ML20009B407

Research Info Ltr 88:transmits Results of Completed Research Re Establishment of Design Criteria for Closely Spaced Nozzles in Pressure Vessels & Resulting Change to ASME Code Rules

ML20009B407
Person / Time
Issue date:	04/25/1980
From:	Budnitz R NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES)
To:	Harold Denton Office of Nuclear Reactor Regulation
References
RIL-088, RIL-88, NUDOCS 8107150387
Download: ML20009B407 (32)

Text

{{#Wiki_filter:~ / '0,, UMTED STATES NUCLEAR REGULATORY COMMisslON 8 gj W ASHINGTON, D. C. 20555 E M25W MEMORANDUM FOR: Harold R.'Denton, Director Office of Nuclear Reactor Regulation FROM: Robert J. Budnitz, Director Office of Nuclear Regulatory Research , DESIGN

SUBJECT:

RESEARCH INFORMATION LETTER # po CRITERIA FOR CLOSELY-SPACED N0ZZLES IN PRESSURE VESSELS" This memorandum transmits the results of conpleted research dealing with the establishment of design criteria for closely-spaced nozzles in pressure vessels and the resulting change to the ASME Coda rules (Appendix A). Seven reports (Appendices B through H) issued in the The eighth and final report process of this research are enclosed. (Appendix I) is in the process of publication and will be submitted upon com.letion. o 1.0 Introduction The results described herein were generated in a research program whose objectives were to investigate the state-of-stress at reinforced openings (nozzles) in cylindrical pressure vessels operating at temperatures below the creep range, such as for light water reactor (LWR) vessels, and to assess the rules and criteria that govern the desfgn and qualification of isolated and closely-spaced nozzles in reactor vessels. Two of the more impor' ant parameters investigated are the maximum stresses in the nozzle-Vessel region and the minimum distance between nozzles or between a nozzle and other structural discontinuity. These must be limited to acceptable values to assure that the vessel will not develop failure mechanisms from excessive peak stresses (initiation of /atigue cracks) and from high local membrane stresses (excessive distortion due to material yielding).. Although the ASME Boiler and Pressure Vessel Code, Section III, Nuclear Power Plant Components, contains clear instructions for designing nozzle penetrations including geometric details, reinforcement rules, stress indices, and spacing requirements, there was concern that the Code rules for computing maximum stresses (stress indices) and for maintaining an appropriate distance between nozzles to prevent excessive interaction of stress fields were inadequate, at least over some range of the geometric parameters covered by the rules. There was also a desire to reduce the

ninimum spacing distances in the event that the present criteria are overly conservative.

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s a H. R. Denton 2 2.0 Discussion In order to investigate these questions, ORNL developed and validated two special purpose finite-element stress analysis ccmputer programs, CORTES and MULT-N0ZZLE, for analyzing pressure vessels with a single (isolated) nozzle or with two or more closely-spaced nozzles. under loading conditions of internal pressure and/or force and moments applied to the end(s) of the nozzle (s). These computer programs were used to conduct parametric studies of the ASME Code endorsed nozzle designs over a wide range of dimensionless geometric parameters. Work was carried out to correlate the calculated maximum stress data developed with experimental data and to compare these correla' ions with the ASME Code calculated stress indices. The information developed as described above led to the establishment of a new criterion for defining an " isolated nozzle condition." And finally, the work carried out led to the development of proposed alternate criteria, both for computing the maximum stress intensity (not to be confused wich the stress intensity of fracture mechanics terminology) for a given nozzle design and loading condition and for limiting the m'.r' mum distance between nozzles. These criteria are given in a form that can be introduced into the ASME Code to replace the present rules. ~ 3.0 Results Results of the studies (see Appendix G) show that the Code stress index for computing the maximum design stress intensity at the inside corner of the nozzel-vessel junction can be unconservative for values of the parametric relation: n = (d /Di)0 133 (Di/T)o.18 > j,1 (1) t where dj = ins 1de diameter of nozzle Dj = inside diameter of vessel a T = actual wall thickness of vessel minus corrosion allowance. The degree of this unconservatism is dependent upon the amount and placement of nozzle reinforcement material allowed by the lctitude permitted by Code reinforcement rules. Since many (or most of the l

H. R. Denton 3 reactor vessel designs of current interest have values of the parameter n, less than 1.1, it is rs:ommer.Jed that use of the current Code indices be limited to values of n < l.1. This is somewhat more restrictive than the present Code limit of: p = (dj/0j)/Dj/T < 0.8 (2) ~ For nozzle designs with n > 1.1, such as occur routinely in piping applications, more elaborate stress index formulas were developed for both internal pressure and applied moment loadings to replace t::e present Code indices. These recommendations, in the fom of ~ prooosed Code rule revisions, have been presented to the ASME Boiler and Tressure Vessel Code Committee and are summarized in Appendix A. Results of the studies addressed to the question of nozzle spacing (see Appendix I - to be supplied at a later date) indicate that the Code rales are inadequate in several respects, primarily due to the lack of a sufficient data base. Nozzle spacing rules as given in various portions of the Code are not consistent. Of more importance, however, is the fact that a given rule may be conservative in one respect, such as for nozzles rpaced around the circumference of a vessel, but unconservative in another respect, such as for nozzles spaced in a longitudinal plane or in some nonorthogonal plane. Further, the Code rules may be unconservative for smaller nozzles with all the required reinforcement placed in the nozzle wall but excessively conservative for larger nozzles with a eignificant portion of the reinforcement in the form of increased vessel wall thickness. ( To resolve these problems two items were needed: (1)anacceptable definition of the isolated nozzle condition in tems of the dimen-sional extent of the region in which the nonle has a significant influence on the primary membrane stresses in the vessel, and (2) a computational rule for limiting the minimum distance between nozzles so that their local primary membrane stresses regions do not interact significantly. To define the isolated nozzle condition, the criterion that a primary membrane stress intensity greater than 10 percent above nominal would be considered significant, and that the directional distance from the nozzle centerline to the 1.1 T contourwouldbeconsideredtheboundaryoftheisolatednozzim n e region was adopted. The region was then further defined in terms of the dimensional parameters of the nozzle and vessel, the directional

H. R. Denton 4 orientation of the nozzles, and a vessel-wall reinforcement parameter, based on analytical results obtained from the finite-element parameter studies and existing experimental data. A new nozzle spacing rule based on the additional condition that no two nozzles should be closer than the sum of the distances to the boundary of their respective isolated nozzle has been formulated. This new rule is being proposed as a replacement for the four or more rules in current use. Figure 1, extracted from Appendix I (report not yet available) shows a comparison between the longi-tudinal spacing requircnent of the r.ew rule and the current rules for Class 1 nuclear pressure vessels (and piping) as a function of the nondimensional pr ameter. A = (dj + d2)//RjTr (3) where dj, d2 = inside diameters of nozzles Ri = inside radius of the vessel (or pipe) Tr = minimum vessel wall thickness required by Code to resist design pressure. The new rule, which includes the influence of the additional nondimensional parameters D (Ta and T /Tr, where D is the to/T ir.3idediameterofthevessdi,Tais$heactualvesselwa!1 thickness, a and tn is the nozzle wall thickness, is illustrated for parametric values of Dj/Ta = 10 and 100 and Ta/Tr = 1 and 2. This range effectively brackets the range of current pressure vessel design. Values of t /Ta were chosen to satisfy the enda rolac fnr 100 n percent reinforcement specified in paragraph NP-3338 of Section III of the Code. Figure 1 (enclosure 1) shows that although the current rules are simpler, since they are expressed only in terms of the one parameter A, they are somewhat u1 conservative for values of A < 2.75 (which includes most nuclear applications) when T /Tr = 1. On the other a hand, when the nozzle course of the vessel is thicker than the minime required, i.e., T /Tr > 1 and/or when A > 2.75 (which a includes most piping installations), the current rules tend to be excessively conservative. Thus, application of the new rule wil4 not only contribute to an increase in effective margins of s,fety but will also allow for design options that are not available."ider the current rules without detailed and expensive analyses. P

] H. R. Denton 5 4.0 Recommendations and Conclusions The proposed Code revisions for nozzle spacing and for stress indices for nuclear Class 1 vessels [NB-3300, NB-3338.2(d)(3) and NB-3339.l(f)] and nuclear Class 1 piping branch connections [NB-3600 and NB-3683.8] are enclosed as Appendix A. The latter are given in the proposed complete rewrite of the present ASME Code paragraph NB-3683 and stress index table [ Table NB-368i(a)-1]. The impact of this research program, leading to better design rules for vessel-nozzle, piping-branch design, does not require any reexamination of existing configurations. Such configurations have been traditionally designed with wall thicknesses in excess of Co-3 minimums and, where they have been designed to Code minimums, the resultant modest decrease in safety factors, as shown in this program, does not compromise the safety of the structures in question. This is due to the large. inherent factors of safety built in the Code directly, particularly as apply to stress limits for the approved vessel, nozzle and piping material. Robert J. Budnitz, ector Office of Nuclear Regulatory Research

Enclosures:

1. Figure 1 2. Appendices A-H (see attached sheet)

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l a o, Fig. 1. Proposed minimum normalized center line-to-center line dis-tance Lo//RfTp between nozzles in a longitudinal plane of a nuclear class 1 cylindrical pressure vessel or straight pipe as a function of the dimen-sionless sum-of-inside-diameters parameter 1 = (d + d )//R Tp, where La i 2 f is the centerline distance measured along the inside surface of the shell, Rf is the inside radius of the vessel (or pipe), Tp is the minimum required wall thickness of the vessel computed by the equations given in Code paragraphs NB-3324.1 or NB-3641.1. The lines identified by parametric values, e.g., D/Ta = 10, To/Tp = 1 are plots of the proposed rule for various values of the vessel inside diameter-to-actual wall thickness ratio D/Ta and the excess vessel thickness parameter T /T.. The lines a p identified by Code paragraph number, NB-3338, NB-3339, and NB-3643 are plots of the current rules under the sjub ect paragraph. The dashed line (old NB-3339) is the so-called 21/2 /RT rule given in the Code prior to the 1977 edition. F l

Appendices A. Proposed Revisions to ASME Boiler and Pressure Vessel Code, Section III, Paragraphs NB-3300, NB-3338.2(d)(3), NB-3339.1(f), NB-3600, NB-3683.8 and Table NB-3681(a)-1 B. B. R. Bass, J. W. Bryson, and S. E. Moore, " Validation of the Finite Element Stress Analysis Computer Program CORTES-SA for Analyzing Piping Tees and Pressure Vessel Nozzles," Pressure Vessels and Piping Computer Program Evaluatior and Qualification, PVP-PB-024, pp. 9-25, ASME (1977) ~~ C. J. W. Bryson, W. G. Johnson, and B. R. Bass, " Stresses in Reinforced Nozzle-Cylinder Attachments Under Internal Pressure Loading Analyzed by the Finite-Element Method - A Parameter Study," ORNL/NUREG-4 (October 1977) D. F. K. W. Tso et al., " Stress Analysis of Cylindrical Pressure Vessels with Closely Spaced Nozzles by the Finite-Element Method, Volume 1. Stress Analysis of Vessels with Two Closely Spaced Nozzles Under Internal Pressure," ORNL/NUREG-18/V1 (Nevember 1977) E. F. K. W. Tso and R. A. Weed, " Stress Analysis of Cylindrical Pressure Vessels with Closely Spaced Nozzles by the Finite-Element Method, Volume 2. Vessels with Two Nozzles Under External Force and Moment Loadings," NUREG/CR-0123, ORNL/NUREG-18/V2 (August 1978) ~ F. F. K. W. Tso and R. A. Weed, " Stress Analysis of Cylindrical Pressure Vessels with Closely Spaced Nozzles by the Finite-Element Method, Volume 3. Vessels with Three Nozzles Under Internal Pressure and External Loadings," NUREG/CR-0507, ORNL/NUREG-18/V3 (May1979) G. E. C. Rodabaugh and S. E. Moore, " Stress Indices and Flexibility Factors for Nozzles in Pressure Vessels and Piping," NUREG/CR-0778, ORNL/Sub-2913/10 (June 1979) H. J. W. Bryson, W. G. Johnson, and B. R. Bass, " Stresses in Reinforced Nozzle-Cylinder Attachments Under External Moment Loadings Analyzed by the Finite-Element Method - A Parameter Study," NUREG/CR-0506, ORNL/NUREG-52 (August 1979) i I. S. E. Moore and J. L. Mershon, " Design Criteria for the Sp3cing of Nozzles and Reinforced Openings in Cylindrical Class 1 Nuclear j Pressure Vessels," (Draft) l

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P J t J~/ APPENDIX A PiiOPOSED ASME CODE RULES MODIFICATIONS RELATIVE TO N0ZZLE SPACING IN NUCLEAR CLASS I PRESSURE VESSELS AND PIPING Class 1 Vessels (NB-3300) 1. Delete the last sentence of NB-3331(d)... "If fatigue analysis is not required, the restrictions on hole spacing are applicable unless there will be essentially no pipe reactions." 2. Add a new subsubparagraph to NB-3331: NB-3331(h) For openings in a spherical shell or head, the arc dis-tance measured between the center lines of adjacent nozzles along the inside surface of the shell shall be not less than two times the sum of their inside radil. For openings in a cylindrical shell, their centerline distance along the Inside surface of the shell shall be such that ((L /2)2 + (g f3)2)1/2 is not less than F times e g e the sum of their inside radii, where P(D/t)-0.075(3 f3)0. I C t/tr - C l## x2 3 Fe = 4e + f[1 + (0.4 - 0.1 t/t,)/A], A = (di + d ) /2 /Re,, 2 n" (# nl

• 2 t

n and wnere the magnitude of t/c used in computing the minimum nozzle spacing is not greater than 2.5. Numerical values of the constants C, C, and C3 are tabulated below for the appropriate range of A: 1 2 A C1 C2 C3 0 to 1 1.53 0.20 0.53 1 to 3 1 53 0.62 1.39 3 to 8 1.46 0.62 1.43 If t/c,. Is greater than 1.0, the thickened portion of the vessel shall extend"a distance from the center line of either nozzle not less than 3F times the diameter of the larger nozzle in the longitudinal direc-e tion and not less than 2 Fe times the diameter of the larger nozzle in the circumferential direction. Symbols used in the computations for minimum nozzle spacings are defined as follows: D = Inside diameter, in the corroded condition, of the vessel shell, In. d,d2 = inside diameters, in the corroded condition, of the two i openings under consideration, in. F = a correction factor which compensates for the membrane stress attenuation in the vessel as a function of nozzle dimensions.

