Annex B. Limit Load Solutions (Based on SINTAP and R6)

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1 (0 y 006) ITET K7 Annx iit od olutions (sd on ITAP nd 6) iit od iit od...-. oncltu...-. Intoduction lt plts lt plt ith though-thicknss l lt plt ith suc l lt plt ith long suc l lt plt ith ddd l lt plt ith long ddd l lt plt ith dg l lt plt ith doul dg l...-. Cuvd shlls phs Pips o cylinds Though-thicknss ccks in cylind ointd xilly Intnl suc l in cylind ointd xilly ong intnl suc l in cylind ointd xilly Extnl suc l in cylind ointd xilly ong xtnl suc l in cylind ointd xilly Pips o cylinds ith cicuntil ls Though-thicknss l in cylind ointd cicuntilly Intnl suc l in cylind ointd cicuntilly ong intnl suc l in cylind ointd cicuntilly Extnl suc l in cylind ointd cicuntilly ong xtnl suc l in cylind ointd cicuntilly ound s nd olts Eddd ls in ound s Cntlly ddd xil llipticl dcts olid ound ; cntlly ddd xtndd dct Tuul joints T- nd Y-Joints ith xil lod T- nd Y-Joints ith in-pln nd out-o-pln nding K-Joints ith xil lods K-Joints ith in-pln nd out-o-pln nding X- nd DT-Joints ith xil lod X- nd DT-Joints ith in-pln nd out-o-pln nding til istch Cck in th cnt lin o th ld til Cck in th intc tn ld tl nd s plt Cck in th intc o i-til joint Cck in th cnt lin o th ld til Cck in th intc tn ld tl nd s plt Cck in th intc o i-til joint Cck in th cnt lin o th ld til Cck in th intc tn ld tl nd s plt Cck in th intc o i-til joint Cck in th cnt lin o th ld tl Cck in th intc tn ld tl nd s plt...-8 ITET 006 All ights svd -

2 ITET K7 Annx.9. Cck in th intc o i-til joint Cck in th cnt lin o th ld tl Cck in th intc tn ld tl nd s pip Cck in th intc o i-til joint i-til (cld) cnt though thicknss cckd plt und tnsion Cnt cckd i-ly (cld) plt ith pi ld ITET 006 All ights svd

3 (0 y 006) ITET K7. oncltu c D E H p p i, o ci, co P P c P hl l lngth o though-thicknss l, l hight o suc l o hl hight o ddd l spcin thicknss, sction thicknss in pln o l hl l lngth o suc o ddd ls dit Young s odulus pplid nol lod nol yild liit lod yild liit lod o istchd ldnts yild liit lod o s til spcin hight pip o spcin lngth nolisd liit ont nolisd liit nol lod nolisd liit pssu nolisd liit coind pssu nd tnsion lod ( o n???) istch tio coss ldnt givn y W / pplid in nd out o pln onts o tuul joints ully plstic onts o cckd tuul joints clcultd o in nd out o pln lods pplid nding ont liit nding ont pplid xisytic though ll nding ont p unit ngl o coss sction liit xisytic though ll nding ont p unit ngl o coss sction pplid xil lod on tuul joint collps lod o cckd tuul joint yild liit pssu p Applid pssu P iit pssu ITET 006 All ights svd -

4 ITET K7 Annx i o W u t inn dius out dius n dius Yild stss istch lo stss o ldnt yild o poo stngth o ld tl yild o poo stngth o s tl cto to llo o th psnc o xil nd ont lods in th chod. stngth cto hich vis ith th joint nd lod typ thicknss o stuctul sction t Ectiv plt o cylind thicknss o dining locl liit lod W Plt idth o hl plt idth W Ectiv hl plt idth o hl cylind lngth o dining locl liit lod δ σ σ σ n, σ n, ν ϑ cck opning displcnt n stss nding stss n coponnt o collps stss nding coponnt o collps stss od tio o coind tnsion nd nding Poisson s tio cck ngl; 90 i ppndicul to th suc,,,θ,ϕ,,ξ,ζ dinsionlss cck siz - ITET 006 All ights svd

5 (0 y 006) ITET K7. Intoduction In clssicl solid chnics th liit lod is dind s th xiu lod coponnt o lstic-idlly plstic til is l to ithstnd, ov this liit lignt yilding cos unliitd. In contst to this dinition, l tils stin hdn ith th consqunc tht th pplid lod y incs yond th vlu givn y th non-hdning liit lod. otis stin hdning is oughly tkn into ccount y plcing th yild stngth o th til y n quivlnt yild stngth clld lo stngth (usully th n o yild stngth nd ultit tnsil stngth) in th liit lod qution. In ITET nlysis th plstic liit lod ks th lod t hich th plstic zon spds coss th hol lignt hd o th cck. o uthos p th t yild lod instd o liit lod in od to distinguish it o th high plstic collps lod hich is chd hn th lignt hs copltly stin hdnd nd th coponnt ils und stss contolld loding. Th stition o liit lod o givn cck/coponnt goty is citicl input to itnss-o-svic ssssnt. This Annx o th Volu III o th ITET copils th K-solutions nd liit lod solutions long oth ndd inotion to conduct nlysis. Cophnsiv st o liit lod solutions coplid to sv s n ccut nd us-indly dt. Th sults o th 790, ITAP nd 6 soucs usd to gnt this Annx. ITET 006 All ights svd -5

