nozzle FEA

BPC HIBISCUS INFRASTRUCTU INFRASTRUCTURE RE & UTILITY UPGRADING UPGRADING PROJECT

DOCUMENT

STRENGTH CALCULATION

TITLE

FINITE ELEMENT ANLYSIS FOR NOZZLE N8

TOTAL No. OF PAGES

24

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Table o f Cont Co ntent entss Spill Back Inlet (Nozzle N8): FEA Results...............................................................................................................1/22

i

Spill Back Inlet (Nozzle N8): FEA Res ults Results were generated with the finite element program FE/Pipe®. Stress results are post-processed in accordance with the rules specified in ASME Section III and ASME Section VIII, Division 2. Analysis Time Stamp: Fri Nov 04 17:46:03 2016. Model Notes Load Case Report Solution Data ASME Code Stress Output Plots Stress Results - Notes ASME Overstressed Areas Highest Primary Stress Ratios Highest Seco ndary Stress Ratios Highest Fatigue Stress Ratios Stress Intensification Factors Allowable Loads Flexibilities Graphical Results Model Not es Model Not es I nput Echo: Model Type

: Coni cal Shel l

Pare nt Outs i de Di amet er : Thi ckness : Cone Lengt h : Cone OD at Top : Knuc kl e Radi us @ Top : Knuc kl e Radi us @ Bot t om: Fi l l et Al ong Shel l : Parent Propert i es: Col d Al l owabl e Hot Al l owabl e Mater i al I D #2 Ul t i mat e Tensi l e ( Amb) Yi el d St r engt h ( Amb) Yi el d St r engt h ( Hot ) El ast i c Modul us ( Amb) Poi ssons Rati o Wei ght Densi t y Nozz l e Outs i de Di amet er Thi ckness Lengt h Noz zl e Wel d Lengt h RePad Wi dt h RePad Thi c knes s Locat i on perpendi cul ar t o t he head ce nt erl i ne

: : : : : : : : : : : : : : : :

12080. 600 6. 499 1200. 000 230. 604 0. 000 0. 000 11. 000

mm. mm. mm. mm. mm. mm. mm.

108. 0 MPa 108. 0 MPa Low Al l oy Steel 379. 0 MPa 207. 0 MPa 190. 0 MPa 201893. 0 MPa 0. 300 0. 7682E- 04 N / c u. mm. ( NOT USED) 168. 275 8. 100 179. 290 11. 000 114. 155 8. 000

mm. mm. mm. mm. mm. mm.

4500. 000 mm.

Nozzl e Ti l t Angl e

:

0. 000 deg.

Nozzl e Propert i es Col d Al l owabl e Hot Al l owabl e Mater i al I D #2 Ul t i mat e Tensi l e ( Amb) Yi el d St r engt h ( Amb)

: : : : :

118. 0 MPa 118. 0 MPa Low Al l oy Steel 414. 0 MPa 241. 0 MPa

1/22

Yi el d St re ngth ( Hot ) El ast i c Modul us ( Amb) Poi ssons Rati o Wei ght Densi t y

: : : :

Desi gn Operati ng Cycl es Ambi ent Temper at ure ( Deg. )

: :

221. 0 MPa 201893. 0 MPa 0. 300 0. 7682E- 04 N / c u. mm. ( NOT USED) 0. 21. 00

Uni f orm t hermal expansi on produces no st res s i n t hi s geomet ry. Any t her mal l oads wi l l c ome t hr ough ope r at i ng f or c es and moments appl i ed t hrough t he nozzl e. Nozz l e Pre ss ure Vess el Pr es s ure

: :

0. 017 MPa 0. 017 MPa

FEA Model Loads : These are t he user def i ned l oads appl i ed to t he FEA model at t he end of the nozzl e i n gl obal coordi nates. Forc es(

N)

Moment s ( N- m)