2 R = 1/2 D = Inside radius of the vessel shell, In. t = wall thickness of the vessel shell in the region of the opening, In. t = thickness of the vessel shell which meets the requirements of NB-3221.1 in the absence of the opening, in. = thicknesses of the two nozzles under consideration (see ty3,tn2 fig. NB-3338.2-2), in. A = nondimensional stress attenuation parameter. 3 Replace NB-3332.l(b) with the following: NB-3332.I(b). No two unreinforced openings shall have their centers closer to each other, measured along the inside surface of the vessel wall, than 0.3/Rc, plus 2.4 times the sum of their diameters. 4. Replace NB-3338.2(d)(2) with the foilowing: NB-3338. 2 (d) (2). The arc distance measured between the center lines of adjacent nozzles meets the requirements of NB-3331(h). ~ 5 Replace NB-3339.l(d) with the following: NB-3339.l(d). The arc distance measured between the centerlines of adjacent nozzles meets the requirements of NB-3331(h). Class 1 Piping (NB-3600) I. Add a new subsubparagraph to NB-3643.1: NB-3643.l(g). For branch connections in a pipe, the arc distance measured between the centerlines of adjacent branches along the outside surface of the run pipe shall be such that [(4 /2)' + (L /3)231/2 g is not less than F t!mes the sum of their inside radl,e, where --0.075 0.1 F = 4e <i p/tm(0 F) ( bl + Tb2) C T /t -C3 - T 2 p m T, 2 T, c 0.4 - O.1 T,/t,], j +y(1+ A = (di + d )//2(o, - 2T,): 2 Numerical values of the constants C, C, and C3 are tabulated below 1 2 for the appropriate range of A: C1 C2 C3 x l 0 to 1 1.53 0.20 0.53 i to 3 1.53 0.62 1.39 i l 3 to 8 ?.46 0.26 1.43

t 3 I 2. Replace NB-3643.3(b)(1)(b) with the following: (b) No two unreinforced openings shall have their centers closer together, measured on the outside surface of the run pipe, than 0.3/0 5(0, - 2T,)c, plus 2.4 times the sum of their diameters. 3 Replace new NB-3683.8(c)(1) with the following: (1) For branch connections in a pipe, the arc distance measured between the centers of adjacent branches meets the requirements of NB-3643 l(g). i

%.s e. w. ~ : s.' ' ~ APPENDIX A .o r s: ' ' l',j . NB.3338.2-ND.3339.I . SECTION !!!, DIVISIOS . '.. for hillside connections in spheres or cylinders K = K,(1 + 2 sin 2 y) ~ for lateral connections in cylinders K = K, [I + (tan g)V3] where . r.. K -the o inside stress index of Table ND-i

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. 3338.2(c) l for a radialconnection - I ' ' K -the estim.ited o. inside stress index for the A,.; ~ ~ - -

• nonradial connection

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.(2) ne arc distance measured between the center lines of ad'acent noules alon8 the inside J

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surface of the shell is not less than three times the [.2.,('Y. sum of their inside radii for openings in a head or 'f'

.jip;..along the longitudinal axis of a shell and is not less r-

..t than two times the sum of their radii for openings ~ W (along the circumference of a cylindrical shell. When M ~; a-two nonles in a cylindrical shell are neither in a JC - longitudinal line nor in a~ circumferential arc, their ' Q.,. ,, center line distance along the inside surface of the w'.:

• shell shall be such that [(L,/2)'+ (L/3)']"'is not less

-9 '. N than the sum of their inside radii, where L,is the

.$.:-. component of the center line distance in the circum-

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.. J..? ferential direction and I, is 'he component of the ~~ . ;W.f..' center line distance in the longitudinal direction. s- ..S77 . (3) The dirnensional ratios are not greater than ~.Y13.-@ the following: v- ~ ~

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. Cylinder Sphere ~ Indde shell diam,ter D 100 tM

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[-[WS Insidtnozzle diamcaer 4 0. 0..'O

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Ins,de shell diameter D 0.80 O' EE S gy In the case of cylinbAc! total nqM-7,.., ...,..c..,. _ reinforcement area on the transverse axis of the , ; connections including any outside of the reinforce. 4 a. 2 ment limits, shall not exceed 200% of that required for

the longitudinal axis (compared to 50'"epermitted by f..-

, Fig. ND 3332.21) urJess a tapered transition section ' 7. J is incorporated into the reinfurcament and the shell, Jr. * ? meeting the requirements of NB.3361. .m --- (4) In the case of spherical shells and formed .U ' heads, at Icast 40"o of the total noule reinforcement . f area shall be located beyond 'the outside surface of s P. - the minimum required vessel wall thicknew. ' " ' * ' ' ~ ' (J) The inside corner radius.r,(Fig. ND-3338.2 ' ~ 2). is between 10"o and 100", of the shell thickness, t. ,- ~ *",y. (6) The outer corner radius, r,(Fig. ND-3338.2 . ] f 2), is large enough to provide a smooth transition .',N; between the noules and the shell. In addition, for -. r, ..,r; ...K...

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/ 9- /r )N 1 - SUBSECTION ND opening diameters greater than 1% times shell thickness in cylindrical shells and 2:1 c!!ipsoidal heads and greater than three shell thicknesses in spherical shells, the value of r shall be not less than 2 one-half the thickness of the shell or nonle wall, whichever is greater. (7) The radius, r (Fig. NB-3338.2-2), is not less - a, 3 than the greater of the following: (a) 0.002 0d,, where d,is the outside diameter j ',,. ~ of the nonle and is as shown in Fig. NB-3338.2-2, ,7g,, ~ ' ' and the angle B is expressed in degrees; .., (b) 2(sin 6)3 times offset for the configuration s.g 'shown in Figs. NB-3338.2-2(a) and (b).

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jj . m. -* **, ; l f. ' t j '* - C. , g * * **f .. '.s; I - - NB-3339 ' Alternative Rules for Nonle Design . ~ -...,. 1,~ Subject to the limitations stip'ulated in NB-3339.1, the requirements of this paragraph constitute an y,., ' f. * ~,.. acceptable alternative to the rules of NB.3332 .~b i.;. ~ through NB-3336 and NB-3338. 9 "- H NB-3339.1 Umitations, nese alternative rules are - : ~: Pr-applicable only to nonles in vessels within the...u.. c... - - 4j ;.. . w..e.... -- -~ limitations stipulated in (a) through (f) below. ,'f,y ,l ' ' ~ [* c ;,c 'O,.. e--. (a) ne nonle is circular in cross section and its .-?... axis is normal to the vessel or head surface. '~E n-(b) The nonle and re.1 forcing (if required) are welded integrally into the vessel with full penetration welds. Details such as those shown in Figs. NB-4244(a)-1, NB-4244(b)-1 and NB-4244(c)-1 are ac- .,..' a. ceptable. However, fillet welds shall be fmished to a -/ ht. '.'. - radius in accordance with Fig. NB-3339.! 1. C N:. (c) In the case of spherical shells and formed heads, at least 40"o of the total nonle reinforceme.. ... t. ' M-area shall be located beyond the outside surfare of ' ' the minimum required vessel wall thickness. (d) The spacing betweert the edge of the operiing 377 and the nearest edge of any other opening is not less W79 '. - than the smaller of 1.25(d + d ) or 2.5 Vir, but in i 2 t any case r.ot less than d, + dr. d, sad d are the inside ~.h a diameters of the openings. ,[.., and vessel adjacent to the nonle shall have a ratio of (c) The material used in the nonie. reinforcing., f,,{. ~,. " ~" UTS/YS of not less than 1.5 where .f. ' / '.< -. M : UTS=specified minimum ultimate tensile streagth, .,..,..s :,, c, YS = specified minimum yield strength d-- . -.,. - ;. u.. (/) The following dimensional limitations are met: S77 W79. - N.... - .,,. Nonels m. Sphen. cal ,. 5. : ; *. -. ' c r.~#: g... -'

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~ t0 to 200 .i'.kk.'-l'~~ l0 to 100, ;:.g. ..Qf:!' ' u .*v. D:1, . ~: 'c. .. u -, .q:. e;e r.g h. 0 33 mat. f:;;'89'd1+ 0.5 max. l.i ef'@l*'- ~' n.t., {, fr., :. :.,.,.,~,".......c ss;o, d.'D .. +., g.p.,: qg:s,0.s.m.;,:h.~.<q m. ... " ',. J '... l.,3 ;i.... - 0 '- ode - #f.O I v.. $. E,;4W,'E,,,b* ',Q3.F..U.IM.,,-/,.:,.g.WN /. w. i. 3 ,, f e (p" K*. %.no, q:,.;1 ; d,';&,,,* ;.~,..; n. ,c,...., a l,

,,,..,

. ;. s x,. c..., -

Q ...:.y' y . a ;.,, t. /* W;... W w :+w'u.W<.M.;.Wj'h,F,t * *#;."P..:.-M.b **',d' !.@ ~. . - s- .,..~m.... 6 . %:,;.. n -..~. u, i m. ..:::: s : w,. ..,.n ;.+ :.... :; :.. e ,..v - ;;. -,.- - v .,,4..,-;9 3-.n...:,,;.,.'. e,; ,.-l._,y

Outline for NB-3683 NB-3683 STRESS INDICES FOR USE WITH NB-3650 NB-3683.1 Nomenclature (a) Dimensions (b) Material properties (c) Connecting weld. (d) Loadings NB-3683.2. Applicability of Indices -- General (a) Abutting products (b) Out-of-round products NB-3683.3 Straight Pipe Remote from Welds NB-3683.4 Connecting Welds (a) Longitudinal butt welds (b) Girth butt welds (c) Girth fillet welds NB-3683.5 Welded Transitions (a) NB-4250 transitions (b) T....sitions within a 1:3 slope NB-3683.6 Concentric Reducers (a) Primary plus secondary stress indices (b) Peak stress indices NB-3683.7 Curved Pipe or Butt-Welding Elbows (a) Primary stress index (b) Primary plus secondary stress indices NB-3683.8 Branch Connections per NB-3643 (a) Applicability (b) Primary stress indices (c) Primary plus secondary stress indices (d) Peak stress indices NB-3683.9 Butt Welding Tees (a) Primary stress indices b) Primary plus secondary stress indices c) Peak stress indices h e e

NB-3683 STRESS INDICES FOR USE WITH NB-3650 The stress indices given herein and in Table NB-3681(a)-1, and subject to the additional restri.+.ione specified herein are to be used with the analysis methods of NB-3650. For piping products outside the applicable range, stress indices shall be established in accordance with NB-3681. NB-3683.1 Nomenclature (a) Dimensions. Nominal dimensions as specified in the dimensional standards of Table NB-3132.1 shall be used for calculating the numerical values of the stress indices given herein and in Table NB-3681(a)-1 and for evaluating Eqs. (9) through (14) of NB-3650. For ANSI B16.9, ANSI B16.28, MSS SP 48 or MSS SP 87 piping products, the nominal dimensions of the equivalent pipe, e.g., sched. 40, as certified by the manufceturer, shall be used. Not more than one equivalent pipe size shall be certified for given product items of the same size, shape, 2nd weight. For piping products such as reducers and tapered-wall transitions which have different dimensions at either end, the nominal dimensions of the large or small eni, whichever gives the larger value of D,/t shall be used. Dim;nsional terms are defined as follows. D, nominal cutside diameter of pipe, in. u nominal inside diameter of pipe, in. D = g 2R, = (D, - T,) = mean diameter of designated run pipe, in. See D = m NB-3683.8(c) and Fig. NB-3683.3(a)-1. D,,= = maximum outside diameter of cross section, in. Dg = minimum outside diameter of cross section, in. nominal outside diameter at large end of concentric reducer, Dr = in. See NB-3683.6. nominal outside diameter at small end of concentric reducer, D2 = in. See NB-3683.6. d, nominal outside diameter of attached branch pipe, n, = i d nominal inside diameter of branch, in. = g (d t ) = nominal mean diameter of reinforced or unreinforced d, = g y branch, in. See NB-36S3.S(c). tR/r2 = characteristic bend parameter of a curved pipe or butt-h = welding cibow. 0.0491 (Dy - Dj) = moment of inertia of pipe, in. I =

L 2 Li = height of no::le reinforcement far branch connections, in. See Fig. NB-3643. 3(a)-1. L,42 = length of cylindrical portion at the large end and small end i of a reducer, respectively. See NB-3683.6. R = nominal bend radius of curved pipe or elbow, in. j R, = (D, - T )/2 = mean radius of designated run pipe, in. See r NB-3683.8 and Fig. NB-3643.3(a)-1. r = d /2 = inside radiu: of branch, in. See Fig. NB-3643.3(c)-1. g g r, = (D, - t)/2 = mean pipe radius, in. ry = (d - Tj)/2 = mean radius of attached branch pipe, in., see g Fig. NB-3643.3(a)-1. r = outside radius of reinforced no::le or branch connection, in. P See Fig. NB-3643. 3(a)-1. ri,r2 P3 = designated radii for reinforced branch connections and concentric reducers, in., see NB-3683.6, NB-36S3.8, and Fig. NB-3643. 3 (a)- 1. T = nominal wall thickness of attached branch pipe, in., see 3 Fig. '4B-3643. 3(a)-1. Tf = wall thickness of branch connection reinforcement, in., see Fig. NB-3643.3(a)-1. T, = nominal wall thickness of designated run pipe, in., see Fig. NB-3643.3(a)-1. t = nominal wall thickness.. pipe, in. For piping products purchased to a minimum wall specification, the nominal, wall thickness shall be taken as 1.14 times the ninimum wall. t = wall thickness of no::le or branch connection reinforcement, in. See NB-3683.S; also used for concentric reducers, see NB-3633.6. t = maximum wall thickness of a welding transition within a distance ea.: of Q from the welding end. See NB-3683.5(b). = nominal wall thickness at large end of concentric reducer, in. ti See NB-3683.6 = nominal wall thickness at small end of concentric reducer, in. t2 See NB-3683.6. = minimum wall thicknesses at the large end and small end of a tim,t2n reducer, respectively. that is required to resist the design pressure P in accordance with Ec. (1), NB-3641.1.

1 ~ 3 2J/D, = section modulus at pipe, in.3 2 = 3 w(rf)2Tf = approximate section modulus of attached branch pipe, in.3 2 = w(R,)2T, = approximate section modulus of designated nm pipe, in.3 2, = cone angle of concentric reducer, deg. per NB-3683.6. a = 6 = the average permissible mismatch at girth butt welds as shown in Fig. NB-4233-1. A value of 6 less than 1/32 in. may be used provided that the smaller mismatch is specified for fabrication. For " flush" welds as defined in NB-3683.1(c). and for t > 0.237 in., 6 may be taken as zero. A = radial weld shrinkage measured from the nominal outside surface, in. 0 = slope of nozzle-to-pipe transition for branch connections, degrees. See Fig. NB-3643. 3(a)-1. (b) Haterial Properties. Unless otherwise specified, materials prop-erties at the appropriate temperature, as given in Appendix I shall be used. Terms are defined as follows. E = modulus of elasticity for the material at room temperature, psi, taken from Table I-6.0. M = materials constant. = 2 for ferritic steels and nwnferrous materials except nickel-chrome-iron alloys and nickel-iron-chrome alloys. = 2.7 for austenitic steel, nickel-chrome-iror. alloys and nickel-iroi.-chrome alloys. See NB-3683.2(b). S = yield strength of the material at the Design Temperature, psi, ~ taken from Table I-2.0. v = 0.3 = poisson's ratio. .(c) Connecting Felds. Connecting welds in accordance with the require-ments of this Subsection are defined as either flush or as-ceZded welds. (2) Flush ecZds are defined as those welds with contours as defined in the following sketch.~ The total thickness (both inside and outside) of the weld reinfo'rcement shall not exceed 0.lt. There shall be no concavity on either the interior or exterior surfaces and the finished contour shall nowhere have a slope greater than 7 deg., where the angle is measured from a tangent to.the surface of the pipe, or on the tapered transition side of the weld, to the nominal transition surface. -=--e a v-m- o

= 4 7 dog. man. 7 deg. man. h l t

g. men.