6

7 (0 y 006) ITET K7 ITET 006 All ights svd -7 nding stsss s unctions o onts tuctu typ nding stss, σ ith 6 noncltu nding stss, σ ith ITAP noncltu oction Pln Wt 6 d 6 tnsil stss t ll suc (W is plt idth) Pip ith intnl cicuntil dct (xisytic nd) A t 6 ( ) ( ) t 6 t A A 6 A tnsil stss t inn ll suc Pip ith xtnl cicuntil dct (xisytic nd) t 6 ( ) ( ) t 6 t 6 tnsil stss t out ll suc Pip ith intnl o xtnl cicuntil dct (cntilv nd) ( ) ( ) ) t t( t π ) ( π pk tnsil stss t out ll suc

8 ITET K7 Annx olid ound ith cntlly ddd cicul dct (xisytic nd) - 9 tnsil stss t cnt o olid ound ith xtnl cicuntil dct (xisytic nd) - 96 tnsil stss t suc o olid ound (cntilv nd) - π pk tnsil stss t suc o -8 ITET 006 All ights svd

9 (0 y 006) ITET K7. lt plts.. lt plt ith though-thicknss l 6 Applicl clus(s): (.) olution:, W, W γ Pln stss Tsc, pln stss iss nd pln stin Tsc solutions: o 0 < (.) Pln stin iss solution: ( ) o 0 < γ (.) Vlidity liits: Th plt should lg in copison to th lngth o th cck so tht dg cts do not inlunc th sults. iliogphy: [.] A G ill, vi o liit lods o stuctus contining dcts, Int J Ps Vs Piping, 97-7 (988). ITET 006 All ights svd -9

10 ITET K7 Annx -0 ITET 006 All ights svd.. lt plt ith suc l 6 Plts und coind tnsion (pin-lodd) nd nding: Applicl clus(s): glol solution (.), (.), (.5), (.6), (.7), (.8) locl solution (.9), (.0), (.), (.), (.), (.) olution: Dinition: W, W, σ σ 6,, W c, c Glol solution: ( ) > 0 0 o o d d d d (.) ( ) > 0 0 o o d d d d (.) h ( ) ( ) d (.5)

11 (0 y 006) ITET K7 ITET 006 All ights svd - ( ) ( ) d (.6) 0 (.7) o pu tnsion ( 0) nd pu nding ( ) o 0 o 0 (.8) Extndd suc ccks (st ): quivlnt to th solution oly in IV..8.. Though-ll ccks (st ) ocl solution (W c nd ): ( ) ( ) ( ) ( ) > 0 0 o o d d d d (.9) ( ) ( ) ( ) ( ) > 0 0 o o d d d d (.0) h ( ) d (.) ( ) ( ) d (.) ( ) 0 (.) o pu tnsion ( 0) nd pu nding ( )

12 ITET K7 Annx o 0 0 (.) o Vlidity liits: o locl cs th solutions liitd to < iliogphy: [.] [.] Y i, J-intgl nd liit lod nlysis o si-llipticl suc ccks in plts und nding, Int J Ps Vs Piping 8, - (00). Y i, A glol liit lod solution o plts ith si-llipticl suc ccks und coind tnsion nd nding, AE/JE Pssu Vssls nd Piping Connc, n Digo, July , PVP-Vol. 75, 5- (00). - ITET 006 All ights svd

13 (0 y 006) ITET K7.. lt plt ith long suc l Plts und coind tnsion (pin-lodd) nd nding 6 Applicl clus(s): (.5), (.6) olution:, W σ,, 6 σ W t-sction collps solution (pln stss Tsc): ( ) ( ) ( ) o < (.5) ( ) ( ) ( ) o < (.6) o th cs o pu tnsion ( 0) qn. (.5) pplis nd o th cs o pu nding ( ) qn.(.6) pplis. Vlidity liits: (Th solution is liitd to / 0.8. Also, th plt should lg in th tnsvs diction to th cck so tht dg cts do not inlunc th sults.) iliogphy: [.] A A Willoughy nd T G Dvy, Plstic collps in pt-ll ls in plts, AT TP 00, Aicn ocity o Tsting nd tils, Phildlphi, UA, (989). ITET 006 All ights svd -

14 ITET K7 Annx.. lt plt ith ddd l Dcts in plts und coind tnsion (pin-lodd) nd nding 6 Applicl clus(s): IV..6. olution:, W σ c,,,, W 6 σ W p k, c o syticlly ddd ccks, k 0. Glol solution: Extndd ddd ccks st uc ccks st 0.5 k Though-ll ccks st k 0 nd 0.5 c o in(, ) ( ) ( ) c (.7) c o < [ ( ) k] [ ( ) k] c c o in(, ) ( ) ( ) c (.8) c o < [ ( ) k] [ ( ) k] c h - ITET 006 All ights svd