Load Cas e FX FY FZ MX MY MZ --------------------------------------------------------------------------WEI GHT: 1000. 0 - 9000. 0 - 2000. 0 2000. 0 - 2000. 0 5000. 0 The " t o p" o r " po s i t i v e" e nd of t h i s mo de l i s " f r e e " i n t h e ax i a l and t r a ns l a t i o nal di r e c t i o ns . St re ss es ar e NOT averaged. No pad wel d di mensi ons have been gi ven f or t he pad connect i on t o the shel l . Few cor rel ati ons have been perf ormed to i nvesti gat e the sensi ti vi t y of peak st resses t o t hi s val ue. Reasonabl e l engt hs have been assumed. Vess el Cent er l i ne Vec t or : Nozzl e Cent erl i ne Vect or: Zero Degree Ori entat i on Vect or:

0. 000 0. 000 1. 000

1. 000 1. 000 0. 000

0. 000 0. 000 0. 000

Table of Contents Load Case Repor t FE/ Pi pe Ver s i on 7. 0 Rel ease d Jul 2014

Jobname: SPI LLBA 5: 45pm NOV 4, 2016

Load Cas e Repo r t

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I nner and oute r e l ement t emperat ures are t he same t hro ughout the model . No thermal r atc het i ng cal cul ati ons wi l l be perf ormed. THE 1

9

LOAD CASES ANALYZED ARE:

WEIGHT ONLY

( Wgt Onl y)

Wei ght ONLY c ase r un t o get t he st r es s r ange between t he i nst al l ed and t he operati ng stat es. / - - - - - - - - Lo ads i n Cas e Loads due t o Wei ght 2

SUSTAI NED

1

( Wgt +Pr )

2/22

Sust ai ned case run t o sati sf y l ocal pri mary membrane and bendi ng st res s l i mi t s. / - - - - - - - - Lo ads i n Cas e Loads due t o Wei ght Pre ss ure Case 1 3

2

OPERATI NG Case run t o comput e t he operat i ng st res ses used i n sec ondary, peak and range cal cul ati ons as needed. / - - - - - - - - Lo ads i n Cas e Pre ss ure Case 1 Loads f rom ( Operati ng)

4

RANGE

3

( Fat i gue Cal c Per f or med)

Case r un t o get t he RANGE of st re ss es . as de s c r i be d i n NB- 3222. 2, 5. 5. 3. 2, 5 . 5 . 5. 2 or 5 . 5. 6. 1 . / - - - - - - - - Combi nati ons i n Range Case Pl us St res s Resul t s f rom CASE 3 Mi nus St re ss Res ul t s f ro m CASE 1 5

4

Pro gram Generated - - Forc e Onl y Cas e r un t o c o mput e s i f ' s a nd f l e xi bi l i t i e s . / - - - - - - - - Lo ads i n Cas e 5 Lo ads f r o m ( Ax i a l )

6

Pro gram Generated - - Forc e Onl y Cas e r un t o c o mput e s i f ' s a nd f l e xi bi l i t i e s . / - - - - - - - - Lo ads i n Cas e 6 Loads f rom ( Inpl ane)

7

Pro gram Generated - - Forc e Onl y Cas e r un t o c o mput e s i f ' s a nd f l e xi bi l i t i e s . / - - - - - - - - Lo ads i n Cas e 7 Loads f rom ( Out pl ane)

8

Pro gram Generated - - Forc e Onl y Cas e r un t o c o mput e s i f ' s a nd f l e xi bi l i t i e s . / - - - - - - - - Lo ads i n Cas e 8 Loads f rom ( Torsi on)

9

Pro gram Generated - - Forc e Onl y Cas e r un t o c o mput e s i f ' s a nd f l e xi bi l i t i e s . / - - - - - - - - Lo ads i n Cas e 9 Pre ss ure Case 1

Table of Contents Sol uti on Data FE/ Pi pe Ver s i on 7. 0 Rel ease d Jul 2014


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Sol uti on Data Maxi mum Sol uti on Row Si ze Number of Node s Number of El ement s Number of Sol uti on Cases

= = = =

1218 4067 1320 8

Summat i on of Loads per Cas e Case # 1 2 3 4 5 6 7 8

FX

FY

FZ

1000. 94387. 93387. 0. 0. 0. 0. 93387.