7 deg. mas. ~ 1 1 (2) As-celded celds are defined as welds not meeting the special requirements of flush welds. (d) Loadings. Loadings for which stress indices are given include internal pressure, bending and torsional moments, and temperature dif-ferences. The indices are intended to be sufficiently conservative to also account for the effects of transverse shear forces normally encountered in flexible piping systems. If, however, thrust or shear forces account for a significant portion of the loading on a given piping product, the effect of these forces shall be included in the design analysis. The values of the moments and forces shall be obtained from an analysis of the piping system in accordance with NB-3672. Loading terms are defined as follows. P = design pressure, psi. P, = range of service pressure, psi. P* = the maximum value of pressure in the load cycle under considera-tion, psi. Ng,M M3 = orthogonal moment loading components at a given position in 2 I a piping system, in.-lb. = 4)f + N2 + Nj = resultant moment loading applied during the 3 specified operating cycle for straight through products such as straight pipe, curved pipe or elbows, and concentric reducers. Ngj = orthogonal moment components of a tee or branch connection l as shown in the following sketch where i = x,y,:: and j = 1,2,3. l 6 gMy3 i

M,3 i3/ 'h AMy2 h FI M

1 E M,1 @ o M,2 M,g .,_..>y l

5 y. M 1, and M 2 2 for the run are x,M 2e # 1e M The moment components M t y calculated at the intersection of the run and branch centerlines. The moment components M,3, N 3, and M,3 for a branch connection, where y d/D,s0.5maybecalcu'latedforapointonthebranchcenterlineata ' distance D,/2 from the intersection of the run and bunch centerlines. 9, and M,3 are calculated at the intersection of the run l Otherwise M,3, M 3 r and branch centerlines. M M M = run moment components for use with the stress indices l g y of NB-3633.8 and NB-3683.9. Their numerical values are calculated as follows. If Ngi and Mg2, where i = x,y,a have the same alge-braic sign (+ or -), then H, = 0. If Mgt and Mf2 have opposite g If algebraic signs, then M, equals the smaller of Ngt or Mf2-l g g2 are unsigned, the:. N,may be taken as the smaller Mft and M g of Mgt or Hf2 Combination of signed and unsigned moments from difterent load sources shall be done after determination of t M,. g Mg = /Ng3 + N'3 + N'3 = resultant moment on the branch for branch connections or tees, in.-lb. l except it includes only moments due to thermal expansion My=sameas#3 and thermal anchor movements. M, = /N- + Mg + N{3 = resultant moment on the n2n for branch con-nections or tees, in.-lb. M,* = same as M,except it includes only moments due to thermal expansion ~ and thermal anchor movements. For branch connections or toes the pressure term of Eqs. (9), (10), (11), and (13) shall be replaced by the following. For 50.. (9): St P D, 2I r r For Eqs. (10) and (13): P, D, Ct 2T r

• l 6

l For Eq. (11): KnCnP,D, 2 T, For branch connectirns or tees, the moment term of Eqs. (9), (10), (11), (12), and (13) shall be replaced by the following pairs of terms: For Eq. (9): B, M, B M 2 2y y For Eqs. (10) and (13): C, M, C M 2 2y y 7+ [r b For Eq. (11): C,K,M, K M C 2 2 2y 2y y Z T b r For Eq. (12): C,M,* M* C 2 1y y Z Z, y where the approximate section modulii are: y = n'(ry)2Tf Z 2 Z, = w (R )p l' NB-3683.2 Aoplicability of Indices - General. - The B, C, and K stress indices given.herein and in Table NB-3681(a)-1 predict stresses at 2 weld joint or within the body of a particular prodact. The stress indices given for ANSI B16.9,' ANSI B16.28, MSS SP 48, and MSS SP 87 piping products apply only to seamless products with no connections, attachments, or'other l extraneous si ess raiser on the body thereof. The stress indices for welds are not applicabic if the radial weld shrinkage a is greater than 0.256. For products with longitudinal butt welds the K, X, and K3 indices i 2 shown shall be multiplied by 1.1 for f!ush welds or by 1.3 for as-tJeZded welds. At the intersection of a longitudinal butt weld in straight pipe l with a girth butt weld or girth. fillet weld,' the C, K, C X, and K3 3 3 2 2 indices shall be taken as the product of the respective indices. ~

.~ ~ 7 (a) Abutting Producca. In general and unless otherwise specified it is not required to take the product of stress indices for two piping products, such as a tee and a reducer when welded together, or a tee and a girth butt weld. The piping product and the weld shall be qualified separately. For curved pipe or butt welding elbows welded together or joined by a piece of straight pipe less than 1 pipe diameter long, the stress indices sha!1 be taken as the product of the indices for the elbow cr curved pipe and the indices for the girth butt weld, except for 31 and Cj which are exempted. (b) Out-of-Round Products. The stress indices given in Table NB-3681(a)-1 are applicable for products and welds with out-of-roundness not greater than 0.08c, where out-of-roundness is defined as D -D For g. straight pipe, curved pipe, longitudinal butt welds in straight pipe, girth butt welds, NB-4250 transitions and 1:3 transitions not meeting this requirement, the stress indices shall be modified as specified below. (1) If the cross section is out-of-round such that the cross section is approximately elliptical, an acceptable value of Ki may be obtai.ned by multipl-ing the Kg values in Table NB-3681(a)-1 by the factor F,, where i Dmg;. -- D,r. n 1.5 F,=1+ t 3 7 1+0.455[33,h L) where P4 is the maximum value of pressure in the load cycle under considera- [ tion. (2) If D -D is not greater tnan 0.0SD,, an acceptable value g of Ki may be obtained by multiplying the Kg values in Table NB-3651(a)-1 by the factor Tig, where MS I' Fig = 1 + P D,/2c

• where M = 2 for ferritic steels and nonferrous materials except nickel-chrome-iron alloys and nickel-iron-chrome alloys M = 2.7 for austenitic steel, nickel-chrome-iron alloys, and nickel-iron-chrome alloys.

E

8 NB-3683.3 Straight Pine Remote from Welds. The stress indices given in ' Table Nd-3681(a)-1 apply for straight pipe remote for welds or other dis-continuities except as modified by NB-3683.2. NB-3683.4 Connecting Welds. The stress indices given in Table NB-3681(a)-1 are applicable for longitudinal butt welds in straight pipe; girth butt welds joining items with identical nominal wall thicknesses; and girth fillet welds used to attach socket weld fittings, socket weld valves, slip-on flanges, or socket welding flanges, except as modified herein and by NB-3683.2. (a) Longitudinal Butt Voldn. The stress indices shown in Table NB-3681(a)-1 are applicable for longitudiral butt welds in straight pipe except as modified by NB-3683.2. (b) Girth Butt V'lds. The stress indices shown in Table NB-3681(a)-1, e except as modified herein and in NB-3683.2 are applicable to girth butt welds between two items for which the wall thickness is between 0.875c and 1.lt for an axial distance of Yo,e from the welding ends. Girth welds may also exhibit a reduction in diameter due to shrinkage of the weld material during cooling. Thv indices are not applicabic if A/t is greater than 0.25, where A iJ the radial shrinkage measured from the nominal outside surface. For as-polded girth butt welds joining items with nominal wall thick-nesses e < 0.237, the C2 index shall be taken as: C2= 1.0 + 3(6/t), but not greater than 2.1. (c) Girth Fillot V'lds. The stress indices shown i,n Table NB3681(c)-1 e ~ are applicable to girth fillet welds used to atta:h socket weld fittings, socket weld valves, slip-on flanges, or socket welding flanges except as modified in NB-3683.2. NB-3683.5 Welded Transitions. The stress indices given in Table NB-3681(a)-1, except as modified herein and in NB-3683.2 are applicable for NB-4250 welded transitions as defined under NB-3683.5(c) and for 1:3 welded transition as defined under NB-3683.5(b). Girth butt welds may also exhibit a reduction in diameter due to shrinkage of the weld material during cooling. The indices are not applicable if A/t is greater than 0.25.

9 -(a) #B-4250 Transitions. H e stress indices given in Table NB-3681(a)-1, except as modified herein and in NB-3683.2 are applicable to girth butt welds between an item for which the wall thickness is between .0.875c and 1.lt for an axial distance of /D,e from the welding end and another item for which the welding end is within the envelope of Fig. NB-4250-1, but with inside and outside surfaces that do not slope in the same direction. For transitions meeting these requirements the C, C, and C3 1 2 indices shall be taken as: i = 0.5 + 0.33 (D,/t)0. 3 + 1.5 (6/t); but not greater than 1.8, C C2 = 1.7 + 3.0 (6/t); but not greater than 2.1, C3 = 1.0 + 0.03 (D,/c); but not greater than 2.0. For flush welds and for as-ceZded joints between items with t > 0.237, 6 may be assumed to bc :ero. (b) Transitions Richin a 1:3 Slope. He stress indices given in Table NB-3631(a)-1, except as modified herein and in NB-36S3.2 are applicable to girth butt welds between an item for which the wall thickness is between 0.3752 and 1.It for an axial distance of /D,0 from the welding end and another item for which the welding end is within an envelope defined by a 1:3 slope on the inside, outside, or both surfaces for an axial distance of /D,0, but with inside and outside surfaces that do not slope in the same direction. For transitions meeting these requirements the C, C, t 2 and C3 indices shall be taken as: Ci = 1.0 + 1.5 (6/c); but not greater than 1.8, C,," tm/t + 3 (6/t); but not greater _ than the smaller of 2 [1.33 + 0.04 /D /c + 3 (6/c)] or 2.1, C3 = 0.35 (t /t); but not greater than 2.0, where t is the maximum wall thickness within the transition zone. If (tmar/t) s'1.10 the stress indices given in NB-3683.4(b) for girth butt welds may be used. For flush welds and for as-ecIdad joints between items with t > 0.237, 6 ma; be assumed to be zero. NB-3683.6 Concentric Reducers. The stress indices given in Table NB-3681(c)-1, except as added to and modified herein and in 0 -3683.2 are l applicable to butt welding concentric reducers manufactured to the require-ments of ANSI B16.9, MSS SP 48, or MSS SP a7 if the cone angle a, defined in the following sketch, is less than 60*;

10 L, e i imi,,, o a '2' / y fy g t I 0 12 t2 2 IP l and if the wall thickness is not less than clm throughout the body of the reducer, except in and immediately adjacent to the cylindrical portion on 4 the small end, where the thickness shall not be less than 32 The wall-m thicknesses t, and $ m are the minimum thicknesses required to resist the i 2 design pressure P at the large end and small end, respectively, in accord-ance with Eq. (1), NB-3641.1. (b) Primary Plus Second.1ry Stress Indices. The C1 and C2 stress indices given in (1) or (2) shall be used depending on the dimensions of the transition radii ri and r2-(1) For reducers with vi and r2 1 0.1 Dt C3 = 1.0 + 0.0058 a/D /#n n 0 C2 = 1.0 + 0.36 a.4 (p n)

• n where C,,/t is the larger of D /c3 and D /t.

~ 3 2 2 y (2) For reducer with ri and/or r2 < 0.1D1 Ci = 1.0 + 0.00465 a.285 (p ft )o.39 l C2 = 1.0 + 0.0185 a/D /e y n whcic D /t is the larger c,f D /ti and D /0 - t 2 2 n (b). Peak Stress Indicas. The Ki and K2 indices given in (1), (2), or (3) shall be used depending on the type of connecting weld, amount of mismatch, and thickness dimensions. (1) For reducers connected to pipe with fZ::sh girth butt welds: k' Kg = 1.1 - 0.1 , but not less than 1.0 '/D t,

11 L" K2 = 1.1 -- 0.1 , but not less than 1.0 /D c, where I // Dye, is the smaller of L //D ci and 4 //D 8 - g i i 2 22 (2) For reducers connected to pipe with as-celded girth butt welds where t, $2 > 3/16 in, and 6 /t, 6 /82 s 0.1: 2 i 3 i L* Ki = 1. 2 -- 0. 2 , but not less than 1.0 /D,c, L* K2 = 1. 8 -- 0. 8 , but not less than 1.0 /D,C, whereIg/D,e is the smaller of L //D ti and 5 //D 82 2-t i 2 n (3) For reducers connected to pipe with as-velded girth butt welds, where ti or t2 s 3/16 in, or d /tg or 6 /82 > 0.1: i 2 L* Ki = 1. 2 -- 0. 2 . but not less than 1.0 'U # mm L" K2 = 2. S -- 1. 5 , but not less than 1.0 /D,t, where I //D,e is the smaller of L //D ti and 5 //D 822 i i 2 g n 18-3683.7 Curved Pioe or Butt-Welding Elbows. The stress indices given in Table NB-36S1(a)-1, except as added to and modified herein and in NB-3683.2 are applicabic to curved pipe or butt welding elbows manufactured to the requirements of ANSI B16.9, ANSI B16.28, MSS SP 48, or SGS SP 87. (a) Primars Stress I der. The primary stress index B2 for moment n loadings shall be taken as: B2 = 1.30/h2/3; but not less than 1.0, where h = tR/r,2, (b) Primary Plus Secondary Strees Indices. %Ci and C2' dices shall be taken as 4

I: y o; 12 C1 = (2R - r,)/2 (R '- r,) 2 = 1.95/h /3; but not less than 1.5, 2 C Where h = tR/r2 NB-3683.8 Branch Connections per NB-3643. He stress' indices given in Table NB-3681(a)-1, except as added to and modified herein and in NB-3633.2 are applicable to reinforced or unreinforced branch connections meeting the general requirements of NB-3643 and the additional require-ments of NB-36S3.8(a). Symbols are defined in NB-3683.1 and in Fig. NB-3643. 3 (a)-1. (a) Applicability. The stress indices are applicable provided the fol-lowing limitations are met. (1) For branch connections in a pipe, the are distance measured between the centers of adjacent branches along the outside surface of the run pipe is not less than three times the sum of the two adjacent branch inside radii in the longitudinal direction, or is not less than tvo times the sum of the two adjacent branch radii along the circumference of the run pipe. (2) The axis of the branch connection is normal to the run pipe surface. (3) h e run pipe radius-to-thickness ratio R /T, < 50; and the m branch-to-rt:n radius ratio ry/R < 0.50. (4) The inside corner radius, r1 [ Fig. NB-3643.3(a)-11 for nominal pipe sizes greater than 4" ips shall be between 10*6 and 50's of T,. The radius ri is not required for branch pipe sizes cmaller than 4" ips. (5) The branch-to-run fillet radius, r2, is not less than the larger of Tf/2; T,,/2; or (Tf + y)/2 IFig. NB-3643.~(d-1(c)]. L-(6) The branch-to-pipe fillet radius, r3, is not less than the I larger of 0.002 0 d, or 2(sine)3 times offset IFig. NB-3643.3(n)-1]. where o is exprcssed in degrees. ( .(7) If Li equals or exceeds 0.5/r T, then rf can ha taken as the g3 radius to the center of T. 3 (b) Prinary Stress Indices. The primary stress indices 33,3 and 32, 3 .shall be taken as: 3 = 0.5 C23; but not less than 1.0, B2 = 0.75 C,; but not less than 1.0. B2 2 p 2

.~ 13 (c) Primary Plus Secondary Stress Indices. The C, C23, and C, 1 2 indices (for moment loadings see NB-3683.1(d)] shall be taken as: f 3 .14a ~fp10.182 Id 0.367 I I0,382 1 t 0 Ci = 1.4 [ [ [T

but not less than 1.2.