15 (0 y 006) ITET K7 ITET 006 All ights svd -5 ( ) 8 k c (.9) ( ) k c (.0) ( )( ) ( ) ( ) k k k k (.) ( ) ( ) o pu nding 0 o pu tnsion k k k (.) k (.) ocl solution (d c nd t ): ( ) ( ) < o, in o c k k c c c (.) ( ) ( ) < o, in o c k k c c c (.5) h 8 k c (.6) k c (.7)

16 ITET K7 Annx k k k k (.8) k k ( ) k ( ) ( ) o pu tnsion 0 o pu nding (.9) k (.0) Glol solution (pin-lodd): Equtions (IV..6.-) nd (IV..6.-) to (IV..6.-7) (st 0). (IV..6.-) o ddd xtndd dcts, st nd. ocl solutions (pin-lodd): o ddd xtndd dcts, st nd. () W c, nd W/ > W : Equtions (IV..6.-) nd (IV..6.-) to (IV..6.-7) (st 0). (IV..6.-) () d c k, t ( k) nd W/ > d : k k ( ) (.) Glol solution (ixd-gip tnsion): Equtions (IV..6.-) nd (IV..6.-) to (IV..6.-7) (st 0 nd k 0 s liit lod vlu dos not dpnd on cck position in th coss sction). o ddd xtndd dcts, st nd. ocl solution (ixd-gip tnsion): o W c, nd W/ > W : o ddd xtndd dcts, st nd. ( ) (.) Glol solution (nding): Equtions (IV..6.-) to (IV..6.-7) (st ) (IV..6.-) -6 ITET 006 All ights svd

17 (0 y 006) ITET K7 o ddd xtndd dcts, st nd. ocl solutions (nding): o ddd xtndd dcts, st nd. () W c, nd W/ > W : Equtions (IV..6.-) to (IV..6.-7) (st ) (IV..6.-) () d c k ( k), t ( k) nd W/ > d : k k ( k) (.) Vlidity liits: Glol solutions nt-sction collps solution vlid o > k 0 nd k. ocl solutions vlid o > k 0, k nd < iliogphy: [.5] [.6] A J Ct, A liy o liit lods o ACTUE-TWO, ucl Elctic pot TD/ID/EP/09 (99). Y i nd P J uddn, iit lod solutions o plts ith ddd ccks und coind tnsion nd nding, Int J Ps Vs Piping 8, (00) ITET 006 All ights svd -7

18 ITET K7 Annx..5 lt plt ith long ddd l 6. hn cw/ st nd st Applicl clus(s): olution: Vlidity liits: iliogphy: -8 ITET 006 All ights svd

19 (0 y 006) ITET K7..6 lt plt ith dg l 6 Applicl clus(s): Copct tnsion spcin (CT) ; Pln tss & tin (iss & Tsc) (.) - (.7) Th-point-nding spcin (TP); Pln tin (iss & Tsc) (.8), (.9) ingl dg cckd plt und tnsion (ECP); Pln tss & tin (iss & Tsc) (.0) - (.5) ingl dg cckd plt und nding (EC); Pln tss & tin (iss & Tsc) (.6) - (.9) olution: Copct tnsion spcin (CT) ; Pln tss & tin (iss & Tsc), W, W γ Pln stss Tsc solution: ( ) o 0 < (.) Pln stss iss solution: ( γ )( γ ) ( γ ) o 0 < (.5) Pln stin Tsc solution: o (.6) (.70 ) o 0.09 < < Pln stin iss solution: ( ) γ o (.7) γ [ (.70 )] o 0.09 < < Th-point-nding spcin (TP); Pln tin (iss & Tsc) ITET 006 All ights svd -9

20 ITET K7 Annx, W, W γ is th lodd lngth o th spcin : uppot distnc Pln stin Tsc solution: (...9 )( ).( ) o (.8) o 0.8 < < Pln stin iss solution: (...9 )( ) γ ( ) γ o (.9). o 0.8 < < ingl dg cckd plt und tnsion (ECP); Pln tss & tin (iss & Tsc), W, W γ, γ pin-lodd: Pln stss Tsc solution: ( ) o 0 < (.0) Pln stss iss solution:. o (.).70 ( 0.79 ( )) ( ) ( 0.79 ( )) o 0.55 < < Pln stin Tsc solution: [. ] γ o (.).70γ ( 0.79 ( )) ( ) ( 0.79 ( )) o 0.55 < < Pln stin iss solution: [. ] γ o n (.).70γ ( 0.79 ( )) ( ) ( 0.79 ( )) o 0.55 < < ixd gip: Pln stss Tsc nd iss, nd pln stin Tsc solutions: o 0 < (.) -0 ITET 006 All ights svd

21 (0 y 006) ITET K7 Pln stin iss solution: ( ) o 0 < γ (.5) ingl dg cckd plt und nding (EC); Pln tss & tin (iss & Tsc), W, W γ Pln stss Tsc solution: ( ) o 0 < (.6) Pln stss iss solution: ( )( ).07( ) o (.7) o 0.5 < < Pln stin Tsc solution: ( )( ).606( ) o (.8) o 0.95 < < Pln stin iss solution: ( )( ) γ ( ) γ o (.9).606 o 0.95 < < Vlidity liits: iliogphy: [.7] A G ill, vi o liit lods o stuctus contining dcts, Int J Ps Vs Piping, 97-7 (988) [.8] A J Ct, A liy o liit lods o ACTUE-TWO, ucl Elctic pot TD/ID/EP/09 (99). ITET 006 All ights svd -