- 24737. 496489. 505489. 562048. 0. 0. 0. 521225.

- 2000. - 2000. 0. 0. 0. 0. 0. 0.

Table of Contents ASME Code St r es s Out put Pl ot s FE/ Pi pe Ver s i on 7. 0 Jobname: SPI LLBA Rel ease d Jul 2014 5: 46pm NOV 4, 2016

ASME Code St r es s Out put Pl ot s

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1) Pl <( 1. 5) ( S) ( SUS, Membrane) Case 2 2) Qb

3) S1+S2+S3

<4S ( SUS, S1+S2+S3) Case 2

4) Pl +Pb+Q

8) Pl +Pb+Q+F
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Str ess Resul t s - Not es FE/ Pi pe Ver s i on 7. 0 Rel ease d Jul 2014


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Str ess Resul t s - Not es - Resul ts i n thi s anal ysi s el ement sol uti on met hod.

were

generated usi ng the f i ni te

- Usi ng 07- 12 ASME Sec t i on VI I I Di vi si on 2 - Use Pol i shed Bar fat i gue curve. Assume press ure i ncr eases al l ot her st res ses. - Ass ume f ree end di spl acements of att ached pi pe are secondary l oads wi thi n l i mi ts of nozzl e rei nf orcement . - Use Equi val ent St res s ( Von Mi ses ) . - S1+S2+S3 eval uati on omi t t ed f rom operat i ng st ress . I ncl ude S1+S2+S3 eval uati on i n pri mary case eval uat i on. Ass ume bendi ng st re ss not l oc al pri mary f or S1+S2+S3. - Use l ocal t ensor val ues f or averaged and not averaged stresses.

Table of Contents ASME Over st r es s ed Ar eas FE/ Pi pe Ver s i on 7. 0 Rel ease d Jul 2014

ASME Ove r st r es s ed Ar eas


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Noz z l e 1 Pad Wel d Ar ea Qb 588 MPa

SPS 397 MPa

Pr i mar y Bendi ng Load Cas e 2 Pl ot Ref erence: 2) Qb
SPS 397 MPa

Pr i mary+Seco ndary ( I nner ) Load Case 4 Pl ot Ref erence: 13) Pl +Pb+Q
SPS 397 MPa

Pr i mar y+Sec ondar y ( Out er ) Load Cas e 4 Pl ot Ref erence: 14) Pl +Pb+Q
148% Pl +Pb+Q 517 MPa 130% Pl +Pb+Q 654 MPa 164%

5/22

Shel l I n Nozzl e 1 Vi ci ni t y Qb 462 MPa

SPS 397 MPa

SPS 397 MPa

SPS 397 MPa

116% Pl +Pb+Q 398 MPa 100% Pl +Pb+Q 509 MPa 128%

Table of Contents Hi ghest Pri mary St res s Rati os FE/ Pi pe Ver s i on 7. 0 Jobname: SPI LLBA Rel ease d Jul 2014 5: 46pm NOV 4, 2016

Hi ghest Pri mary St res s Rati os

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Pad Next t o Noz zl e 1 Qb 247 MPa

SPS 397 MPa

62 % Nozzl e 1 Next t o Shel l Pl 112 MPa

( 1. 5) ( S) 177 MPa

Pr i mary Membrane Load Case 2 Pl ot Ref erence: 1) Pl <( 1. 5) ( S) ( SUS, Membrane) Case 2

63 % Noz z l e 1 Pad Wel d Ar ea Qb 588 MPa

SPS 397 MPa

148% Shel l In Nozzl e 1 Vi ci ni t y Qb 462 MPa

SPS 397 MPa

116%

6/22

Nozzl e 1 Pl 46 MPa

( 1. 5) ( S) 177 MPa

Pr i mary Membrane Load Case 2 Pl ot Ref erence: 1) Pl <( 1. 5) ( S) ( SUS, Membrane) Case 2

25 % Pad at Nozz l e 1 Qb 166 MPa

SPS 397 MPa

41 %

Table of Contents Hi ghest Secondary St res s Rati os FE/ Pi pe Ver s i on 7. 0 Jobname: SPI LLBA Rel ease d Jul 2014 5: 46pm NOV 4, 2016