L ') k"> \\") LJ If.r2/t > 12, use r2/b 12 fcr computing C. = t n n P 'f I '\\ (g 12/ 3 p1 1/2 T r b = 3 [') [

but not less than 1.5 C2 L

\\ m) L'l.\\P) b-\\1/t. J '= 1.15

but not less than 1.5,

~r t (") where, for Figs. NB-3643.3(a)-1(a) and (b): t t 0.5 (d T )1/2 t =T if L 3 3 = Tf if Li < 0. 5 (d T ) l mb For Fig. NB-3643.3(a)-1(c) t = Tf + (2/3)y if 0 s 30" n i if 0 > 30*. =Tf+0.335L For Fig. NB-3643.3(a)-1(d) Tf=T. b e 3 n (d) Peak Stress Indices. The peak stress indices X23 and X2 for p moment Icadings 'see NB-3633.1(d)] shall be taken as: K23 = 1.0, X2p y 1.75, and K2 C2 shall be a minimum of 2.65. ~' p p NB-3683.9 Butt-Weld'ng Tees. The strer.s indices given in Table NB-3681(a)-1, except as added to and modified herein and in NB-3683.2 are anplicable to butt-welding teet, manufactured to the equire:r.ents of ANSI t$16.9, M U SP 48, or MSS SP 87. I (a), Mnary Stress Indices. The primary stress indices 323 and 32f shall be taken is: 23 = 0.4 (R/T )2!3; but not 'ess than 1.0, B r = 0.5 (RgT,)2/3; but not less than 1.0. 327 c. z---

e 14 l (b) Primary Plus Secondary Stress Indices. The C and C, stress 2g 2 indicas for moment loadings (see NB-3683.1(d)] shall be taken as: 23 = 0.67 ' (R/T,)2/3; but not less than 2.0, 'C 0.67 (RgT,)2/3; but not less than 2.0. C2 = p. (c) Peak Stress Indices. The peak stress' indices K23 and X2 for p moment loadings [see NB-3683.1(d)) shall be taken as: K23 = 1.0, K2 1.0. = p e i I I l i. _j w 0 ,i' 9 l^ i, I b r s .. ~. - e.. s.--

7 ~... ' ... _. ~....... .9y ...y : r. Lv.... ~ . 2:7 7 -~ '~~~***'**~.-. Q.7 ~~7'~~... Q :~.,~.";.*,' Q~ f ( F Table N8-3631's)-1 STRESS INDICES FOR USE W!iH QUATIONS IN NS-3650 Applicable for D,/t s 100 for C or K indices; D,/t s 50 for 8 indices D U Piping Products and Joints" Internal Pressure . Moment Loading Therr.a1 Loading See Note B: C1 K1 82 '2 K2 C3 CI ~K3 Straight pipe, remote from welds 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 d sr other discontinuities Lodgitudinst butt welds in straight I P Pe (a) Flush 0.5 1.0 1.1 1.0 1.0 1.1 1.0 1.1 e ~ (b) As-welded; * > 3/16 in. 0.5 1.1 1.2 1.0 1.2 1.3 1.0 1.2 e (c) As. welded; * $ 3/16 in. 0.5 1.4 2.5 1.0 1.2 1.3 1.0 1.2 a 'frth butt welds between nominally !dentical wall thickness items (a) Flush. 0.5 1.0 1.1 1.0 1.0 1.1 0.60 0.60 1.1 f -(b) As-welded 0.5 1.0 1.2 1.0 1.0 1.8 0.60 0.50 1.7 f '. Girth fillet weld to socket weld Fittings, socket weld valves, 0.75 1.8 3.0 1.5 2.1 2.0 2.0 1.0 3.0 g slip-on or socket welding flangss NB-4250 **ansitions '(a) F1'ush 0.5~ Note 1.1 1.0 Note 1.1 Note 1.0 1.1 h (b) - As. welded 0.5 Note 1.2 1.0 Note 1.8 Note 1.0 1.7 h Transitions within a 1:5 slope envelope

• ~

(a) Flush' O.5 Note 1.1 1.0 Note 1.1 Note 0.60 1.1 i -(b).As-welded 0.5 Note 1.2

1. 0 - Note 1.8 Note 0.60 1.7 i

- Butt *1 ding concentric reducers per 1.0 Note Note 1.0 Note Note 1.0 0.5 1.0 f ANSI B16.9 or 816.28 Curved pipe or butt welding elbows 0.5 Note 1.0 Note Note 1.0 1.0 0.5 1.0 k - Brtneh connections per N8-3643 0.5 Note 2.0 Note Note Nete

k. S 1.0 1.7 4

_ Butt welding tees 0.5 1.5 4.0 Note Note Note 1.0 0.5 1.0 m "For definitions, applicability, and specific restrictions, see NB-3683. For the calculation of pressure and moment loads and special instructions regarding Eqs. (9) through (13), see NB-3683.1 (d).

1. or special instructions regarding the use of these indices for welded products, intersecting welds, abutting F

products or.out-of-round products, see NS-3683.2. See N8-3653.3 " Straight pipe Remote from Welds."

1. See NS-3633 4(a) " Longitudinal Butt Welds."

ISee N8 3653.4(h) " Girth Butt Welds." ~ ISee N8 3683.4(c) " Girth Fillet rel'ds." hSee NS-3683.5(a) "NBE4250 Transitions." 'See NS-3653.5(b) " Transitions Within a 1:3 Slope." 'See NS-3653.6 " Concentric Reducers." ~ g. .See also NB-3683.2(a) and (b). i See NS-3653.7 " Curved Pipe or Butt helding Elbows." 'See NB-3633.8 "Brard. Connections per NB-3643." See also NB-3683.1(d). 1 "See NS-3655.9 " Butt' Welding Tees." '. See also N5-3683.1(d). s 4 e -e---- y

NS-3677.3-NB-3683.I SECTION III DIVISION i-SUBSECTION NB . lines be used, but if two or more reliefs are ccmbined. O the discharge piping shall be designed with sumcient B C KorI-y flow ares to prevent undue back pressure. (c) When the umbrella or drip pan type oi where connection between the pressure relieving safety device and the discharge pipingis used, the discharge o = elastic stress due to load, L piping shall be so designed as to prevent binding due S= nominal strest due to load, L to expansion movements and shall be so dimensioned For B indices, a represents the stress magnitude as to prevent the possibiliiy of blow back of the corresponding to a limit load. For C or Kindices, o effluent. Individual discharge lines shall be tis'ed in represents the maximum stress intensity due to loaci, this application. Drainage shall be provided to L For i factors, o represents the principa' ' tress at a remcve water collected above the safety valve seat. Parucular point, surface and direction dc.oload L (f) Discharge lines from pressure relieving safety ne nominal stress, S, is defined in detailin the tabks

f. y devices within the scope of this Subsection shall be ofstress mdices, g

designed to facilitate drainage if there is any possibili-(b) He general definition of a stress index fer ty that the efluent can contain liquid. thermalloadsis: C. K = & T where NB-3680 STRESS INDICES AND FLEXIBILITY FACTORS o-maximum stress intensity due to thermal difference. AT ~ NB 368I Scope E= modulus ofclasticity W78 (a) There are two types ofanalyses allowed by the a = coefficient of thermal expansion a T= thermal difference rules of this Subarticle. The applicable B. C, and K indices to be used with Eqs.(9).(10),and(II)of NB. De values of E, a and AT are defined in detail in 3650 are given in Table NB-3681(a)-1. The applicable NB-3650[exibihty factors are identified herein 7cj p indices to be used with the detailed anal 3200 are given in NB-3685 and NB6'-.ysis of NB-with appropriate subscripts. He general definition of 833y. N##I#'" (b) Methods of determining flexibility factors for some commonly used piping products are given in e N B-3687. b k~ y~. (c) Values of stress indices are tabulated for commonly used piping products and joints. Unless g,,, specific data, which data shall be referenced in the Stress Report, exist that would warrant lower stress B = rotation of end a, with respect to end b, due indices than those tabulated or higher tiexibility. to a moment load, M., and in the direction of factors than those calculated by the methods of NB-y 3$8I,0the stress i., dices given shall be used as B, = nominal rotation due to moment load M minimums and the flexibility factors shall be used as The flexibility factor k and nominal rotation B_are maximums. defmed in detail for specific components in NB-3687.' (d) For piping products not covered by NB-3680, b stress indices and flexibility factors shall be estab-lished by experimental analysis ( Appendix II) or NB-3683 Sacss Indices for Use With NB-3650 theoretical analysis. Such test data or theoretical analysis shall be ir :luded in the Stress Report. p NB-3683.10clinitions for Stress Indices g p,,,, D,= norran'al'euuide diam. For ANSt B16.9 NB-3682 Definitions of Stress Indices ana 3,,['jr . in; s tjg:s o /l penducts,4hese are n Flexibility Factors eier or pipe, in. p,p t= nominal wall thicknd dimensions o (a) The general definition of a stress inder, for or pipe, in. / the equivalent mechanicalloads is: ,(-89MD.D.'). in

• 4

, pip'- E .'2

NB-3000 - DESIGN N" 3683.1-NB-3685A h ] sions o(thin end of taper,(af For Tapered Transition Joints: Use dimen-D,(D ) = maximum (minimum) outside diameter of 2 g j elbow with out of round cross section (b) For Reducing Branch Connections or Reduc- - essentially describable as an ellipse or ovat j ingTees:\\ / shape (Fig. N B-3685,.2-1),in. Z=section modulusofcrosssection = 0.0982 ~f (1) Pressure dependent term: Use dimensions of run or branch, whichever gives larger'value of D,/t; f, (D,4 - D,4)/D,, in.3 lk (2) Moment loads: See Notes'5,7, & 9 ofTable E = modulus of elasticity, psi (Table I-5.0) NB 3683.21. \\-' NB-3685.3 Stress From Stress Indices. To obtain I l

• ", 'e ependent term: Ose dimensions of stresses from stress index:

large or small end,;hiche r gives the larger value of Load Multiply stress Index by:

1. Q (2) Momen: dependent term: Use dimensions '

Internal Pressure P cf small end./ l u, u.cz D/ lh 7 3 u, u,iz "W78 NB-3683.2 B, C, and K Indices. Table NB-3681(a)-1 s u, u,/z givejs (alues of B, C, and K ind'ces, along with ( i additional dimensional defmitions and dimensional ) re'strictions. i NB-3685.4 Classification of Stresses. For analysis f' of a curved pipe or welding elbow to NB-3210, the ~ following rules shall apply to the classification of NB-3684 Stress Indices for Detailed Analysis stresses developed under a load coqtrolled in-plane or out-of plane moment as distmguished from a dis-NB-368 4.1 Definition cf Stress Components. Die plac : ment controlled loadina. symbols for the stress components and their (a) The entire membrane portion of the axial, defmitions are given in Fig. NB-3684.1-1. These circumferential, and torsional stresses shall be consid-definitions are applicable to all piping products, and cred as primary (P ). t the stress indices given in the tables m NB-3685 and (b) Seventy-five percent (75c) of the through-wall c N B-%66 are so dermed. bending stresses in both the ax61 and the circumfer- ,y NB 3685 Curved Pipe or Welding Elbows NB-3685.1 Applicability of Indices. The indices V given in Tables NB-3685.1-1 and NB-3685.1-2 give stresses in curved pipe or elbows at points remote [% from girth or longitudinal welds or other local discentinuities. Stresses in elbows with local discon-4 tinuities such aslongitudinalwelds,supportlugs, and i h branch connections in the elbow shall be obtamed by ks appropriate theoretical analysis or by experimental j6 g analysis in accordance with Appendix II. 6 NB 3685.2 Nomenciature(Fig.NB-3685.2-1) P= internal pressure, psi D,= nominal outside diameter ofeross section, =the suess c ng nent in the plane of-the section under. consideration and parallel to tha boundary of the section a = the stress component normal to the plane of the section n e, = the stress conponent normal to the boundary of the section t.,= minimum,pecified wall thickness, in. o s tensity (combined stress) at the point undes A - an additional thickness, in. (N B-3641.1) = the jera 9ns R = bend radius, in. r= mean cross section radius ir.. A = r.,R/r2 gg. y2 (Table NB-3685.1-2 limit-FIG. NB-3684.1-1 DIRECTION OF STRESS ed to A 2 0.2) 00MFONENTS 153

Talle NB.M81( )-! SECTION III. DIVISION 1 - SUBSECTION NB

• W78 TABLE NB-3631(a)-1 S79 STRESS INDICES FOR USE WITH EQUATIONS IN NB-3650 n

W79 jNoLApplicable fot f_> 100) D Internal Moment Thermal Pressure Loading

• Loading

( Piping Products and Joints 8t C K 8: C t t 3 Ke C ' C's /K 3 Straight pip (remote from welds' or other disco.itir uitses , ' 0.5 1.0 [1.0' 1.0 1.0 1.0 1.3 1.0 ~ t Girth butt wefd between straight pipe or between pfpe and butt weldirig components m la) flush ( j 0.5 1.0 1.1' - 1.0 1.0 1.1 1.0 0.5 1.1 .b) as welded t>3/16 in. [and 6/tS0.1] 0.5 1.1 1.2' 1.0 1.0 1.8 1.0 0.5 1.7 g Lc) as welded t$3/16 iri. dor 3/t>0.1] 0.5 1.1 1.2' 1.0 1.4 2.5 1.0 0.5 1.7 \\ + l Girth fillet weld to socket weld fittings or ket weldsng flanges \\ 0.75 2.0. 3.0 1.5 2.1 .0 1.8 1.0 3.0 \\ Longitudinal butt welds in straigtr pipe - } (a) flush 0.5 1.0

• 1.1' 1.0 l

j.0 1.1 1.0 1.1 (b) as welded t>3/16 in. 0.5 1.1 1.2' 1.0.* 1.2 1.3

• 1.0 1.2 (c) as welded if3/16 in.

0.5 1.4 2.5' 1.0 ' 1.2 1.3 1.0 1.2 i .Tacered transition joints per NB.4425 l and Feg. NB-4223-1"'8 J }a) flush or no girth wela closer than V6 0.5 6 1 1.2 j 1.0 1.1 4 1.0 1.1

b) as welded 0.5 6

1.2 1.0 1.8 1.0 1.7 \\ /22 '.7 n B h connections per NS 36438" 0.5 1.5 1.8 1.0 Curved pipe or butt welding elbows per (2R-r/[2 ANS! B16.9, ANSI B16.28, MSS SP-87, 0.5 y (R-**j 1.0' g 1.0 1.0 0.5 1.0 o'r M S S S P-4 8 '*" l f Note (4)) j Bu wefdeng tees'per ANSI B16.9, MSS SP 87, c'r MSS SP-48'*" 1.0 1.0 0.5 b.0 .5 1.5 4.0. But welding reducers per ANSI B16.9, MSS SP-87, - \\ or, MSS S P.48'*" / 1.0 1.0 1.0 0.5

1.0 NOTES

[ (1)(4) The values of K, shown to-these components are (c) If Oma. - Dm n is ' ot greater than 0.08 Do, and ac. n jaopticaote for cornponents with.out of roundness not ftpeater than 0.08r where out of roandness is defined as ceptable value of K, rnay be obtained by rnultiplying the tabulated v' lues of K, by the factor Fib: ) a Dman - Omen, and \\\\ MS Dmaa

• maxemum outsede, diametst of cross section, in.