22 ITET K7 Annx..7 lt plt ith doul dg l..7. init idth plt Plt und tnsion (DECP) 6 Applicl clus(s): (.50) - (.5) olution:, W, W γ Pln stss Tsc solution: o 0 < (.50) Pln stss iss solution: ( )( 0. 5 ) γ ( ) o (.5) o 0.86 < < Pln stin Tsc solution: ( ) ln ( ) o (.5).57( ) o 0.88 < < Pln stin iss solution: γ ( ) ln ( ) o (.5).57γ ( ) o 0.88 < < Vlidity liits: - ITET 006 All ights svd

23 (0 y 006) ITET K7 nc(s): [.9] A G ill, vi o liit lods o stuctus contining dcts, Int J Ps Vs Piping, 97-7 (988). ITET 006 All ights svd -

24 ITET K7 Annx. Cuvd shlls.. phs... Though-thicknss l in sph n stss 6 Applicl clus(s): (.5) olution: t, θ P θ 8 cos θ (.5) Vlidity liits: iliogphy: [.0] udkin nd T E Tylo, ctu in sphicl vssls, J ch Engng cinc, (969) - ITET 006 All ights svd

25 (0 y 006) ITET K7.5 Pips o cylinds.5. Though-thicknss ccks in cylind ointd xilly n stss 6 Applicl clus(s): (.55) olution: t, φ t P.05 φ (.55) Vlidity liits: Th cylind should long in copison to th lngth o th cck so tht dg cts do not inlunc th sults. iliogphy: [.] A G ill, vi o liit lods o stuctus contining dcts, Int J Ps Vs Piping, 97-7 (988). [.] J Kin, W A xy, J Ei nd A Duy, ilu stss lvls o ls in pssuisd cylinds, AT TP 56, Aicn ocity o Tsting nd tils, Phildlphi, UA, 6-8 (97). ITET 006 All ights svd -5

26 ITET K7 Annx.5. Intnl suc l in cylind ointd xilly Pssu-Excluding o Including Cck cs; Glol & ocl Collps 6 Applicl clus(s): (.56) - (.60) olution:, t t, φ c () Glol solutions: (i) Without dct-c pssu: P g ln (.56) h g.05 (.57) φ (ii) With dct-c pssu: P g ln (.58) () ocl solutions: (i) Without dct-c pssu (d c s ( - ) nd t ): -6 ITET 006 All ights svd

27 (0 y 006) ITET K7 ITET 006 All ights svd -7 ( ) ( ) ln ln s c c s P (.59) h ln g c s (ii) With dct-c pssu (d c s ( - ) nd t ): ( ) ( ) ln ln s c c s P (.60) h ln ln g c s Vlidity liits: iliogphy: [.] A G ill, vi o liit lods o stuctus contining dcts, Int J Ps Vs Piping, 97-7 (988). [.] A J Ct, A liy o liit lods o ACTUE-TWO, ucl Elctic pot TD/ID/EP/09 (99).

28 ITET K7 Annx.5. ong intnl suc l in cylind ointd xilly Pssu-Excluding o Including Cck cs 6 Applicl clus(s): (.6), (.6) olution:, t t Without dct c pssu: P ln (.6) With dct c pssu: P ln (.6) Vlidity liits: iliogphy: [.5] A J Ct, A liy o liit lods o ACTUE-TWO, ucl Elctic pot TD/ID/EP/09 (99). -8 ITET 006 All ights svd

29 (0 y 006) ITET K7 ITET 006 All ights svd Extnl suc l in cylind ointd xilly n nd nding stss 6 Applicl clus(s): (.6) - (.68) olution: n, σ, n, σ, σ σ 6, t, t c, W c t o n xtndd xil xtnl suc cck ocl solutions (W t c nd t t): ( ) ( ) ( ) ( ) > 0 0 o o d d d d (.6) ( ) ( ) ( ) ( ) > 0 0 o o d d d d (.6) h

30 ITET K7 Annx d (.65) ( ) [ ( )] ( ) d (.66) ( ) 0 (.67) o pu tnsion ( 0) nd pu nding ( ) o 0 0 (.68) o Vlidity liits: Th solutions liitd to iliogphy: [.6] I W Goodll nd G A Wst, Thoticl dtintion o nc stss o ptilly pntting ls in plts, Int J Ps Vs Piping 78, (00). [.7] Y i, J-intgl nd liit lod nlysis o si-llipticl suc ccks in plts und nding, Int J Ps Vs Piping 8, - (00). [.8] Y i, A glol liit lod solution o plts ith si-llipticl suc ccks und coind tnsion nd nding, AE/JE Pssu Vssls nd Piping Connc, n Digo, July , PVP-Vol. 75, 5- (00). -0 ITET 006 All ights svd

