ML20107E203

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Forwards Westinghouse Pump & Valve Documentation,Per 850109-10 Design Documentation Audit Meeting W/Bechtel in Norwalk,Ca.Stress Rept on ASME Code Class 1 Valves,Bechtel Pump Spec X4AF03 & Agenda for Feb 1985 Meeting Discussed
ML20107E203
Person / Time
Site: Vogtle  Southern Nuclear icon.png
Issue date: 01/31/1985
From: Rodabaugh E
E.C. RODABAUGH ASSOCIATES, INC.
To: Scott Moore
OAK RIDGE NATIONAL LABORATORY
References
NUDOCS 8502250428
Download: ML20107E203 (16)


Text

.

. , - PDLlCC E. G. cRodaGauga casoctaus, Dnc.

4625 CEMETERY ROAD e HILLIARD, OHIO 43026 g-1 * */

614/876-5719 Januaw 31, 1985 Mr. S. E. Moore Oak Ridge National Laboratory P.O. Box Y Oak Ridge, TN 37830

Subject:

Vogtle, Design Documents Audit, Meeting at Bechtel Offices, Norwalk, CA, January 9 & 10, 1985

Dear Sam:

I have organized this letter under the headings:

(1) Documents Requested / Furnished (2) Stress Report on AS4E Code Class 1 Valves (3) Responses (by Bechtel) to Questions from 11/8,9/84 Meeting

-(4) Vogtle Action Items from 1/9,10/85 Meeting (5) Bechtel Pump Spec. 14AF03'(ECR No. 19) and Seismic Analysis of AFW Pump (ECR No. 22)

(6) Agenda for February '85 Meeting with Westinghouse (1) Documents Reouested/ Furnished My letter to you dated November 10, 1984 listed docunents which we re--

quested, at our m'eeting on November; 8, 9,1984, be furnished to us. Docu-ments'were received from Westinghouse vith a letter from Rahe to Denton, dated 12/10/84 Documents were received from Bechtel with a letter from Malcom to Denton, dated 12/5/84. ' These ' documents are. essentially. those cer--

- responding- to the ~ 35 documents requested; > vith the '5 exceptions _ shown on En-closure

~

4 1.~

ECR Nos. 2 and 3 vere reviewed by me during our Jan. 885' meeting arid.I found them to be acceptable. ECR Nos.10 and 18 vill be reviewed during ouri

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i:

planned visit to Westinghouse, Feb. 7, 1985. The status of ECR No. 22 is discussed in Par. (5) of this letter.

(2) Stress Reoort on ASTE Code Class 1 Valves This Stress Report, ECR No. 8, Westinghouse Engineering Memorandum No.

5405, as furnished was incomplete in at least two aspects:

(a) Table of Contents was not included.

(b) There was no cvidence that the Report had been reviewed and ac-cepted by the Owner (or his authorized agent) as required by the ASME Code.

(c) The Report includes about 300 pages that are not numbered. There

, is no way to tell if the furnished Report is complete. -

At the Jan. '85 coeting, the missing Table of Contents was supplied and a form sheet was supplied which is purported to indicate that Georgia Power (or agent) has reviewed and certified the document. However, the.name Georgia Power does not appear on-the form sheet furnished. Copies of these

-two sheets are included herewith as Enclosure 2.

I intend to discuss this Stress!

. Report further at our Feb. '85 meeting with Westinghouse.

0

-(3) Resnonses (by Bechtcl) to Questions from Nov. 884 Meeting-Bechtel's letter (Malcom to Denton,12/5/84) included five questions and responses as shown in Enclosure 3. These questions / responses were discussed ,

at.the Jan.85 meeting.. '

.(i) Minimum Wall.ThicknesL-Control.

The response,' in conjunction with definitions of." minimum wall-thickness"

.in Spec. X4A.Q01, 10.11.1B., vas accepted.

- (ii)Valuboff-factor The response was accepted.-

= .

_l

- a- _$

~3-(iii) Purchase Order for an Elbow and Tee The response was deemed not acceptable. A purchase order was examined at the Jan. 885 meeting and is to be furnished; see Vogtle Action Items, Par. (4) herein.

(iv) Pressure Design of Branch Connections A copy of branch connection calculations for the 4x28 AFW pump turbine steam line connection to the main steam line is to be furnished; see Vogtle Action Items, Par. (4) herein.

(v) Values of i-factors Bechtel prepared (while we were at the Jan. 885 meeting) a list of moments and calculated stresses at the 4x24 branch connection between the 4 NPS line to the AW pump turbine and the ~28" 0.D. main steam line. This is

, Node 138 on the main steam line; Node 1 (Data Pt) in the 4 NPS line. The .

three sheets prepared by Bechtel are included herewith as Enclosure 4.

With the data in Enclosure 4, the i-factor used can be chcked and I have done so as indicated on Enclosure 4 For the branch, Node 1, the i-factor used is 1.00. This is not the 1-factor given on p. 4A of 15, Calc.14CP-7075A furnished us; there the i-factor is 1.551. The i = 1.551 is stated 'to be calculated "using Bonney Forge and Foundry Equation". Bechtel, after preparing Enclosure (3),

stated that p. 4A of 15 was incorrect because the branch connection is not fabricated with a Weldolet. Rather, Bechtel now states, the branch connec-tion is an extruded outlet. Bechtel indicated they used Bonney Fsrge8s Sweepolet 1-factors; see' Enclosure St. As you know, the Code does not give i-factors for extruded outlets and (with the' exception of a Report-I. pre-pared for General Electric on a few extruded Butlets with well-defined dimensions), I am not aware of any published paper or report that gives 1-factors for extruded outlets. Bechtel's assumption that Sweepolet 1--

factors can be~used for extruded outlets is indicative.of'a generic prob -

lem in the casual and sometimes questionable une of 1-factors in. nuclear power plant piping evaluations. ,

However, with respect to the specific 4x28 branch connection in our, audit, the Code equations for " Branch Connections".(which I deem appropriate for extruded outlets with d/D < 0.5) give i-factors less than' unity.for both'-

run and branch;and would be controlled by the specified lover. bounds of-(1.Cforbranch,-1.5forrun. Hence, Bechtel'a f use of-i = '1.0 for. the branch; 1.5 for the run is deemed' appropriate. ?I do not'believe the generic l. prob lem should be continued as part of our Vogtle audit. Accordingly, I con--

sider this Vogtle response as acceptable.