Eab

• I D,n.n
• minimum outside deameter of cross section, in, P Do/2t t

g t a nominal wall thickness. in. where M = 2 for ferritic steel's and nonferrous materials - / except nicket. chrome-iron alloys and (b) If the cro:s section is out of round such that the cross l section is approximately elliptical an acceptable value of nickel. iron. chrome alloys K, may be obtained by multiplying the tabulated values M = 2.7 for austenitic steels, nickel-chromium. iron. of K, by the factor F,,: alloys, and nickel-eron. chromium alloy; { Sy = yield strength at design t'emperature psi L5 (Tables 12.0) f Dmu - Dm;n F'*/ n + p = ces,gn Pressure. psi t g Doand t are defi%J in (a) and (o). (2) Welds in accordance with the requirements of this where Do = nominal outside diameter,in. Subsection. p = internst pressure, psi (#1 Flush welds are defined as those welds with contours as W78 (use maximum value of pressure in the load defined in the following sketch. Thickness of weld rein-cycle under consideration) forcement (total inside and ~outside) shall not exceed \\' E = moculus of elasticity of material at room tem-0.1t. There shall be no r:oncavity on either the interior perature, psi . ;x,enor sustua* % finished contour shall nowhere jhee edwelined in ( !. have a slope (angle measured t sm tangent to surface of i I 154

NB.3000 - DESIGN Table NB.368!(a).1 - j pipe or,on tapered transition side of weld, to the nominal ForMb ~ ransition surf ace) greater than 7 deg., see sketch below. Mb

• MM'as*M'ys*M't, = sesultant moment o branch

[ 7 deg. max. p 7 dog.% max. Mr = VM ',,+M' yr+M' fra resultarit moment on run "} { where M,r, M eand M rare determine'd as follows: a y g a s' j 7 deg. max. g 7 deg. max. If Mj, and Mj, have the same algebraic sign, then M =). If ir 7 I Mj, and Mj. have d/ferent algebraic signs, then M,, is the \\* [ smaller of M,1, or M;, where n, y, t ~ i For branch connectic ns of tees, the Mj term of Equations (b) Aswe/ded is defmed es welds not meeting the special (9), (10), (11), or (12),shall be replaced by the foliom og 4 requirements for flush welds. At the intersection of a pairs of terms: 4.s. longitudmal butt weld in stra;ght pipe with a gstth butt M Mr weld or girth fillet weld. J + 8s t Ze Equation (9) Rab Zs 8, = 0.5 and B, = 1.0 3 ..y.. '6 ,g \\~ ,. c.~ y i ..s. l 8 ...I/* l. The C., K., C, K, and K indices shall be the product . Equations 10) Si (12) Cab + Ca r j of the respective mdices for the longitudmal weld and Ib 2a v' S " - g s girth weld. For example, at the intersection of an w. asweided girth butt

• eld with an aswelded longitudinal Equation (111 CabTab

+ Car # r . 'e f butt weld, C, h 1.1x 1.1 =1.21. C, for a girth fillet weld. / Zs Zr ( . v.' (intersectmg a longitudinal weld shall be taken as 2.0.

• t

,- (3)The stress indices given are applicable only to branch where connections in straight pipe with branch axis normal to the / I * 'I'. l Ib l i e-poe surface and which meet the dimensional requirements. b m f. and timetations of N8-3686 and Fig. NS 3686.1 1. g /[ . g a 7, (4) R = curved pipe or elbow radius,ia. j r a mean radius of crost section,m. For branch connections per NS 3643 see Note (3) above $ (Do - t)/2, where t = nommal well thickness /g W78 (5) The values of moment, M. shall be obtained from an

1. m. T'b. Rm, and Trare defined ia Fig. NB-3686.1 1 t

'. analysis of tP3 piping system in accordance with N8 3672. For butt welding tees per ANSI B16.9, MSS SP-87,or MSS SP 48: M is defmed as the range of moment loadeng applied during ~ j. t . the specified operatmg cycle. rm

• mean radius of designated branchpipe {

' g T'b = nommal well thickness of designated branch .g ,My 3 p y A p'pe Rm = mean radius of designated run pipe {t. ...? '. ; J Straight Through Pipe /rM Tr = nommal wall thickness of designated run pipe t C g-- 7 3 j ,M a moment at Point A t 7 g. 'yf. qu a,y s y a ? M \\ r y 2 j (6) Indices are applicable to tapered transition joints with a girth i a a N l / g butt, weld at the thm end of the transition, j,' M A Cu' red Pipe or We! ding Elbow C, 31.3 + 0.003 (Do/tI + 1.5 (6/t) l r i j -y out not greater than 2.0 C

• U.+ 0.00 8 W M + 3.0 M M = moment at Poi.it A 8

a r but not greater than 2.1 i . lM

• YMM M C
• 1.2 + 0.008 (Do/t)

? C ~.' Qq T y j t i s.v 0 -' ' \\' ),;(If.,l \\.- . ( ? Branch Pipe i-

• a -

- } r-s. Y.- l ...e A. (7) 8,.'.= 0.50C,, but not less than 1.0 g ;* '.S79 8, = 0.75C.,, but not less than 1.0 . Moments calculated for point at intersection of run and branch center lines Ca - 3(R./T,)8 8(r'./R.)'d(T*,/T,) (r',ft,1, but not less than i 3 gy 1.5. (R., T,, r'., T'a, and r, are defined in Fig. .. N S-3686.1-1.) %. i 9."*.. \\.. .). X,/ =~ 1.0 .N ' 'e P ~-d - { - ',,[,

• F C, = 0.8(R,,,/T,3 8 Str',fR.),\\

] but not less than 10 ' j... ;, tMx3 .j,. C. p-33

1. ', = 2.0 T., d '.

4 The product of Ca,K, shall be a minimum of 3.0.l [- Mg', g jM y2. y y ..r_ . avf $yl,, ' b'. A.' [ g g3

...q.

M ..c s ~. :... ... g.,.., y .~, .C . iB)~C ~ii'135/be'*/but et less than 1.5 [.wg..; . S79 ~,. 'h .z ... M

===='"'"C"~~ @. .....Mm2 - 'N [,,s h t '= nomir.at pipe wali th!

A D),.

y#1 gM .r: f, bend radius of curved pipe or elbow; r - met.i pipe radius, (D. - f)/2 9 *.; s2 ,~ ' i, + :/ 155 1,. ',1. - J ,[ q I

3 e NB-3688t)1 SEQON 111. DIVISION I-SUBSECTION NB Y $79 f g). s, 0.40caJF:,% u.tharQ0_ (c) Reducers in which r, and r, a 0.1D, S79 $,, = J5(#./T,)**, but not less than 1.0 fe C.,N = 0.67(R./7,)*8, but not less than 2.0, where {/ = N. = mean radius of designated run pipe; C, = 1 + 0.0058aVD./r. T, nominal wall thickness of designated r y, C,=y.0.- a m y ( g.,,,. . Wyg.(10)The K indices given for ti 'ngs per ANSI 816.9, ANSI where D.#. is the larger of D,4, and6:sts. 8j6.28l MSS SP47, or MSS SP 48 apply only to seec,iess y - i g figtings with no connections, attachments, or other ex. . /d/ Reducers in which t, and/or r, 0.10, troneous stress raisers on the bodies thereof. For fattings, ? .' * ~ whh ic.igi tudenal bu tt welds, the K indioss shown shall be mul. . = 1 + 0.00h,, (Onha, P tiplied by 1.1, for //ush welds as defined in Note (2h by j ~ 1 3 for welds not meeting the requirements.for flush welds. , C, = 1 + 0.018,5a/ N VDn/r,, (11) T is stress indices given predict stresses whethwccur in the. L '- - b4dy of a fitteng. It is not required to take the'13 rod'uct of f $. where D.h. is the far er of D,h,'and D,/r. s stfess endices for two piping prorfucts such as a tee and a f / j ' M' reducer, or a tee and a girth butt weld when welded together . (14) The K indices given in (a), (b), and 'c) apply for reducers edcept for the case of curved pipe or butt welding ' elbows welded together of joined by a piece of straight pipe attached to the connecting pipe with f/ush or as sve/ded tfie length of which as less than 1 pipe diameter..For this girth welds as defined in footnote (2). Note that the I specific case the stress enden f or *he curved pip'e or butt - connecting girth weld must e6so be checked separately for Weld ng elbow must be multiplied by that for the girth butt , compliance. / wee 8d. E xcluded from this multaplication are the B, and C's , a(a) For reducers connected to pipe with flush girth butt indices. Their value es to be: 8, = 1.0, C', = 0.50. weids: l (12)e es defined as the rnanimum permissible mismatch as shown ../ lm e Fig. NB.41331. A value cf 4 less than 3/32 m. may be /K, = 1.1 - 0.1 , but not less than 1.0 dsed prowded the smaster mismatch es specified for VDm'm fhbrication. For flush wetas, defined m footnote (2), e may tie taken as sero, g l K

• 1.1 - 0.1

, but not less than 1.0 l (13l t il Nomenclature VDmim L) 'where Em/VDmf is the smaller of L,/M and m L, /QD, t, .-e-I f /b/ For reducer, connected to pipe with as we/ des / girth dg t att welds where t, t, > 3/16 in. and 6,/t,,,6,/r, < a gf i T ,,,y \\ tg /1 km 9 K. 1.2 - 0.2 , but not less than 1.0

1. ' 'g VD.,t D (2 l

a 1 r* 1 m I I I' D /2 .I lm ' A t2 2 l K, = 1.8 - 0.8 .but not less than 1.0 JDmt I m I n u o

1. b" t, a nomenal well thickness large end g "'

t.

• nomenal wall thickness, small end S

O = nomenal outside diameter,large end c For reducers connected to pipe with as-wetata girth i D. = nominal outs.co diameter, small end g -

s. = cone angle, degj butt welds, where f, or t, 4 3/16 in, or 6, /t, or &,/t, >

0.1: Ib) The endices geven a (c) and (d) apply of the alloweng (, sonditions are met.[does not K,

• 1.2 - 0.2

, but not less than.1.0 'll Cone angte, nd exceed 60 deg. and the . VDm m d t reducer is concentric. { ( / The wall thickness is not less than t m throughout the-Em "p ~ ~ i body of,the reducer, except in and immediately 8 VD A I adiacent.to the cylindrical portion on, the small end, where the thickness srall not be less than tam. Wall mim is tM smam M QM, and or' m thicknesses r,m ards rim are to be obtained by quation (1), N8-3641,1. 4 /b-A 156 I r .p

NB.3000 - DESIGN NB-3685.4-NB-3686.1 % t Direction % n Direction b j p 7%- -~ U

1. v I

Round Doss bedon R Moment Loads rm, k d0 I l a 1 Out of Round Cross Section I l FIG. NB-3685.21 NOMENCLATURE ILLUSTRATION FOR ELBOWS ential directions shall be classified as primary (P,). '[ distance measured between the centers (c)g For branch connections in a pipe. the are The remaining 25% shall be classified as secondary (p). branches along the surface of the run pipe is not less The stresses induced by displacement contro!!cd in-than three times the sum of their inside radiiin the plane or out-of. plane moments shall be classified as ! I ngitudinal direction or is not less than two fimes the ' f sum of their radii along the circumference of the run secondary (Q). P Pe- \\ / f i

• i (d) For branch connections in a formed head. the NH-3686 Branch Conhections With Branch /Run arc distance measured between the centers of adja-Diameter Ratio Not Oser One-Half cent branches along'the surface of'the head is not less

.Q NB;3686.1 Applicability of Indices. 'D}e dices than three times the's im of,their inside radii. The given iii Table NB-3686.1 1 apply if the conditions in radius of curvature of the formed head is essentially [ f NB-3643 constant and equal to R 'for a distance of (r',, E (a) through (hj are met. -(a) The reinforcing area requir M) measured along th,e surface of the formed ents o h head from the center of the branch connection. are met, (b) The axis of the, branch pipe is normal to the / - surface of the run pipe wall.:2 <j For hillside connects / \\ ns in pipe: \\ 12 "i [I + 2(sin g)2]' i 821f the uis of the braneh pipe makes an angle. S. with the normai to the run pipe wall, an estimate of the e,indet on the where ans e m be obtained from the following equations. prosided jadial connection \\ For lateral connections in pipe: 1 "the '5t2 mated e,, inside streu Ma' f~ ' -^ ~adia k 2 12 "i [I + (tan g)tJ3 f / 159 i

NB 3686.1-NB-3687.2 SECTION 111. DIVISION I - SUBSECTION NB k ---TABtE NB 3686.11 T,aneminal thickness of formeJ head, in. O BRANCH CONNECTIONS WITH RESTRICTIO]NS , j T,for branch connectton m pipTinT/, in. GIVEN IN NB 3686, INTERNAL PRESSilRE j 1T.for branch connection in formed head, j =outside diameter of branch,in. / I (a) Branch Connections in Pip [t, N Tp S ri, r2. rJ, r, andy are dermed in Fig. NB-3686.,1 1 Stress Inder, I f t,= minimum required thickness of run pipe, Longitudinal Plane Transve,rse Plane calculated as a plain cylinder,,/ 'a = minimum required thickness,of formed hela Stress \\!nside outside Inside outside calculated as a spherical'shell of injide f.'o 2.1 I radius, R. \\ [ e. \\3.1 1.2 g ! P= internal pressure, psi 1 -42 10 r.2 2.6 o j if' f' , o,are stresses as defmed l o =stressintensity psi' (in NB-3680, psi 12 26 a, t g y (b) Branch Connections,in Forrned Heads NB-3686.3 Stresses fro Stress Indices { f'** (a) For branch connections in pipe, multiply stress 'II Stress Inside Corner / Outside Corner indices by: / j ,f PR, j e. 2.0 2.0 g e, -0.2 'g 2.0 1 / -2r o \\, (b) For.' branch connections in formed heads, multiply stress mdices by: A\\.; I\\ PR. / l,l (e) Dimensionalratiosa\\ v re limited as follows: 11r.mch Connections.! Branch Conneetmns le O in Pipe / in Formed Heads NB.368/ 's Flexibility Factors g / \\, NB 368,7.1 Straight Pipe 'le / 1 T, - i k = 1.0 8 ** - g El ~ \\' --* r" 5 0.5 --6 for Af - AI, or Af2 '\\ I, ' 0.5 R R .m L-- -pu3 j m k_l0 g** _ s GJ / (/) The inside et.rner radius.r,(Fig. NB-3686.!-1), for Af - Af / 3 \\ is between 10"o,and 50"o of T,. / - one pipe t!iameter "2 Od The outer radius, r (Fig. NB-3636.1-1) is not / = plane moment ofinertia in.4 s less than the, larger of T'./2 (T'. + y)/2,[ Fig. NB-J = polar moment ofinertia, in.4 3656.I-l(c)]or T,/2. \\ E = modulus of clasticity, psi (h) The outer radius, r (Fig. NB 3686.1-1), is not G= shear modulus, psi h a less than the larger of \\ (1) 0.00. Od, \\c NB-3687.2 Cuned Pipe and Welding Elles. The' (2) I(sin B)1 times the ofTse, for the con-0exibility fr.ctors may be calculated by the equations figurations shown in Figs. NB-3686.1-l(a) and NB-given below for k, provided 3 that: 3686.1-Ilb)). 1 (a) R/ris not less than 1.7; J t (b) Ce iter line length (Ra )is greater than 2r; NB-3686.2 Nomenclature (Fig. NB.3686.1-1) (c) There are no flanges or other similar stiffeners rb r'/, = insiue radius of branch pipe, in. mean radius of branch pipe. in. rThe neubdity or a curved pipe or welding elbow is reduced by T's = nominal thickness of branch pipe. in. end egnu. provided either by the sdpcent straight pipe or by the R,,,= mean radius of run pipe. in. Preurruty or other relatisely stiff rnernbers which inhibit '*h" " *f 'h* " '"'* ' '" "*'n cases, these end efects R* = mean radius of formed head in the vicinit7)of rnay also reduce the stress. Additional work is underway to y' the b axh conneenon mr provide guidance for both flembaity factors and stress indices t 'T,= nominal thickness of run pipe,in. where end efun are significant. 160

, o o' e NB-3000 - DESIGN - Fig. NB-3686.1 1 .p T + .m. Ty 4 g -- f~ Branch Pipe ~ f .--n + Y r3 b r r3 d, a g %6,L . '..t K / L \\ j % S.g deg. b T'y s' ) T

.M-Of fset k

kk .J E r - Of f set 1 N 2 L1 2 'o - 'o Ib r p I 1 b y ah,-{ 7, f h ,1 s 2 2 3 g s\\\\\\q- { / 7, l s {t b ga} ,e 'R T,' / R m m (a) 2 (b) 2 Branch Pipe s r '\\ t

• Ti

\\/ -~ - TL-Tb ,j Branch Pipe ) YY 5

1. o (f '3

. / N 1 h l N 'f \\, d ) a A_ = { k h N: /. ~ 'o =~ 1 r' s \\ \\ I 2 w 6 Branc,h t N f I,"'l - W\\ / T,12 ' 'm ). ,fy - I. r /'2 .r. (\\

M l

hhe 7 / {f%\\ f'4 ,t r, ( k $

k ' t T

,2"::'

&'A

i n

4 y w at n R T, _ A m m 2 2 ~ + +,, c. I (c) (d) i, ~ T, for branch connection in pipe 8 7 for branch connection in formed head g, 3 " NOTE: If t, equals or exceeds 0.5 6 then r'm can be takeri as the radius 7o the cent-r of Ia '.) $;l f.', - ~ ~ ','. :.. ' FIG. NB.3686.1-LNQZZLE_DIMENS10NS W78 i l

3..;

'Q. 2 e E o ' ~ 161 i I

• s, as V 4..,. s*.'..