31 (0 y 006) ITET K7.5.5 ong xtnl suc l in cylind ointd xilly n nd nding stss 6 Applicl clus(s): IV.9. ith k VI t in th ist pts o qns. (.6) & (.6) nd qn. (.65) to otin th solution o n xtndd xil xtnl suc cck in cylind und n nd nding stsss. olution: Vlidity liits: iliogphy: [.9] I W Goodll nd G A Wst, Thoticl dtintion o nc stss o ptilly pntting ls in plts, Int J Ps Vs Piping 78, (00). [.0] Y i, J-intgl nd liit lod nlysis o si-llipticl suc ccks in plts und nding, Int J Ps Vs Piping 8, - (00). [.] Y i, A glol liit lod solution o plts ith si-llipticl suc ccks und coind tnsion nd nding, AE/JE Pssu Vssls nd Piping Connc, n Digo, July , PVP-Vol. 75, 5- (00). ITET 006 All ights svd -

32 ITET K7 Annx.6 Pips o cylinds ith cicuntil ls.6. Though-thicknss l in cylind ointd cicuntilly n nd nding stss, glol nd locl solution 6 Applicl clus(s): Thick-lld cylinds und coind tnsion nd nding: (.77) Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: (.7) o though-ll dcts, olution: Thick-lld cylinds und coind tnsion nd nding, π t t,,, θ, t π Glol solutions: Whol cck insid th tnsil stss zon (θ π): θ π π ( ) sin ( ) sinθ c c 6 Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: - ITET 006 All ights svd

33 (0 y 006) ITET K7 ITET 006 All ights svd -, t π, t, t c θ p t P t P t p p π χ ( ) p p p χ (.69) ( ) p p π π (.70) χ χ p p (.7) χ χ p p (.7) Glol solutions: Whol cck insid th tnsil stss zon (θ π) p π θ π (.7) ( ) [ ] sin sinθ (.7) Vlidity liits: iliogphy: [.] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). [.] Y i nd P J uddn, iit lod solutions o thin-lld cylinds ith cicuntil ccks und coind intnl pssu, xil tnsion nd nding, J tin Anlysis 9, (00).

34 ITET K7 Annx.6. Intnl suc l in cylind ointd cicuntilly 6 Applicl clus(s): Thick-lld cylinds und coind tnsion nd nding: (.75) - (.8) Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: (.85) - (.9) olution: Thick-lld cylinds und coind tnsion nd nding:, π t, t, t t c, θ t (.75) π o though-ll dcts, nd o ully cicuntil dcts, θ π. Glol solutions: Whol cck insid th tnsil stss zon (θ π): π θ π (, ) (.76) ( ) sin c (, ) sinθ (.77) Pt o th cck insid th copssion zon (θ > π): - ITET 006 All ights svd

35 (0 y 006) ITET K7 ITET 006 All ights svd -5 ( ) [ ] ( ) π θ π,, (.78) ( ) ( ) ( ) ( ) θ sin, sin, d d (.79) In qns. (.76) to (.79) (.80) (.8) c (.8) ( ) ( ) d 6 (.8) (.8) Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: t, t, t π, t c θ nd o ully cicuntil dct θ π p t P t P t p p π χ ( ) p p p χ ( ) p p π π (.85)

36 ITET K7 Annx -6 ITET 006 All ights svd χ χ p p (.86) χ χ p p (.87) Glol solutions: Whol cck insid th tnsil stss zon (θ π) p π θ π (.88) ( ) [ ] θ sin sin (.89) Pt o th cck insid th copssion zon (θ > π) ( )( ) ( ) p π θ π (.90) ( )( ) [ ] θ sin sin (.9) Vlidity liits: This is nt-sction collps solution. Whn θ > π, cck closu is ignod. o th css o coind pssu nd nding, this solution y usd y convting th pssu into n quivlnt xil lod. Hov, o vy shllo dcts, this ttnt y ovstit th liit lod s th pssu inducd hoop stss s ignod in th divtion o this solution. iliogphy: Thick-lld cylinds und coind tnsion nd nding: [.] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: [.5] Y i nd P J uddn, iit lod solutions o thin-lld cylinds ith cicuntil ccks und coind intnl pssu, xil tnsion nd nding, J tin Anlysis 9, (00).

37 (0 y 006) ITET K7.6. ong intnl suc l in cylind ointd cicuntilly 6 Applicl clus(s): Thick-lld cylinds und coind tnsion nd nding: IV.8. ith k III o ully cicuntil dct θ π Thick Pip und intnl pssu: IV.8. Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: IV.8. ith k III o ully cicuntil dct θ π Thin-lld Cylind und xil lod: IV.8.5 olution: Thick-lld cylinds und coind tnsion nd nding: t,,, π t t t, θ π (.9) π Glol solutions: [ (, )] (, ) (.9) π ( ) [ (, ) sin ] d (.9) In qns. (IV..8.-) to (IV..8.-5) ITET 006 All ights svd -7

38 ITET K7 Annx -8 ITET 006 All ights svd (.95) (.96) c (.97) ( ) ( ) d 6 (.98) (.99) Thick Pip und intnl pssu: t, t With dct c pssu: ln P (.00) i > othis ln P (.0) Without dct c pssu (sld dct): ( )( ) ln P (.0)