Hi ghest Secondary St res s Rati os

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Pad Next t o Noz zl e 1 Pl +Pb+Q 276 MPa

SPS 397 MPa

69 % Nozzl e 1 Next t o Shel l Pl +Pb+Q 269 MPa

SPS 462 MPa

58 % Noz z l e 1 Pad Wel d Ar ea Pl +Pb+Q 654 MPa

SPS 397 MPa

164% Shel l In Nozzl e 1 Vi ci ni t y Pl +Pb+Q 509 MPa

SPS 397 MPa

128%

7/22

Nozzl e 1 Pl +Pb+Q 69 MPa

SPS 462 MPa

SPS 397 MPa

15 % Pad at Nozz l e 1 Pl +Pb+Q 203 MPa 51 %

Table of Contents Hi ghest Fati gue St ress Rati os FE/ Pi pe Ver s i on 7. 0 Jobname: SPI LLBA Rel ease d Jul 2014 5: 46pm NOV 4, 2016

Hi ghest Fati gue St res s Rati os

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Pad Next t o Noz zl e 1 Pl +Pb+Q+F 186 MPa

Damage Rat i o 0. 000 Li f e 0. 015 St res s

Al l owabl e 12, 361. 9 MPa 1%

Pr i mar y+Sec ondar y+Peak ( Out er ) Load Cas e 4 St ress Concentrat i on Factor = 1. 350 St rai n Concent rat i on Fact or = 1. 000 Cycl es Al l owed for thi s St ress = 28, 422. " B31" Fat i gue St r es s Al l owabl e = 270. 0 Markl Fati gue St res s Al l owabl e = 1689. 2 WRC 474 Mean Cyc l es t o Fai l ure = 221, 706. WRC 474 99% Probabi l i t y Cycl es = 51, 504. WRC 474 95% Probabi l i t y Cycl es = 71, 507. BS5500 Al l owed Cycl es ( Curve F) = 33, 426. Membrane- t o- Bendi ng Rat i o = 0. 256 Bendi ng- t o- PL+PB+Q Rat i o = 0. 796 Pl ot Ref erence: 16) Pl +Pb+Q+F
Nozzl e 1 Next t o Shel l Pl +Pb+Q+F 182 MPa Al l owabl e 12, 361. 9 MPa 1%


Pr i mar y+Sec ondar y+Peak ( I nner ) Load Cas e 4 St ress Concentrat i on Factor = 1. 350 St rai n Concent rat i on Fact or = 1. 000 Cycl es Al l owed for thi s St ress = 30, 589. " B31" Fat i gue St r es s Al l owabl e = 295. 0 Markl Fati gue St res s Al l owabl e = 1689. 2 WRC 474 Mean Cyc l es t o Fai l ure = 357, 090. WRC 474 99% Probabi l i t y Cycl es = 82, 955. WRC 474 95% Probabi l i t y Cycl es = 115, 173. BS5500 Al l owed Cycl es ( Curve F) = 35, 914. Membrane- t o- Bendi ng Rat i o = 0. 531 Bendi ng- t o- PL+PB+Q Rat i o = 0. 653 Pl ot Ref erence: 15) Pl +Pb+Q+F
8/22

Noz z l e 1 Pad Wel d Ar ea Pl +Pb+Q+F 1, 584 MPa


Al l owabl e 12, 361. 9 MPa 12%

Pr i mar y+Sec ondar y+Peak ( Out er ) Load Cas e 4 St ress Concentrat i on Factor = 1. 350 St rai n Concent rat i on Fact or = 3. 588 Cycl es Al l owed for thi s St ress = 72. " B31" Fat i gue St r es s Al l owabl e = 270. 0 Markl Fati gue St res s Al l owabl e = 1689. 2 WRC 474 Mean Cyc l es t o Fai l ure = 26, 541. WRC 474 99% Probabi l i t y Cycl es = 6, 166. WRC 474 95% Probabi l i t y Cycl es = 8, 560. BS5500 Al l owed Cycl es ( Curve F) = 990. Membrane- t o- Bendi ng Rat i o = 0. 203 Bendi ng- t o- PL+PB+Q Rat i o = 0. 831 Pl ot Ref erence: 16) Pl +Pb+Q+F
Shel l In Nozzl e 1 Vi ci ni t y Pl +Pb+Q+F 543 MPa