~ s

• NB.%87.2-NB-3692 SECTION !!!, DIVISION I-SUBSECTION NB Q;s y;

... s (S[M.t(w~ithin a' distance'r'from'either end of the curved, -,"", Md_ 3.- .m Y-

• J. ; '

.i section of pipe or from the ends of welding elbows.. + E4, w. . " -:..?; ' - g:yp or Mz: s?.- .e a s.. e- .-;, ' ~. :: (vpWq t : r M f o. f *.' + '

r*.

- D n r, 's $. %,.,.'Fo W. ' A s' N'h,.?. T.%. ,-.? k - 0.27 T, T, D for M o.. g.".. '. ' ". n: 1.63 / I ) N8, '5'E[. ,,5'h 18.{ .. Pr dh l', wherc * ' ' . g$@th.M I /' h N

• l d [; -j s-c

. g u. .h. h 4 a.c.x but not wss tha.n 1.0,,.' \\. M....MNra M. which are defmed in fcc7,.ca 5,e. dOf d cf q^ - h.. s.- .. N,* ; n M N,i 0's - - " "' ~ p~u n .f ' "M;D = run p'pe outside diameter, nn.1; m 3. W c~.? n. n r$,,t -,' m.. ~ ' " ' ~ ~ - e.1.3.3. 4. ,o t ~ U . ~ .A

2..'N 9.. A

• e.,

a m 9 7 ;p d=branchp.ipe outside diameter,in. u-- m Ag 1 -.. m.a m. qsj3 Qa.?..v,.. r.,,e c,. El. f, M,.(.da) - Na er. _ j;;;.c.- 2 .,. g " y. . ?.

WT,= run pipe nominal wall thickness, in.

,e ..p-f, C.. ..".1,c.1 For M : ' q.W.,# @'. '/,. M e 6 S ~.,

• .T T',= branch pipe ncminal wall thickness, m.

3 ' hWa= cquivalent thickness,in.}f pg. fQ;*g;qc.; @.l? V 1: : i N f k [' [k.,'g,o'l_~?'-- m-gg) Q c g'[ ' l ' D "'[ (b) 'For branch connections per Fig. NB:36S6+1 "[ k .I,hkh.. h';M 8 = -: sketches (a),(b)..md (d) and extruded outlets per NB, ['. T c.x./ m. both cases.T[h.... :t *,c/ [ M (d") a A v. -,,a3643 v,.~,-~ ~.u-

n. 7

N.k$h:h'$U'

~ ; : ;;:. :; - n. s ?.e .a. h tR/ ~ ~ ~ b >.iR= bend radiuk in.' ' S '. ~ ," M iI' i (c) For branch connections per ' ig. NB-368@9=t-r -- u ,y . y m.,

P = m.ternal pressure, ps

. 7 3

s. ketch (ci f.

h. ;,37.

.., ~ * , r=, pipe or elbow mean g radius, in. u[ - T, - T, + A-br % ' d ,4:' 4,. d

t = pipe or elbow nominal

.y j, :'$ - wall thickness,in. T, - T, + y for Ma j E;. X, = 6(rls)'* (R!r)* W..N.h ' / = plane moment ofinertis ofeross section, in.4 where e J-polar moment ofinertia ofeross section,in.* = actual area of reinforcing within the zone of 7* E= modulus orelasticity, psi reinforcement given in NB.3643.3(b\\ sq in.

• 7'.

G= shear modulus orelasticity, psi /,= moment ofinertia of branch pipe,in.* a = are angle, radians E= modulus of elasticity, psi (d) For load displacement relationship not cov-NB- .3 Stifer Bends.The requirements of NB-

5 ered, use NB-3637.4.

., s.3681(d) apply..,.t. g> s; 9 .,.t ,3 4.- NB-368;.4 Welding Tee or Branch Connections. 7 4 " For welding tees (ANSI B16.9) or branch connectio.ns -[. ' i.'. -(NB-3643) not included in NB-36 .5, the loaa A NB-3690 - DIMENSIONAL REQUIREMENTS 1. displacements relationships sha!! be obtained by w 7

• e.

. J.;, : assuming that the run pipe and branch pipe er. tend to ' FOR PIPING PRODUCTS %f S '7,, the intersection of the run pipe center line with the NB-3691 Standard Piping Products 2,5-7 <,f. branch pipe center line. ne imaginary juncture is to 1 0 ' be assumed rigid, and the imaginery length of branch Dimensions of standard piping products shall., ~ ' pipe from thejuncture to the run pipe surfaceis also c mply with the standards and specifications listed m Tab!c NB-3132-1. However, comp ance with tiiese , to be assumed as rigid. h ec e I standards does not replace or elimint te the require-ments ofNB-3625. NH.368.7.5 Bra..ch Connection m. Pipe Meeting the ~

1. ' r.cquirements of NB 3640. For branch connectior.s in -

~ j ' piping meeting the requirements of NB-3640 and with NB-3692 Nonstandard Piping Products branch diameter to run diameter ratio not over one- -. third, the requirements of(a) through (d), apply. The dimensions of nonstandard piping products.. '. %. (a) The values ofk are given below. c'c, ~.shall be such as to provide strength and performance ~ '_ as required by this Subsection. Nonstandard piping

/. R' D

M T'n d A - 0.09 for Mo .c,:" products shall be designed in accordance with NB-

• • 14.,*

T, T D L. :., < *.:3640.. . A..

j,

'y' J. .' gs. - w g i.,J. ~ l?~.. l. q -, ^ y . 7.,;.- 1 ..;. 2 - ,.+ .. ]., r ~ ~ L-

c... :~ ~;,-

g.y.,"y;: <c.v, ,ql ?::.. k. ;.... ;.' '..,,.~ * ~

g.,..A w

n,..... p. e. e.3 e,y.,... .x, ,..- m -- _ ~. O. ",> ^ D 'i ' :. :%m :j'f h',c.,, y x en.Dd 2'%$5.fj kffs'.fdtl* N.' ' '.,. .. ~ 'q.' v .r. 2 4 :' ~'.y v 3:. t. L-gi,

1. f,.

4

VALIDATION OF THE FINITE ELEMENT STRESS ANALYSIS COMPUTER PROGRAM CORTESSA FOR ANALYZING PIPING TEES AND PRESSURE VESSEL NOZZLESL2

8. R. Sass Computer Science Division Union Caro.de Corporation Can Ridge, Tennessee J. W. Brymn and S. E. Moore Er9neermg Technology Omsion Oak Ridge National Laboratory Oak Ridge, Tsanessee ABSTRACT The finite element computer program CORTES-SA, which is basically a modified version of SAP 3 with a special purpose input processor for setting up a wide variety of tee joint and reinforced pressure vessel nozzle geometries, was vali-dated by comparison of calculated stresses and displacements with results from six experimental models. During its evolution, CORTES-SA had been worked on and modified by several different people. As a consequence no single eerson was intimately familiar with the entire program. Validation thus requ.ted solutions

. for a number of probless that might be encountered in the development and/or ' validation of any special purpose finite element computer program. This paper presents an account of the problems encountered and the steps taken to effect their solutions. Among the problems discussed are those resulting from non-participation in the original program development; incomplete documentation at all stages of the program development; the lack of complete sets of calculated output including displacements and equilibrium forces at boundary nodes for checking purposes; the absence of adequate output graphics; and the absence of a comparable computer program for cross-checking purposes. Results from the various analytical-experimental comparison studies and other theoretical check calculations are presented. INTRODUCTION The ORNL Design Criteria for Piping and Nozzles Program (1-4) conducts experimeatal and analytical stress analysis studies of piping system components (products) to validate and/or improve design rules, criteria, and stress analysis methods for light water reactor (LWR) nuclear power-plant installations. In support of this effort, a five-progran package of finite element compt.cer programs called CORTES (California, Oak Ridge TEES,), was developed at the University of California, BerEeley, speciticaIly foTstress analyses of ANSI Standard 316.9 tees subjected to internal pressure, force. moment, and thermal loadings. The I Research sponsored by Oak Ridge National Laboratory, operated by Union Carbide Corporation for the Energy Research and Development Administration. Work performed by Union Carbide Corporation for the U.S. Ntclear Regulatory Commission under Interagency Agreement 40-551-75 and 40-532-75. 9

l program CORTES-SA (for Stress _ Analysis) in this group was designed to perform linear elastic stress analyses of standard tees for any one of the 13 basic mechanical loadings or an arbitrary combination of loadings (S-7). A second program. CORTES-EP (for Elastic-Plastic Analysis) has the additional capability of performing elastic-plastic analyses based on constitutive materials laws that use a von Mises yield criterion with either isotropic or kinematic hardening (8). The other programs in t:is group are CORTES-THFA (7) (Transient H_ eat Flow Analysis), SHFA (9) (S_teady-state Heat Flow palysis), and TfA (7) (Thermal Stress Analysis). All five programs fea_ture the same automatic mesh generation routine with options that permit the modeling of a wide variety of tee-joint geometries such as tees, branch connections, and pressure vessel noz:les with a minimum of input data. CORTES-SA has been modified several times at Oak Ridge in efforts to expand its usefulness and improve its efficiency. As a result, the present version includes contribu* ions by a number of people in addition to the original authors. This paper describes the validation of the most recent version of CORTZS-SA as releasci to the Argonne Code Center for general distribution. This version has been used extensively at Oak Ridge in conducting parameter studies of reinforced and unreinforced nozzles in cylindrical pressure vessels (10,11). An account of the problems encountered and the solutions employed during the validation of CORTES-SA follows, emphasizing those 9xperiences which should be of interest in the development and/or validstion of similar special purpose numerical programs. In addition, sample results from six validation model studies are reviewed. PROGRAM DEVELOPMENT AND VALIDATION The CORTES package of programs was originally intended for use in stress analysis parameter studies of ANSI Standard 816.9 tees (see Fig.1) subjected to internal pressure, force and soment loadings on the branch and run pipe exten-sions, and arbitrary temperature distributions. The results of these studies were to be used in conjunction with experimental studies of tees under similar loadings to develop broad-based sets of analytical results for use in onfirming and/or improving design rules and structural safety criteria. fDIAPHRAGM l./ BRANCH P!PE (CY LI N D ER) TEE BRANCH j (SHALLOW CONE) CLAMPED TRANSITION l g RUN PIPE j [ y 2( (CYLINOER) I 4, Z+x. _ l l l(TEE RUN DIAPHRAGM (SHALLOW CONE) Fig. 1. Basic cylinder-to-cylinder intersection geometry. i l 10 l i L i l t L s

4 The general guidelines for the original program development were to produce a 3-D code with isoparametric brick typ eleneats capable of modeling a wide variety of tee joints and reinforced and unreinforced pressure vessel nostles. Because of the anticipated usage for conducting parameter studies, automatic mo h generation with minimum input data requirements was considered to be of primary importance. The resultant program was a modified version of SAP 3 (12) with a special purpose input processor that automatically models a variety of complex tee joints with several hLandred finite elements, using only nine cards of input data. Initial experiences with CORTES-SA at ORNL revealed the need for improving the input-output (I/0) efficiency and the need for certain post-processing and additional output fencures. Although the Program automatically sets up the finite element zesh, ORNL-compatible graphics capability was needed for display-ing and designing suiteble mesh layouts for later stress analysis. A graphics package had been developed for use with the Oak Ridge computing facilities. Post-processing and additional grat

• capability was also needed to interpret and display selected quantities f ~ h substantial amount of output expected from large-scale parameter stuc:

A second need was to augree. we M 'nal output with additional information, partly for checking purposes. In t

• cr tal version of CORTES-SA, the computed output consisted mainly of the surfac.

coordinates and direction cosines of the tangent plane at the surface nodes 1 the generated mesh and the tangent plane stress components at the surface ncJes (the model any consist of up to tive layers of elements through the wall thickness). Three desirable output features not provided in 'the original version were the calculated displacements. the boundary node fixity conditions, and the force reactions at the fixed bound-ary nodes. The nodal : mint displacements were needed for later use in developing flexibility factors for piping system and pressure vessel analyses, whereas the other quantities were needed to validate the finite element model and computed results. A third need was to improve the cost-time efficiencc of the program at the Oak Ridge facility, which utilizes an IBM 360/195 computer rather than the CDC 6400 computer on which it was developed at the University of California. The CPU and wall clock times, core storage, and I/O requirements of large scale problems tun on CORTES-SA seriously affected turnaround after job submission at j the ORNL facility. In this list of additions and modifications to SA, first priority was given to the preparation of graphics software that could be used to display the finite element models. For this purpose a software package, GRFPAK (13), was designed specifically for the CORTES input processor to display orthographic projections 2 and cross-sectional views of the generated mesh. GRFPAK was eventually expanded to include certain node displacement and stress display options. Before the other features enumerated above could be added, the Oak Ridge computing personnel needed time to study the internal structure of the program and to design the N necessary modifications. Flow diagrams and programmed comment cards would have made this job much easier. When sufficient progress had been made on the graphics software, several models which had previously been analyzed experimentally (14-16) were analyzed for internal pressure loading and the results were compared with the experimental data. Although these initial comparisons were generally in good agreement, there was an unexplainable " spike" in the calculated stress distributions in the transverse plane (y-s plane in Fig. 1) near the nottle-to-cylinder junction for the two thin-walled models (14,15). This stress " spike" was not present in any [ of the experimental data, and was not evident in the University of California results (7). The problem appeared to be related to the number and arrangement of elements in the finite elet model and was less noticeable or absent for thicker walled models. Although varicus :tra.tegias for defining en acceptaoie mesh layout were attempted and numerous individuals, including the original program authors were consulted, we were not able to find an error in the program or to. establish reliable guidelines to avoid the problem. By trial and error, i however, we were able to generate results which did not have the spikes. As sentioned earlier, all five programs in the CORTES package use the same finite element zesh generator, and the elastic-plastic analysis progtum CORTES-EP 11 i e' .t ,--w - _ - -. ~ -, - - - ,n c