39 (0 y 006) ITET K7 ITET 006 All ights svd -9 i ( )( ) ln ln > othis ln P (.0) Thin-lld Cylind: t π, t ( ) ( ) > o o Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: t, t, t π, π θ p t P t P t p p π χ ( ) p p p χ ( ) p p π π (.0) χ χ p p (.05)

40 ITET K7 Annx p p (.06) χ χ Glol solutions: p ( ( ) ) ( )( ) π (.07) [( )( ) sin ] (.08) Thin-lld Cylind und xil lod:, π t t ( ) o (.09) ( ) o > Vlidity liits: iliogphy: Thick-lld cylinds und coind tnsion nd nding: [.6] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). Thick Pip und intnl pssu: [.7] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). Thin-lld cylinds und coind tnsion nd nding ith intnl pssu [.8] Y i nd P J uddn, iit lod solutions o thin-lld cylinds ith cicuntil ccks und coind intnl pssu, xil tnsion nd nding, J tin Anlysis 9, (00). Thin-lld Cylind und xil lod: [.9] A Ainsoth, Plstic collps lod o thin-lld cylind und xil lod ith ully cicuntil cck, ucl Elctic Engining Advic ot EPD/GE/EA/0085/98 (998). -0 ITET 006 All ights svd

41 (0 y 006) ITET K7.6. Extnl suc l in cylind ointd cicuntilly 6 Applicl clus(s): Thick-lld cylinds und coind tnsion nd nding: IV.8. Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: IV.8. olution: Thick-lld cylinds und coind tnsion nd nding: π t,, t, t t c, θ t (.0) π o though-ll dcts, nd o ully cicuntil dcts, θ π. Glol solutions: Whol cck insid th tnsil stss zon (θ π): π θ π (, ) (.) ( ) sin c (, ) sinθ (.) Pt o th cck insid th copssion zon (θ > π): ITET 006 All ights svd -

42 ITET K7 Annx - ITET 006 All ights svd ( ) [ ] ( ) π θ π,, (.) ( ) ( ) ( ) ( ) θ sin, sin, d d (.) In qns. (IV..8.-) to (IV..8.-5) (.5) (.6) c (.7) ( ) ( ) d 6 (.8) (.9) Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: t, t, t π, t c θ p t P t P t p p π χ ( ) p p p χ ( ) p p π π (.0) χ χ p p (.)

43 (0 y 006) ITET K7 ITET 006 All ights svd - χ χ p p (.) Glol solutions: Whol cck insid th tnsil stss zon (θ π) p π θ π (.) ( ) [ ] θ sin sin (.) Pt o th cck insid th copssion zon (θ > π) ( )( ) ( ) p π θ π (.5) ( )( ) [ ] θ sin sin (.6) Vlidity liits: iliogphy: Thick-lld cylinds und coind tnsion nd nding: [.0] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: [.] Y i nd P J uddn, iit lod solutions o thin-lld cylinds ith cicuntil ccks und coind intnl pssu, xil tnsion nd nding, J tin Anlysis 9, (00).

44 ITET K7 Annx.6.5 ong xtnl suc l in cylind ointd cicuntilly 6 Applicl clus(s): Thick-lld cylinds und coind tnsion nd nding: IV.8. ith k III o ully cicuntil dct θ π Thick Pip und intnl pssu: IV.8. Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: IV.8. ith k III o ully cicuntil dct θ π Thin-lld Cylind und xil lod: IV.8.5 olution: Thick-lld cylinds und coind tnsion nd nding: t,,, π t t t, θ π (.7) π Glol solutions: [ (, )] (, ) (.8) π ( ) [ (, ) sin ] d (.9) In qns. (IV..8.-) to (IV..8.-5) - ITET 006 All ights svd

45 (0 y 006) ITET K7 ITET 006 All ights svd -5 (.0) (.) c (.) ( ) ( ) d 6 (.) (.) Thick Pip und intnl pssu: t, t ln P (.5) i > othis ln P (.6) Thin-lld cylinds und coind tnsion nd nding ith intnl pssu: t, t, t π, π θ p t P t P t

46 ITET K7 Annx -6 ITET 006 All ights svd p p π χ ( ) p p p χ ( ) p p π π (.7) χ χ p p (.8) χ χ p p (.9) Glol solutions: ( )( ) ( ) ( ) p π (.0) ( )( ) [ ] sin (.) Thin-lld Cylind: t π, t ( ) ( ) > o o (.) Vlidity liits:

47 (0 y 006) ITET K7 nc(s): Thick-lld cylinds und coind tnsion nd nding: [.] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). Thick Pip und intnl pssu: [.] Jons nd J Eshly, iit solutions o cicuntilly cckd cylinds und intnl pssu nd coind tnsion nd nding, ucl Elctic pot TD/ID/EP/00 (990). Thin-lld cylinds und coind tnsion nd nding ith intnl pssu [.] Y i nd P J uddn, iit lod solutions o thin-lld cylinds ith cicuntil ccks und coind intnl pssu, xil tnsion nd nding, J tin Anlysis 9, (00). Thin-lld Cylind und xil lod: [.5] A Ainsoth, Plstic collps lod o thin-lld cylind und xil lod ith ully cicuntil cck, ucl Elctic Engining Advic ot EPD/GE/EA/0085/98 (998). ITET 006 All ights svd -7