Pr i mar y+Sec ondar y+Peak ( Out er ) Load Cas e 4 St ress Concentrat i on Factor = 1. 000 St rai n Concent rat i on Fact or = 2. 132 Cycl es Al l owed f or t hi s St ress = 1, 081. " B31" Fat i gue St r es s Al l owabl e = 270. 0 Markl Fati gue St res s Al l owabl e = 1689. 2 WRC 474 Mean Cyc l es t o Fai l ure = 57, 959. WRC 474 99% Probabi l i t y Cycl es = 13, 464. WRC 474 95% Probabi l i t y Cycl es = 18, 694. BS5500 Al l owed Cycl es ( Curve F) = 2, 813. Membrane- t o- Bendi ng Rat i o = 0. 177 Bendi ng- t o- PL+PB+Q Rat i o = 0. 850 Pl ot Ref erence: 16) Pl +Pb+Q+F

Pr i mar y+Sec ondar y+Peak ( I nner ) Load Cas e 4 St ress Concentrat i on Factor = 1. 000 St rai n Concent rat i on Fact or = 1. 000 Cycl es Al l owed f or t hi s Str ess = 1. 0000E11 " B31" Fat i gue St r es s Al l owabl e = 295. 0 Markl Fati gue St res s Al l owabl e = 1689. 2 WRC 474 Mean Cyc l es t o Fai l ure = 22, 043, 640. WRC 474 99% Probabi l i t y Cycl es = 5, 120, 932. WRC 474 95% Probabi l i t y Cycl es = 7, 109, 770. BS5500 Al l owed Cycl es( Curve F) = 2, 092, 197. Membrane- t o- Bendi ng Rat i o = 1. 067 Bendi ng- t o- PL+PB+Q Rat i o = 0. 484 Pl ot Ref erence: 15) Pl +Pb+Q+F
Al l owabl e 12, 361. 9 MPa 4%

Nozzl e 1 Pl +Pb+Q+F 35 MPa Al l owabl e 12, 361. 9 MPa 0%

Pad at Nozz l e 1 Pl +Pb+Q+F 137 MPa Al l owabl e 12, 361. 9 MPa 1%


Pr i mar y+Sec ondar y+Peak ( Out er ) Load Cas e 4 St ress Concentrat i on Factor = 1. 350 St rai n Concent rat i on Fact or = 1. 000 Cycl es Al l owed for thi s St ress = 91, 807. " B31" Fat i gue St r es s Al l owabl e = 270. 0 Markl Fati gue St res s Al l owabl e = 1689. 2 WRC 474 Mean Cyc l es t o Fai l ure = 550, 720. WRC 474 99% Probabi l i t y Cycl es = 127, 937. WRC 474 95% Probabi l i t y Cycl es = 177, 625. BS5500 Al l owed Cycl es ( Curve F) = 83, 842. Membrane- t o- Bendi ng Rat i o = 0. 409 Bendi ng- t o- PL+PB+Q Rat i o = 0. 710 Pl ot Ref erence:

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16) Pl +Pb+Q+F
Table of Contents St r e s s I nt e ns i f i c a t i o n Fa c t o r s FE/ Pi pe Ver s i on 7. 0 Jobname: SPI LLBA Rel ease d Jul 2014 5: 46pm NOV 4, 2016

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Str ess Intensi f i cati on Factors

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Branc h/ Noz zl e Si f Summary Axi al : I npl ane : Out pl ane: Torsi on : Press ure:

Peak 59. 927 8. 864 10. 132 2. 058 2. 717

Pr i mar y 15. 620 2. 918 3. 727 1. 156 3. 935

Sec ondar y 88. 780 13. 132 15. 010 3. 049 4. 025

SSI 3. 195 2. 578 2. 123 1. 788 1. 569

The above stress i ntensi f i cati on f actors are t o be used i n a beam- t ype anal ysi s of t he pi pi ng syst em. Inpl ane, Out pl ane and Torsi onal si f ' s shoul d be used wi th the matc hi ng branch pi pe whose di amet er and t hi ckness i s gi ven bel ow. The axi al si f shoul d be used to i nt ensi f y t he axi al st ress i n t he branch pi pe cal cul ated by F/ A. The pressure si f shoul d be used t o i nte nsi f y the nomi nal pre s sur e st r es s i n t he PARENT or HEADER, cal c ul at ed f rom PDo/ 2T. B31 cal cul ati ons use mean di amet ers and Sect i on VII I cal cul ati ons use out si de di ameter s. SSIs are based on peak st ress f actors and correl ated t est resul t s. Pi pe OD : Pi pe Thk: Z approx: Z exact :

168. 275 8. 100 163218. 312 155758. 938

( SSI = SI F^x) SIF/ SSI Exponent s:

mm. mm. cu. mm. c u. mm. Axi al 0. 672

I npl 0. 491

Outpl 0. 568

Tors 0. 200

Pres 1. 370

SIF/ SSI e xponent based on rel ati onshi p bet ween pri mary and pe ak s t r e s s f a c t o r s f r o m t h e f i ni t e e l e me nt a nal y s i s . B31. 3 Branch Pres sure i - f act or = Header Press ure i - f actor =

510. 838 5. 437

The B31. 3 pressure i - f act ors shoul d be used wi th wi t h F/ A, where F i s the axi al f orc e due to pressure, and A i s t he ar ea of t he pi pe wal l . Thi s i s equi val ent t o f i ndi ng t h e pr e s s ur e s t r e s s f r o m ( i p) ( PD/ 4T) . B31. 3 ( Branch) Pe ak St r e s s Si f . . . .

B31. 1 ( Branch) Pe ak St r e s s Si f . . . .

WRC 330 ( Br anc h) Pe ak St r e s s Si f . . . .

0 . 000 36. 323 48. 015 1. 000

Ax i a l I npl ane Outpl ane Torsi onal

0 . 000 48. 015 48. 015 48. 015

Ax i a l I npl ane Outpl ane Tor si onal

0 . 000

Ax i a l

10/22

38. 524 48. 015 38. 524

I npl ane Outpl ane Tor si onal

Table of Contents Al l owabl e Loads FE/ Pi pe Ver s i on 7. 0 Rel ease d Jul 2014


Al l owabl e Loads

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SECONDARY Load Type ( Range) : Axi al Forc e I npl ane Moment Outpl ane Moment Tor si onal Moment Pres sure

( N ( mm. ( mm. ( mm. ( MPa

) N) N) N) )

Maxi mum I ndi vi dual Occ uri ng 18227. 4708800. 4119581. 20278014. 0. 11

Cons er vat i ve Si mul t aneous Oc curi ng 5145. 939813. 822213. 5723632. 0. 02

Real i s t i c Si mul t aneous Occ uri ng 7717. 1993645. 1744177. 8585449. 0. 02

) N) N) N) )

Maxi mum I ndi vi dual Occ uri ng 45193. 9448355. 6770002. 23858384. 0. 04

Conse r vat i ve Si mul t aneous Oc curi ng 9283. 1727470. 983359. 7304012. 0. 02

Real i st i c Si mul t aneous Occ uri ng 13925. 3664518. 2086020. 10956017. 0. 02

PRI MARY Load Type: Axi al Forc e I npl ane Moment Outpl ane Moment Tor si onal Moment Pres sure