---

,",--,-r,a g

nv-,n

l l l 1 is also capable of performing elastic analyses. There were, aowever, several differences between the CORTES-SA and -EP programs which made it difficult to compare results directly. First, and most importantly, the two programs calcu-lated and output the stresses at different points in the elements. CORTES-SA printed " average" element stresses at the surface nodes expressed in the local coordinates of the tangent plane, whereas CORTES-EP printed the stress tensor components at the internal Gauss integration points expressed in global coordi-nates. In addition, CORTES-EP printed the nodal point displacement referenced to the global coordinate system. But, because of difficulties related to the use of superposition in the CORTES-SA solution logic, installation of a dis-placement output option in CORTES-SA had been delayed pending further study of the algorithm. There was also an apparent difference in the mathematical formulation of the finite elements in CORTES-SA and CORTES-EP. The element originally installed in CORTES-SA (and reported in Ref. 7) was the Wilson incompatible element (17), obtained by adding nine incompatible deformation modes to the eight-node iso-parametric brick element of Irons and Zi?nkiewies (18). A paper by Irons et al. (19), however, pointed out that the addition of incompatible modes produces an element which violates the " patch test" and any therefore give poor results for elements that are not regular parallelepipeds. For a more complete discussior. of the patch test and its importance see Ref. 20. An improved finite element which used a repair technique proposed by Taylor et al. (21) tc satisfy the patch test was incorporated into CORTES-EP (g) before it was released to ORNL even though studies by Powell had failed to show any appreciable difference. At this point in ties, CORTES-EP was modified at Oak Ridge to compute and print out the tangent plane stress components at the surface nodes using a bi-linear-least squares Causs point stress extrapolation procedure developed by Hinton and Campbell (22). Using this modified version we were able to compare results directly with experimental data and with results from CORTES-SA. The spiking problem, which had been so prominent with CORTES-SA, did not asteria'.ize with PORTES-EP, nd the calculated stresses showed excellent agreement with tMe experimental test model results. A close examination of the programming revealed, however, that the element formulations in the two programs were identical, thus eliminating the patch-test as the source of the spiking problem. Apparently, CORTES-SA had been modified earlier to conform with theory. The modification was not recorded, however, in any of the documentation supplied to ORNL by the University of California. Subsequent comparisons of stress results from CORTES-SA and CORTES-EP also eliminated the node point stress calculation routines as the source of the stress spiking problem. Concurrently, the modification of CORTES-SA to print out surface displace-ments was completed. An improved matrix solving routine (borrowed from EP) was incorporated, and the standard Fortran I/O statements were replaced with local machine language routines.' Calculations for a number of test cases were then traced through each code and compared at strategic points in the computational process. Those comparisons led to identification of a logic defect in the algorithm which automatically generates tu boundary conditions for the symmetry plane nodes in CORTES-SA. l The error caused one of the nodes in the y-z syneetry plane to be incorrectly restrained (fixed) for certain combinations of mesh generstion parameters. When the algorithm was repaired, the excessive bending stresses at the fixed node were removed and the spike disappeared. Subsequent l comparisons with experimental results, as discussed in the next section, pro-vided sufficient evidence to claim validation for CORTES-SA. l l VALIDATION MODELS AND RF.SULTS I During the validation pr~ess, CCRTES-SA =as usca to analyse six models for I which experimental stress :.n etis data were available for internal pressure loading. This set includes two thin-walled cylinder-to-cylinder models without btandard Fortran I/O is retaic.el in the version released to the Argonne Code Center. 12 1 l9

t o transition fillets: ORNL-1 (14) and ORNL-3 (IS); sa ANSI Standard B!6.9 tee: ORNL-TS (16); a thick-walled steel pressure vessel: HSST-ITV9 (23); and two photoelastic pressure vessel models tested at Westinghouse: NC-12D and WC-1000 -(24). This group represents a wide range of vessel diameter-to-thickness ratios (4.S < D/T < 100.0) and nozzle-to-cylinder dimeter ratios (0.1 < d /D, < 0.Si), i as listed in Table 1. The two thin-walled models, ORNL-1 and OR$L-3, ire essen-tially unreinforced at the nozzle-to-cylinder transition; the B16.9 tee ORNL-T8 has a generous radius transition, while the pressure vessel models HSST-1TV9, WC-100, and WC-1000 have reinforced nozzles designed according to the rules of the ASME Soiler and Frcssure Vessel Code (2S), as shown in Fig. 2. In the ' following, comparisons between the calculated stresses from CORTES-SA and the experimental results for internal pressure loading are presented for four of the six models. Results from the other two scdels, ORNL-T8 and WC-1000, were equally good. Table 1. Geometric parameters for CORTES-SA validation models Model D /T' J /t o /D Type of reinforcement g g g g ORNL-1 98.0 98.0 0.2 None ORNL-3 43.0 3.68 0.1 Extra wall thickness ORNL-TS 32.0 21.66 0.S1 ANSI bi6.9, Schedule 40 HSST-ITV9 4.5 2.2S 0.33 Standard WC-10D 10.0 12.0 0.129 Standard V"-1000 100.0 100.0 0.A10 Standard

1. Ratio of inner run diameter to run thickness.

Ratio of inner branch diameter to branch thickness.

1. atio of inner branch diameter to inner run diameter.

R ote do~

1. 3 r 9145*

{ OFrSET ':n = 2 /,, _. 1 er I V' 4( Fig. 2. ASNE Code standard reinforcement design. 13 l l

1 Cylinder-to-Cylinder Model GRNL-1 ORNL.1 is an idealized thin-shell steel structure consisting of two circular cylindrical shells (D /T = 98, d /D There are no transitions, rkinforcemenks, or= 0.5) intersecting at right angles. fillets in the junction region. An isometric view of the outer surface finite element cesh is shown in Fig. 3. The finite element model was constructed using a vLry small fillet radjus equal to 0.254 un (0.01 in.) at the transition and one finite element through the wall N ./ s E

EE: ls LONGITUDINAL

~E 7 TRANSVERSE [ TRANSVERSE LONGITUDINAL fy 1 % q \\ s. Fig. 3. Isometric view of outside surface for ORNL-1 generated mesh and definition of stresses for 0 and 90* zections. 14 s

y = thickness. This mo4M was analyzed for an internal pressure of 0.34S MPa (50 psi) which produced a nominal stre:S of S = PD/2T = 17.2S MPs (2SCO psi), the same as that used in the experiment. Comparisons between the experimental data and the calculated results from CCRTES iia are depicted in Fig *. 4 and 5. Longitudinal and transverse stresses (folloi tng the convertion sh wn in Fig. 3) are shown for the 0* and 90' sections (x-y plane and y-z plane respectively) for both the 'nner and outer surfaces of the model. For this model the maximum stress was in the transverse direction in the longitudinal p ane (0* section) at the outer surface of the intersection. In general, the computed results from CORTIS-SA are in good agreement with the experimental data. The relative disagreements shown in Figs. 5(c) and 5(d) - for the 90' section (y-: plane) of the mn pipe are the result of using isopara-metric brick type elements to analyze thin-walled structures, as pointed out in Ref. 26. For thicker walled structures, lake ORNL-3 discussed below, CCRTES-SA gives better agreement with expertaental data in this region. Cylinder-to-Cylinder hiel ORNL-3 ORNL-3 is the second tee joint for which experimental and analytical results from CCRTES-SA were compared. O U L-3 is also an idealized thin-shell s :ucture with no transitions, rainforcements, or fillets in the junction region. In contrast with OML-1, however, CRNL-3 has a much smaller disseter ratio (d,/Dg= 0.1 vs 0.5) and a greater relative wall thickness (D /T = 48 vs 98). Results frca this model shed light on the ability of CORTES bA to accurately predict stresses for models with small relative no:zle diameters (d /D ratios) like g g those used in many pressure vessels. Wo0EL CRNL-4. PmESsumE, o o., to e* ~m { l F%fE GEMENT-l l l { 'S.{;e

• . mTUDINAL _4 10 0 i

, - TRAN Wtast l l r I i I EXPE8huCNiaL' s - 50 i ;$* d, I 9= o L:hGITUCINat

t. 1. '

I . raaNs e sE - so 5 5 ^ %( i a s j ~y+.. 4......+...... ...

• l iM:.:

V, j u* 8 o,5, j l t 3; l oufSiCE HUN QuTS:DE SRANCH {

• • O

..o 2* 1 t is -- l ? I l i ,co 90 } f( l ! fe;. I dso ! i S. K i t o g' e e j - - ;...... 4........... 3 1 N g = l.lo: k I ,g i I w ~ *SO t 6NS.CE *LN ll , 'NS CE B6aNCM .so ' 0 1 2 3 4 S 6C 2 3 4 01S?aNCg recu.iUNC'1cN ( a l 75faNCE F#CM JUNCrlON (.nj Fie. 4 Comparisons of calculated and experimental stress distribution for O' section of model CRNL-1 (1 in. = 23.4 m). i 15 L e b N

Wo0EL CRNL-e, metssuRE,30 geg 90 H-l i 6 , m?k .y i ~ ' ts _ .a la . s.- e*--- 3 *% f I i 3 c gye v 7--- - o g g I l i E l7, I i i i - -zs a i FINITE ELEWENT l .*O ~ ~a1,oNG;TUoiNAL f ouis.DE SRANCM ' -to -*-- TRANSVERSE I

• O ExRE* MENTAL o LoNGITuoiNAL l

l l - 50 . w RsE i l i i i 3

1. ~ ],a' '- 4----- ---.4

.-. y I lr-. I l {_ 1 ts e l I I R j,,= m,.., - - - r - -, g

f.. ;

l l T. W

• g/-

1 l y f** l .g3 a 'S I l i i I t -50 . iNsicE eRANCH l esiCE RuN i I -+0 O e 2 3 4 s 60 e 2 3 4 oisTANCE FRof t JUNCTION (en.) OssTANCE FRoM JUNC'1CN (en.) Fig. S. Comparisons of calculated and experimental stress distributions for 90' section of model ORNL-1 (1 in. = 25.4 mm). Figure 6 shows the outer surface of the f' nite element mesh, constructed like the model for ORNL-1, with a very small fillet at the junction. The mesh layout for ORNL-3 utilizes two elements through the wall thickness. The number of elements through the wall thickness for this model, as well as for the other test cases, is governed by the criterion that the elements in t.*ie junction region should be as nearly cubical in shape as possible, consistent with the selected degree of mesh refinement.n the axial and circumferential directions of the branch and run. The model was analyzed with an internal pressure of 2.068 MPs (300 psi) or a nominal stress of S = 50.67 MPa (73S0 psi). Comparisons between the experimental and analytical results are shown in Figs. 7 and 8 for the 0 and 90' sections, respectively. TP maximum stress for ORNL-3 is in the tr nsverse direction in the longitudinal plane at the inner surface of the intersection. Westinghouse Photoelastic Model WC-12D To demonstrate the capability of CORTES-SA to analyze reinforced pressure vessel nozzle configurations, comparisons between the experimental and analytical .esults are presented for one of the two photoelastic models tested by Leven (24), WC-120, and for the HSST vessel ITV9. 7 e photoelastic model WC-12D had a relative nozzle si:e (d,/D = 0.129) near that of ORNL-3 but with reinforcement as prescribed by the AS.0E Boiler and Pressure Vessel Code shown earlier in Fig. 2. The vessel was relatively thick-walled with a diameter-to-thickness ratio c,f D /T = 12.0. g All of the test cases which were reinforced in the junction region, includ-ing WC-1000 which is not shown here and the HSST model discussed below, required 16

l w qllll i[$a fililll l ud$ DIM n W l / lf / I:q ~4 $j/ '+ ~~, // C w~ . ]lll + j 'I Il ~ m hg\\ \\ \\ \\ Fig. 6. Isometr'; view cf outside surface for ORNL-3 generated mesh, more elements through the wall thickness than were needed for the unreinforced models. Model WC-123 was analyted using three layers of elements. Since WC-120 was a photoelastic model, the finite element analysis was initially performed using material property values of E = 51.7 MPa (7500 psi) and Poisson's ratio of .e 0.485 A second analysis was also made using material constants E = 206.3 OPa (30 = 10' psi) at:d, = 0.3 (steel properties). An internal pressure of 1.061 MPa (153.9 psi).as used for the analyses for a nominal stress of S = 6.395 MFa (1000 psil. Comparisons between the comput d results and the experimental data are showTt in Figs. 9 and 10. Good agreement was obtained betw='n the calculated results for the photoelastic and the steel models except in the junction region 17 s

MCCEL C ANL-3. 88EssVAE. o ee 95 z f i ' r Natt ELEVENT

• • • "" @(dIUC 7$

to ( --- ?aANsvEm'NAL I l *l l - fle.gk, _ - __- sE EXPE#iMEN'AL 50 .i i i . LoNocuo,w 2 5 %g. 4. 7 -...-.._ _ j 2s,g i . r*ANsvtest g ! k a ha-. N s m i 3 3 ~Y l i I q -25 outsiCE AuN outsiCE OR ANCM + ~2o ; ,, \\, ~ 1 V:. -w. ogM - * --+-.....g '~~. 4 eo - 0 3 -5 k--- -~ j eNsiCE EJN INsiCE 84ANCM g ]-So 90 = 0 9 2 s e 5 60 9 2 3 4 5 DisfANCE F#eu JUNCTICM (.a 3 OtsTANCE FRCM JUNChoN (m.') Fig. 7. Comparisons of calculated and experimental stress distributions for 0* section of model Or5L-3 (1 in. = 2S.4 mm). of the 0* secti u. In this section, the results of the steel analysis compare very favorably with the experikental data, whereas the computed photoelastic results are not as good. The discrepancy in the photoelastic calculations for the O' section reflects the difficulties encountered in using the conventional finite element displacement formulation (the formulation used An CORTES-SA) to analyze structures of nearly-incompressible materials (see, for example, Ref. 27). This displacement formula-tion, which is derived from the minimum potential energy principle, can yield stress results greatly in error as Poisson's ratio approaches 1/2, i.e., as the raterial approaches incompressibility. In the limiting case, i.e., v = 1/2, the formulation is no longer valid. Computationally, the global stiffness matrix ( becomes progressively more ill-conditioned until it becomes singular at v = 1/2 (23). For discussions of modified variational formulations that are applicable to near incompressible and incompressible materials, see papers by Malkus (29), Booker et al. (30), and Taylor et al. (31). Intermediate Test Vessel HSST-ITV3 l l Of the six models analyzed, the Heavy Section Steel Technology Program interme-liate test vessel HSST-ITV9 had the greatest relative wall thickness and not:1e diameter with diment onal ratios of D /T = 4.5 and d /D = 0.33. Both i g 3 3 the experimental and finite element analyses performed on nsST-1TV9 used an, internal pressure of 6.395 SfPa (1000 psi). The finite element model for HSsT-tBf9 was constructed using four layers of eierents through the wall thickness. The calculated stresses for this model l are indicated by the solid data points in Figs.11 and 12 for the 0* and 90* pla.rs respectively. Experimental data, from Ref. 23, are indicated by the open data points for the inside corner of the no::le in both planes and for the outside fillet la the O' piene. The maa, rum stress for this model occurred at the inside corner in the longitudinal (0-) olane. 18 s E

