) (9) (1)

4 16 P. HAKUR Let us defe the dmesoless quttes s follows: / p, / p, 1 1 D. C, 1 FG GH HF p zz z / p, R / b, C C / b K C d 3 R0 / b. (15) Equto (1) o dmesol becomes: 1 1 ( F G H) 1 ( F G) ( F G) 3 d D., (16) 1 ( F G) ( F G) 3 3 wth = 1 t = R. Also 1 1 ( F G H) F G F G D ( F G) ( F G).. (17) d the xl stess becomes: F G ( F H) ( G H) 3 3 zz. (18) F G F G 3 Stess dstbuto equto (16) s solved by Smpso's Rule fo vlues of. Costt D equto (16) s foud by tkg = 1 t = R d the, C s detemed fom equto (15).hus, stesses, d zz e detemed fo vous vlues of fom equtos (16), (17) d (18) fo kow vlues of d. Cuves hve bee dw Fg. 1 fo stess dstbuto log dus fo dffeet vlues of G/F, H/F d = 5. he effect of sotopy s otceble moe o the xl d tgetl stesses. he stess whee the vto log the dus s pomet fo hghe tos of sotopc costts. he esults dcte tht mxmum stess s ot lwys o the sufce. p zz p p z z Fg. 1 Stess dstbuto log the dus of thck wlled cylde ude combed xl Lod d tel pessue.

5 Ceep sto Stesses of Othotopc hck-wlled Cylde ude Combed Axl Lod PARICULAR CASE Cse 1 Fo vshg sotopy, F = G = H = 1 d Equtos (16), (17) d (18) becomes: C d 3 p 1 1 1, (19) C , 3 p (0) zz Equtos (19) d (0) e sme s gve by Fe [7] fo sotopc cse. Cse Ple st ude tel pessue: If = 0 d L = 0, the poblem educes to the thck wlled othotopc cylde tel pessue loe fo the cse of ple st. O substtutg vlues d L equtos (16), (17), (18) d solvg wth boudy codto = 1 t = R, oe gets: 1 b, b () 1 1 b, b (3) d F G zz. F G () Equtos () () e sme s gve by Pooj Kum [15] d Bhtg d Gupt [11] cse of pl st.. (1). CONCLUSION Mtel sotopy s foud to hve lttle effect o dl stess but the effect s moe pomet o the xl d tgetl stesses fo hghe to of sotopc costts log the dus. Nomecltue, b Ie d oute dus of the cylde,, z cyldcl pol co-odte,, z stesses compoets mesue p pessue L Lod

6 18 P. HAKUR C costt of tegto F, G, H costt of the mtels st te vt Geek lettes R = / b; R 0 = /b Rd to Rdl stess compoet ( / p) Ccumfeetl stess compoet ( / p) zz Ccumfeetl stess compoet ( z / Y). REFERENCES 1. Gupt, S.K., Dhm, R.L., 1979, Ceep tsto thck wlled cylde ude tel Pessue, Z.A.M.M., 59(10) pp Gupt, S.K. 'Elstc-plstc d ceep sto of hck-wlled Cylde ude Ufom Pessue', Poc. of It. Symp. o No-le Mech. Khgpu, 1980, pp hku Pkj, Guv Shm,009, Ceep tsto stesses thck wlled ottg cylde by ftesml defomto ude stedy stte tempetue, Itetol Joul of Mechcs d Solds, (1) pp hku Pkj,01,Stedy theml stess d st tes ottg ccul cylde ude stedy stte tempetue, heml Scece, DOI Refeece: 10.98/SCI P. 5. hku Pkj, 01, Stedy theml stess d st tes ccul cylde wth o- homogeeous compessblty subjected to theml lod, heml Scece, DOI Refeece: 10.98/SCI P. 6. Rmott, F.P.J.,1959, Ceep of thck-wlled tubes ude tel pessue cosdeg lge sts, J. Appl. Mech., 81(sees E) pp Kg, R.H. d Mcke, W. W.,1967, Ceep of thck-wlled cylde, J. Bsc Eg., 87(sees D) pp , S., Kotezw, R. d Oht, R.,1965, Ceep of hck-wlled cylde ude tel pessue t elevted tempetue, Poc. 8 th Jp Cogess o estg Mtels, J. Jp Soc. Mt. Sc., 83 pp We, C.D.,1957, he ceep of thck-wlled cylde ude tel pessue, J. Appl. Mech., () pp P, D.H.,1967, Stedy stte ceep lyss of thck-wlled othotopc cyldes, It. J. Mech. Sc., 9 (6) pp Bhtg, N.S. d Gupt S. K.,1969, Alyss of thck-wlled othotopc cylde the theoy of ceep, J. Phys. Soc. Jp, 7(6) pp Fe, I.,1960, Stedy-stte ceep of thck-wlled cylde ude combed xl lod d tel pessue, s. ASME, 8(D) pp Schweke, J.W. d Sdebottom, O.M.,1965, Ceep of thck-wlled cyldes subjected to tel pessue d xl lod, Expt. Mech., 8(1) pp Bhtg, N.S. d Gupt R.P.,1966, O the costtutve equtos of the othotopc theoy of ceep, Joul of the Physcl Socety of Jp, 1() pp Kum Pooj, 006, Ph.D hess, Elstc-Plstc d Ceep Poblems svesely sotopc mtels, Deptmet of Mthemtcs, H.P.U. Shml, pp PUZEĆI RANZICIONI NAPONI OROROPSKOG DEBELOZIDNOG CILINDRA POD KOMBINOVANIM AKSIJALNIM OPEREĆENJEM POD UNURAŠNJIM PRIISKOM Dejstvo zotopje gfčk je lustovo. Utvđeo je d zotopj mtejl m mlo utcj djl po d je utcj mogo zžej ksjlm tgecjlm pom z vše koefcjete zotopksh kostt duž djus. Rezultt ukzuju d mksml po je uvek povš. Ključe eč: pužeje, cld, opteećeje, ptsk, po