48 ITET K7 Annx.7 ound s nd olts.7. Eddd ls in ound s ITAP Applicl clus(s): p. AII olution: Though ll nding o ininit xisytic ody Eddd Dct; Though Wll nding 8 ( ) σ n,, 9 σ n, (.) t uc Dct; Though Wll nding 8 ( ) σ n,, 96 σ n, (.) t Vlidity liits: iliogphy: [.6] A. J. Ct, A iy o iit ods o ACTUE.TWO, ucl Elctic pot TD/ID/EP/09, (99). -8 ITET 006 All ights svd

49 (0 y 006) ITET K7.7. Cntlly ddd xil llipticl dcts ITAP Applicl clus(s): p. AII. 8-9 olution: Tnsion; Glol & ocl Collps Glol Collps c W (.5) W ( W c) ocl Collps c W (.6) W ( W c) Vlidity liits: iliogphy: [.7] A. J. Ct, A iy o iit ods o ACTUE.TWO, ucl Elctic pot TD/ID/EP/09, (99). ITET 006 All ights svd -9

50 ITET K7 Annx.7. olid ound ; cntlly ddd xtndd dct ITAP Applicl clus(s): p. AII. olution: dil Tnsion W (.7) W Vlidity liits: iliogphy: [.8] A. J. Ct, A iy o iit ods o ACTUE.TWO, ucl Elctic pot TD/ID/EP/09, (99). -50 ITET 006 All ights svd

51 (0 y 006) ITET K7.8 Tuul joints.8. T- nd Y-Joints ith xil lod ITAP Applicl clus(s): p. AIII. - Dsciption: T- nd Y-Joints oding: Axil chtic: iit lod olution: Th chctistic stngth o ldd tuul joint sujctd to unidictionl loding y divd s ollos: h T K P c u (.8) sinθ P C chctistic stngth o c xil lod chctistic yild stss o th chod t th joint (o 0.7 tis th chctistic tnsil stngth i lss). I chctistic vlus not vill spciid iniu vlus y sustitutd. sinθ K (.9) is cto to llo o th psnc o xil nd ont lods in th chod. is dind s: ITET 006 All ights svd -5

52 ITET K7 Annx U γ o xt conditions U γ o opting conditions h 0.00 o c xil lod 0.05 o c in-pln ont lod 0.0 o c out-o-pln ont lod nd (.P D) U 0 i o (.50) 0.7D T ith ll ocs (P, i, 0 ) in th unction U lting to th clcultd pplid lods in th chod. ot tht U dins th chod utilistion cto. y st to.0 i th olloing condition is stisid: chod xil tnsion oc th chod. ( ) 0. 5 i o ith ll ocs lting to th clcultd pplid lods in 0.D u is stngth cto hich vis ith th joint nd lod typ: ( ) u 0 u ( ) 8 (o Axil Copssion) (o Axil Tnsion) (.5) is th gotic odii dind s ollos.0 o o >0.6 iliogphy: ( 0.8 ) [.9] Osho Instlltions: Guidnc on Dsign, Constuction nd Ctiiction, outh Edition, UK Hlth & ty Excutiv, ondon (990). -5 ITET 006 All ights svd

53 (0 y 006) ITET K7.8. T- nd Y-Joints ith in-pln nd out-o-pln nding ITAP Applicl clus(s): p. AIII. - Dsciption: T- nd Y-Joints oding: In-pln nd out-o-pln nding chtic: iit lod olution: Th chctistic stngth o ldd tuul joint sujctd to unidictionl loding y divd s ollos: h T d co u (.5) sinθ ci ci chctistic stngth o c in-pln ont lod co chctistic stngth o c out-o-pln ont lod chctistic yild stss o th chod t th joint (o 0.7 tis th chctistic tnsil stngth i lss). I chctistic vlus not vill spciid iniu vlus y sustitutd. is cto to llo o th psnc o xil nd ont lods in th chod. is dind s: ITET 006 All ights svd -5

54 ITET K7 Annx U γ o xt conditions U γ o opting conditions h 0.00 o c xil lod 0.05 o c in-pln ont lod 0.0 o c out-o-pln ont lod nd (.P D) U 0 i o (.5) 0.7D T ith ll ocs (P, i, o) in th unction U lting to th clcultd pplid lods in th chod. ot tht U dins th chod utilistion cto. y st to.0 i th olloing condition is stisid: chod xil tnsion oc th chod. ( ) 0. 5 i o ith ll ocs lting to th clcultd pplid lods in 0.D u is stngth cto hich vis ith th joint nd lod typ: 0.5 5γ sinθ (o In-Pln nding) u (.6 ) (o Out-o Pln nding) (.5) u 7 is th gotic odii dind s ollos.0 o o >0.6 iliogphy: ( 0.8 ) [.0] Osho Instlltions: Guidnc on Dsign, Constuction nd Ctiiction, outh Edition, UK Hlth & ty Excutiv, ondon (990). -5 ITET 006 All ights svd