MoDEL omt.-3. Pat 5sV8E. So see to f i mete ELEWNT E Go 8[3 v= % p. 9-4,. 1 . ~+~ LoNGeruolNat ] I i -. - feaksVERsE i r f4( NQ ^i l l l( l j-o LohGm c hat - Exat*uENTat 7' 8, l i% l I

• T=4Nsvtest 4 20 _

"o o l l l I i$ [ l i I { l li V i - -ao =4 -40 9 1 I I I f) e-i Jo 5 b.as -i*------ g dl I s o[ _,ef* f l l l l ll I I { y - <a " 'W, I i il a = 42o l I l ll[ ,[i.. -- ---- - -- ---. -- - d -t : i i i I i ir r I I i l ii -a -zo l l i=sior am i ii ms:oc saaNci. o i 2 3 4 5 6o i 2 3 4 5 otsTaNCE FPou JUNCTION ( a) ors?&NCE McW JUNC*.CN bnI Fig. 8. Comparisons of calculated and experimental stress distributions for 90' section of model ORNL-3 (1 in. = 25.4 m). As.,Jlustrated in Figs 4 through 12, generally good agreement was obtained between the calculated stresses and the experimental data for the validation models. The calculated ma2imum stress and stress distributior3 for both the longitudinal plane (O' st -ion) and the transverse plane (90* section) closely follow the experimental data with the exception of two cases previously noted. These exceptions pertain either to a thin-walled structure (CRNL-1) for which the finite element formulation in CORTES-SA is only marginal; or to the nearly incompressible behavior of photoelastic materials (WC-1:D) for which the finite element formulation tends to become unstable. In sumary, we consider the correlations to be sufficiently accurate, within the constraints noted, to clais validation for CORTES-SA. SLM4ARY AND CONCLUSIONS in this paper we have described the validation process conducted at ORNL for the special purpose finite element computer program CORTES-SA and have presented comparison results for four of six models that were extensively studied. The discussions h ve focused mainly on the problems encountered during a develop-ment and expansion phase to make the program more useful and a validation phase to prove the value of the program. Some of the major points, which proved to be crucial for the validation of CORTES-SA, are reviewed below from the perspective of general program development. During the development phase of special purpose computer codes such as CORTES-SA, the program output should be carefully designed to make available all of the information needed to completely define the model being analyted, perhaps under control of an output option. It is well to note that output recuirements for vslidation of the program will probably be more extensive than required for 1 star production use, but the option should still be available for later checking. 11 the case of CORTES-SA, the t,oundary point fixity conditions, the boundary point reaction forces, and the computed node joint displacements were needed to 19

j WCoCL act2o. Mt5svet, o LEG.

• 5

.lil j;g e t! -'oo -) .,-l9 i i; } 1 I'[, eit

• i[ ti

FS l

? - 5.o a 0 5.-4.+-- p$- y- / l ; ' y+-.- e - -.--- 3,,3 a 5 ,i tr i .b a I g o ' A fsg

4 l 4

{ i ,a i ' ' ' l; I~ I ' 7 -2.5 -o S N'CCLA5fic CA.CULATfo g .. o ses .. o s 4 (= 750cass (= 3onic'es. y e, a a 3 e xh .t .m y.

y-5

(, s (k # t t l s h \\g\\ \\ \\ 'o i!!I ii! - - 5.c 1i t1 li j, I l i + o ~. ; ;,'t-s s-s-s. ve -s--y e-- g--- g---- s i o bs s s. ' s'*' ./ e-r'~8.e.e-e. -ee 5 a 1 l: t. l - so.o a r .)i s '0 y 1,,, l{,!, j ;. l o (/; - +s o ;; 1 I 3,; e i - 20 0 I eo[l1i!! - 25 0 l l el! i ^ Fig. 9. Comparisons of photoelastic and calestated stress distributions for 0* section of model WC-12D. insure th.t the program was generating the correct boundary conditions. Nch of this information us' not needed for the parametet study discussed in Refs.10 and 11. A second topic of imoortance concerns the impact of graphics software on program validation. For finite element programs like CORTES-SA that generate complex mesh geometries automatically, graphical displays play an importa-t role in finaliting the design of the element mesh to be aralyted. For example, the accuracy of the finite element formulation used in CORTES-SA may be adversely affected by mesh layouts not composed primarily of parallelepipeds. Although it is not possible to construct a mesh layout of perfect parallelepipeds, by exam-ining isometric and cross-sectional plots of successive tri l a *odels generated 20 f

l i uo0tL we 820. PetSSumt. 90 0fG. 2.0 l 11 l ll!l { 6 l ' '0 0 l1 is 1.0 ' - - ^ l t e u i = ' II 8

• 0.5

^^ i ' 58

• ~A i

l ' i. '**% 0 0 ~

• l i

i i l f(!!He I fIl I f l -2.5 -0. S

• M0?ctLastic caLCutatt0
  • Q*e5 n = 0. s E= TSC0 w Ee 30 nt0* n g ______.

e %r4, m i, i s -e.0 -0. 5 ll, j l - 5.0 l 3 O g a i 1 3 0 f,,,, h m 25 JlMiV H4.) i" * 'O m ,e ; j;4p. - 75 ll!! l i e.s +0. 0 Fig. 10. Comparisons of photoelastic and calculated stress distributions for 90* section of model WC-1 D. by SA, it becomes rather easy to construct suitable finite element models for each case. (It was also easier to make minor changes in the mesh generation package.) The availability of additional graphics software with selected stress and displacement plotting capability also makes possible quick and accurate analysis of the large quantity of output Nm the solution process. Much of the information currently available from CORTES !.'. analyses would be extremely difficult to assimilate and interpret without the graphics software. Another importarat consideration in the development and validation process concerns documentatien. External documentation, including flow disgrams ard a complete log of modifications and gdates to the program as well as user instruc-tions, should be conscientiously maintained. Such practice will enable success-ive users of the pmgram to be brought up to date quickly and will prcvide the 21 s L

MODEL Wss?-vt. petssuet, o Oto 2.o ,o,, o o o

9. s

, Go 1 p.s ? i go y g....,.o Illii i l H$ltI o o .o.s -Es Empfeia tufah cALCulafto g a e o n s o , m, o ofoffo f ff ff off1 1 k o o t! !16 1 19 o i o

3... o o

g 5 lI!ll fNll! l [*o! i ! e.o ,ll!!!l l l !! llim ~ l ~ $a so co e Fig. 11. Calculated stress distributions for 0* section of model HSSh.ITV9. experienced users with a permanent record. In our case, CORTES.SA was modified several times by different people after it had been delivered, and different versions of the program were often in use at any given time. Adequate internal documentation, in the form of programmed comment cards should be included during the development phase and conscientiously maintained at each modification. Full internal documentation can be of great assistance either in modifying the program or in locating errors and defects in the algorithms. Finally, we offer some comments concerning our interpretation of the validation procedure. In validating a special purpose program, it is desirable to have a second code (usually a general purpose program) available for 22

-.3s,..e. es. so. 13 no l I ' E39 to 8s . if s 3o <,s o

• I

$'9 ~

• Coe t

,o -.s l t ti_ ! ll l li l o ^ o -2 s -.s ta pt meest orat m atto g 4 o e m.1 .,x, R o ^ o "di 4to i !lH@it"ittiililti Illl l lI"! So' q" 2Ro Fig. 12. Calculated stress distributions for 90* section of model HSST-ITV9. { comparative analyses of test problems. The experience with CORTES-SA demon-strates clearly, however, that such a check may not constitute a true valida-tion of the program in the absence of comparisons with well documented experi-mental data. In particular, the stress-spiking defect in CORTES-SA would probably not have been corrected and the program not properly validated had the experimental data not been available for comparison. Such computational-experimental comparison studies provide the best assurance for a reliable computer program validation. In our opinion the finite element computer program CORTES-SA is fully validated for the elastic stress analysis of cylinder-to-cylinder tee joints. ANSI Standard 816.9 tees, and single reinforced and unreinforced nottles in cylindrical pressure vessels. The favorable comparisons with well documented 23 s L

experimental data over a wide range of geometric parameters supports this conclusion. In addition, the minimal amount of required input (nine cards) and the available graphics software for both pre-and post-processing should make CORTES-SA, as well as the other CORTES programs, all of which may be obtained through the Argonne Code Center, a valuable set of analytical tools for the safe design of nuclear power plant pressure vessels and piping systems. REFERENCES 1. Greenstreet, W. L., Moore, S. E., and Callahan, J. P., F::,rth Annual Progress Report on Studies in Applied Solid Mechanics (Presswa Vessels and Piping Systs, Corponents), ORNL-4925, July 1974 2. Moore, S. E. and Bryson, J. W., " Design Criteria for Piping and Noztles," % E71978 Annual Report of Contra:t Research for the Metallt.vgy c.nd Materiata desearch Branch,.7ivision of Reastor Safety Research, %UREG-01SS, U.S. Nuclear Regulatory Commission Feb. 1977. 3. Greenstreet, W. L., "Sumary and Accomplishmer.ts of the ORNL Program for Nuclear Piping Design Criteria," Pmesadings of the fechnology infom:rion Meeting on Methods for Analysing Piping Integrity, ERDA 76-50, Nov.11-12, 1975. 4 Moore, S. E., " Contributions of the ORNL Piping Program to Nuclear Piping Design Codes and Standards," Journal of Pressure vessel Technology, Vol. 99, Feb. 1977, pp. 224-236. S. Powell, G. H., Clough, R. W., and Gantayat, A. N., Stress Analysis of 328.9 Tees by ths Finite Element Method. ASME Paper 71-PVP-40, May 1971. 6. Clough, R. W., Powell, G. H., and Gantayat, A. N., " Stress Analysis of 816.9 Tees by the Finite Element Method," Paper F4/7, First International Conference on Struat:mst Mechanics in Reactor Technology, Berlin, See any, Sept. 2 >24, 1971. 7. Gantayat, A. N. and Powell, G. H., Stress Analysis of Tee Joints by the Finite Element Method University of California Report UC-SESM-73 6, ORNL/Sub/3193-1 Feb. 1973. 8. Powell, G. H., Finite Element Analysis of Elasto-Plastic Tee Joints, University of California Report UC-SESM-74-14, ORNL/Sub/3193-2. Sept. 1974 9. Textor, R. E., User's Gkids for.SBFA: Steady-State Reat Fiov Analy-sie of Tee Joints by the Finite Elment Method, UCCND/CSD/INF-60, Jan.1976.

10. Bryson, J.

W., Johnson, W. G., and Bass, 8. R., Stresses in Rein-forced Nessle-Cylinder AttacMents Under Internal Pressure Loading Analysed by the Finite Ele est Method - A Parameter Study CRNL/NUREG-4 (to be published). 11. Bryson, J. W., Johnson, W. C., and Bass, B. R., Stresses in Rein-forced 30ssis-Cylinder Atta:Ments Under External Noment loadings Analysed by the Finite Elment - A Pammster Setdy (to be published).

12. Wilson, E. L., finite Element Analysis of Mine Struetkres. University of California Final Report to DOI, Contract No. H0110231, Sept.1972.

13. Fowler, P. G. and Bryson, J. W., User's Manual for the CCR"ES Omph-fos Package CRTPAK (to be published).

14 Corum, J. M., et al., Theoretical and E:perimental Stress Analysis of CRE Thin-Shell Cylinder-to-Cylinder Model No.1, ORNL-4553, Oct. 1972,

15. Gwaltney, R. C., :heoretical and Emperimental Stress Analysis of CRE Thin-Shell Qlinder-to-Cylinder Model 30. 3, ORNL-5020 June 1975.

16. Moore, S.

E., Weed, R. A., and Grigory, S. C., Emperimental Elastio-Response and Fatigue to Failure :sses of Five 12-in. Norrinal Sise ANSI Standant SId.J Tees, ORNL/NUREG-3 (to be published).

17. Wilson, E.

L., Taylor, R. L., Doherty, W. P., and Ghaboussi, J., " incompatible Displacement Models," Americal and Computer Nothods in Stract:m21 .<schanies (ed. S. J. Fenvesjetal), Academic Press, New York,1973, pp. 46. 13. Irons, 8. M. and 21enkiewicz, O. C., "The ISO Parametric Element System - A New Concept in Finite Element Analysis," Proceedings, Co tference en Recent Advance in Stress Analysis, Royal Aeronautical Society, London, England, 1968. 19. Irons, 8. M., Olivers, E. R., and :lenkiewic:. O. C., " Comments on the Paper ' Theoretical Foundatio ns of the Finite Element Methods,' " inc. J. Solids Strat:c'es, Vol. 6,1970. 24

1 20. Strang, G. and Fix, G. J., An Analysis of the Finita E eent Method, Prentice-Hall, Englewood Cliffs, N.J., 1973.

21. Taylor, R.

L., Beresford, P. J., and Wilson, E. L., "A Non-Conforming Element for Stress Analysis " Inc. J. Merr. Nach. 4%J., Vol.10,1976, pp. 1211-1219.

22. Hinton, E. and Campbell, J.

S., " Local and Global Smoothing of Discontinuous Finite Element Functions Using a Least Squares Method," Inc. J.

1. ws. Meth. Eng. Vol. 8,1974. pp. 461-480.

23. Merkle, J. G., Robinson, G C., Holz, P.

P., and Smith, J. E., fast of 6-In.-Thick Pressure Vesents. Series 4: Intemediate Test Vessets V-S and V-9, with Inside Rossle Corner Cmcks, ORNL/NUREG-7 (to be published). 24. Leven, M. M., Stress histribution at 2Do Closely-Spaced Reinforced openings in a Pressurised Cylinder, Research Report 71-9E7-PHOTO-R1, Westing-house Research Laboratories, Apr. 1971.

25. ASMB Soiler and Preasure Vessel Code, Section III, Dio.1, " Nuclear Power Plant Components," American Society of Mechanical Engineers, New York, 1974.

26. Irons B. M. and Hellen, T. K., "On Redt.ced Integration in Solid Isoparametric Elements When Used in Shells with Mesbrane Modes," Inc. J. Merr. Meth. Eng., Vol. 10, 1976, pp. 1179-1182.

27. Hermann, L. R. " Elasticity Equations for Incompressible and Nearly Incompressible Materials by a Variational Theores," AIAA /.. Vol. 3. Nc.10, 196S, pp. 1896-1900.

28.

Fried, I., " Influence of Poisson's Ratio on the Condition of the Finite Element Stiffness Matrix," Inc. I. Solide Structures, Vol. 9,1973, pp.

323-329.

29. Malkus, D.

S., "A Finite Element Displacement Model Valid for Any Value of the Compressibility," Inc. J. Solids Structures, Vol. 12, 1976, pp. 731-738. 30. Booker, J. R. and Small, J. C., "The Economical Solution of Elastic Problems for a Range of Poisson %..:10," Inc. /. #wr. Meth. Eng., Vol. 9, 197S, pp. 847-853.

31. Taylor, R.

L., Pister, K. S., and Hermann, L. R., "On a Variational Theorem for Incompressible and Nearly-Incompressible Orthotropic Elasticity," Int. J. Solids Stasettaws, Vol. 4,1968, pp. 87S-883. t 6 LO

1 i 1 roonnted from Pressure Vessel and Piping Cornouter Program Evolustion and Quanfication, PVP-PS424 Edited by D. E. Dietnch, t977 pubHshed by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 East 47th Street. New York, N.Y.10017 Printed in U.S.A. 8,' i

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