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( N ( mm. ( mm. ( mm. ( MPa

NOTES: 1) Maxi mum I ndi vi dual Oc c uri ng Loads are t he maxi mum al l o we d val ue s o f t h e r e s pe c t i ve l o ads i f al l o t he r l o ad c o mpo ne nt s ar e z e r o , i . e . t h e l i s t e d ax i a l f o r c e may be appl i ed i f t he i npl ane, out pl ane and t orsi onal moments , and t he pres sure are zer o. 2) The Conservati ve Al l owabl e Si mul t aneous l oads are t he maxi mum l oads t hat can be appl i ed si mul t aneousl y. A conservati ve st ress combi nati on equati on i s used that typic al l y produces st resses wi thi n 50- 70% of the all owabl e st ress. 3) The Real i st i c Al l owabl e Si mul t aneous l oads are t he maxi mum l oads t hat can be appl i ed si mul t aneousl y. A more real i st i c st ress combinat i on equati on i s used based on experi ence at Paul i n Research. Str esses are typi cal l y produced wi t hi n 80- 105% of the all owabl e. 4) Secondary al l owabl e l oads are l i mi t s f or expansi on and operat i ng pi pi ng l oads. 5) Pri mary al l owabl e l oads are l i mi ts f or wei ght , pri mary and sust ai ned t ype pi pi ng l oads.

Table of Contents Fl e xi b i l i t i e s FE/ Pi pe Ver s i on 7. 0

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Fl e xi bi l i t i e s

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The f ol l owi ng st i f f nesses shoul d be used " b e am- t y pe " anal y s i s o f t h e i nt e r s e c t i o n. nesses shoul d be i nsert ed at t he surf ace branch/ header or nozzl e/ vessel j unct i on. charact eri st i cs used f or t he branch pi pe Out s i de Di amet er = Wal l Thi c knes s =

168. 275 8. 100

i n a pi pi ng, The s t i f f of the The general shoul d be:

mm. mm.

Axi al Transl ati onal Sti f f ness Inpl ane Rot ati onal St i f f ness Outpl ane Rot ati onal Sti f f ness Tors i onal Rot ati onal St i f f ness

= = = =

679. 1839044. 1240485. 29056072.

N / mm. mm. N / deg mm. N / deg mm. N / deg

Intersect i on Fl exibi l i t y Factors f or Branch/ Nozzl e Fi nd axi al st i f f ness: K = 3EI/ ( kd) ^3 N / mm. Fi nd bendi ng and tor si onal sti f f nesses : K = EI/ ( kd) mm. N per radi an. The EI pro duct i s 0. 26472E+13 N mm. ^2 The val ue of ( d) to use i s: 160. 175 mm. . The resul ti ng bendi ng st i f f ness i s i n uni ts of f orce x l ength per radi an. Ax i a l Fl e xi b i l i t y Fac t o r Inpl ane Fl exi bil i ty Fact or Outpl ane Fl exi bi l i t y Fact or To r s i o nal Fl e xi bi l i t y Fac t o r

( k) ( k) ( k) ( k)

= = = =

1 4. 17 1 156. 850 232. 534 9. 92 8

Table of Contents

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Finite Element Model Finite Element Model Area of Discontinuity at Nozzle 1) Pl < (1.5)(S) (SUS Membrane) Case 2 2) Qb < SPS (SUS Bending) Case 2 3) S1+S2+S3 < 4S (SUS S1+S2+S3) Case 2 4) Pl+Pb+Q < SPS (OPE Inside) Case 3 5) Pl+Pb+Q < SPS (OPE Outside) Case 3 6) Membrane < User (OPE Membrane) Case 3 7) Bending < User (OPE Bending) Case 3 13) Pl+Pb+Q < SPS (EXP Inside) Case 4 14) Pl+Pb+Q < SPS (EXP Outside) Case 4 15) Pl+Pb+Q+F < Sa (EXP Inside) Case 4 16) Pl+Pb+Q+F < Sa (EXP Outside) Case 4 8) Pl+Pb+Q+F < Sa (SIF Outside) Case 5 9) Pl+Pb+Q+F < Sa (SIF Outside) Case 6 10) Pl+Pb+Q+F < Sa (SIF Outside) Case 7 11) Pl+Pb+Q+F < Sa (SIF Outside) Case 8 12) Pl+Pb+Q+F < Sa (SIF Outside) Case 9 Tabular Results

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nozzle FEA

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