55 (0 y 006) ITET K7.8. K-Joints ith xil lods ITAP Applicl clus(s): p. AIII. 5-6 Dsciption: K-Joints oding: Axil chtic: iit lod olution: Th chctistic stngth o ldd tuul joint sujctd to unidictionl loding y divd s ollos: h T K P c u (.55) sinθ P c chctistic stngth o c xil lod chctistic yild stss o th chod t th joint (o 0.7 tis th chctistic tnsil stngth i lss). I chctistic vlus not vill spciid iniu vlus y sustitutd. sinθ K (.56) is cto to llo o th psnc o xil nd ont lods in th chod. is dind s: ITET 006 All ights svd -55

56 ITET K7 Annx U γ o xt conditions U γ o opting conditions h 0.00 o c xil lod 0.05 o c in-pln ont lod 0.0 o c out-o-pln ont lod nd (.P D) U 0 i o (.57) 0.7D T ith ll ocs (P, i, o) in th unction U lting to th clcultd pplid lods in th chod. ot tht U dins th chod utilistion cto. y st to.0 i th olloing condition is stisid: chod xil tnsion oc th chod. ( ) 0. 5 i o ith ll ocs lting to th clcultd pplid lods in 0.D u is stngth cto hich vis ith th joint nd lod typ: ( ) g u 0 (o Axil Copssion) u ( 8 ) g (o Axil Tnsion) (.58) is th gotic odii dind s ollos.0 o o >0.6 ( 0.8 ) 0.5 g.7 0.9ζ ut should not tkn s lss thn.0. iliogphy: [.] Osho Instlltions: Guidnc on Dsign, Constuction nd Ctiiction, outh Edition, UK Hlth & ty Excutiv, ondon (990). -56 ITET 006 All ights svd

57 (0 y 006) ITET K7.8. K-Joints ith in-pln nd out-o-pln nding ITAP Applicl clus(s): p. AIII. 7-8 Dsciption: K-Joints oding: In-pln nd out-o-pln nding chtic: iit lod olution: Th chctistic stngth o ldd tuul joint sujctd to unidictionl loding y divd s ollos: h T d co u (.59) sinθ ci ci chctistic stngth o c in-pln ont lod co chctistic stngth o c out-o-pln ont lod chctistic yild stss o th chod t th joint (o 0.7 tis th chctistic tnsil stngth i lss). I chctistic vlus not vill spciid iniu vlus y sustitutd. is cto to llo o th psnc o xil nd ont lods in th chod. is dind s: ITET 006 All ights svd -57

58 ITET K7 Annx U γ o xt conditions U γ o opting conditions h 0.00 o c xil lod 0.05 o c in-pln ont lod 0.0 o c out-o-pln ont lod nd (.P D) U 0 i o (.60) 0.7D T ith ll ocs (P, i, o) in th unction U lting to th clcultd pplid lods in th chod. ot tht U dins th chod utilistion cto. y st to.0 i th olloing condition is stisid: chod xil tnsion oc th chod. ( ) 0. 5 i o ith ll ocs lting to th clcultd pplid lods in 0.D u is stngth cto hich vis ith th joint nd lod typ: 0.5 5γ sinθ (o In-Pln nding) u (.6 ) (o Out-o Pln nding) (.6) u 7 is th gotic odii dind s ollos.0 o o >0.6 iliogphy: ( 0.8 ) [.] Osho Instlltions: Guidnc on Dsign, Constuction nd Ctiiction, outh Edition, UK Hlth & ty Excutiv, ondon (990). -58 ITET 006 All ights svd

59 (0 y 006) ITET K7.8.5 X- nd DT-Joints ith xil lod ITAP Applicl clus(s): p. AIII. 9-0 Dsciption: X- nd DT-Joints oding: Axil chtic: iit lod olution: Th chctistic stngth o ldd tuul joint sujctd to unidictionl loding y divd s ollos: h T K P c u (.6) sinθ P c chctistic stngth o c xil lod chctistic yild stss o th chod t th joint (o 0.7 tis th chctistic tnsil stngth i lss). I chctistic vlus not vill spciid iniu vlus y sustitutd. sinθ K (.6) ITET 006 All ights svd -59

60 ITET K7 Annx is cto to llo o th psnc o xil nd ont lods in th chod. is dind s: U γ o xt conditions U γ o opting conditions h 0.00 o c xil lod 0.05 o c in-pln ont lod 0.0 o c out-o-pln ont lod nd (.P D) U 0 i o (.6) 0.7D T ith ll ocs (P, i, o) in th unction U lting to th clcultd pplid lods in th chod. ot tht U dins th chod utilistion cto. y st to.0 i th olloing condition is stisid: chod xil tnsion oc th chod. 0.D ( ) 0. 5 u is stngth cto hich vis ith th joint nd lod typ: (.5 ) u (o Axil Copssion) ( 7 ) i o ith ll ocs lting to th clcultd pplid lods in u 7 (o Axil Tnsion) (.65) is th gotic odii dind s ollos.0 o o >0.6 iliogphy: ( 0.8 ) [.] Osho Instlltions: Guidnc on Dsign, Constuction nd Ctiiction, outh Edition, UK Hlth & ty Excutiv, ondon (990). -60 ITET 006 All ights svd

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