^ . -

l-

(4) Voctle Action Items from 1/9. 10/85 Meeting The following is my understanding of docu:aentation which Vogtle (Jan.'85 meeting) agreed to furnish us.

(a) Wall thickness verification measurement record sheet for Valve HV-106.

(b) Copy of purchase order for fittings (see Par. (3), question iii).

(c) Copy of drawing of 4x28 extruded cutlet and calculations showing conform-ance with pressure design requirements of the Code (see Par. (3), ques-tion iv).

(d) Miscellaneous steel calculations for anchor at Point 125, Cale. x4cP-7075A (This request is related to the statement on p. 4D of 15 of the Cale: " Anchor at 125 will be based on upstream and downstream loads.)

. (e) Revised sheets in calculation package X4CP-7075A -

1. Sheet 4A: correct i-factor calculation, Data Pt 1 (See Par. (3), question v).
2. Sheet 7B: correct discrepancy between stress of 13877 on sheet 7B versus 23054 on p. 9.

- 3. Sheet 13E: cite' proper reference that shows that Valve No. 051:

has a moment load capacity equal to that of the attached pipe.

4. Sheet 4:-Add note on appropriate page to indicate that maximum temperature range has been covered by analysis.

.(Problem is that portions of the piping may have temperatures as low as 17 F per sheet 4.)'

-(f) Update of Status of Hot' Functional Test Program.

O This request' arose in connection with a general discussion of binding of sliding supports because of either:

~

1. radial thermal expansion of large. size, hot.(e.g.. main steam).

pipe thet would close the gaps, or-

2. Lack of parallelism between support shoe and suprart such that.

as the pipe-moves axially.'due to thermal expansSn,.the gaps

.might close.

Whilethe' Specs. indicate 1/8"gapsonhotpipingrestraints,-which should.be sufficient,' it appeared that Bechtel agreed that potential ~

. binding (along with other things) would have to be checked during hot '

. functional testing. 2 While several of'the above documents were shown to us at.the'Jan. .'85. meeting,

~ .

we:did not keep them; the Vogtle commitment was to formally l submit them. - 'So -

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far, I have not received anything. It would be desirabic to transmit Par.(4)

, to Georgie Power to make sure we are in agreement as to what is to be furnish-ed.

(5) Bechtel Pump Snec. _X4AF03 (ECR No.19) and Seismic Analysis of AFW Pump (ECR No. 22)

. The copy of Spec. X4AF03 furnished to me with Bechtel's 12/5/84 letter was incomplete; about half of the pages were missing. Accordingly, I could not review Spec. X4A M3 before the January'885 coeting. I requested and re-ceived at the meeting a purportedly complete copy of Spec. X4A M3 I have re-viewed Spec. .X4AF03 subsequent to the January '85 meeting and find-it accept - -

able with two exceptions:

(1)l Attachment 3_(Steam Turbine Leading Diagram). states that:

" Resultant piping loads are shown in Table IV of the design speci--

fication." '

t

~

There is no Table IV in Spec.-X4AF03, although it is mentioned on '

p.12 of the Spec. _ Also,;we received (ECR No. 23) a _ document-X4AM3-2-0, Turbine Allowable Nozzle Loads; however there 'is no. in-dication as to what relationship,"if any, this. document has to -

g Table IV of. Spec. X4AF03.

- .. - . O

.(2) The bidder's. (Ingersall-Rand) .. proposal includes a Section 9.0,

~

" Deviations".(presumably deviations from Spec. X4AW 3). ..Under 9.2, " Technical Provisions or Design Specifications"'the bidder has

~

.apparently stated."See comments attached". There ' are no attached comments. -Accordingly, it appears _that the bidder may have-deviated' .

7 from' Spec. X4AM3, but there 51s:no description of what theseidevia-

.tions might be.

5 . . .. ,

' Related to these' exceptions is ECR No. 22, " Seismic Analysisfof AFW Pump".;,

As indicated by Enclosure _1, this document has not been' furnished. In sieu!

~

4 -

q of questionstabout Spec. X4A503,.I.ithink we;shouldJask for it.again. :-'Accoid-1

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ingito the Code, Design' Specifications'are1 required to,provideithe basis:for; A4,_ .

. . . .. .. ., . . ., Wi; ievaluations of the adequacy of the component and,Eaa part of:our,VogtleTaudit,' "'

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p, .. _ ^

- we 'should'see if thiis: CodeLrequirementihas:been met for7the AFW pumps. .

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Perhaps the nost expeditious way to accomplish this would be to send Par.(5) of.this letter to Georgia Power Co. for Bechtel's response.

(6) Agenda for February '85 Meetine with Westinghouse (c) Stress Report on Pressurizer Surge Line (ECR No.18)

(b) Wording for valve operebility qualification as applicable to Vogtle (ECR No.10)

(c) Westinghouse Engineering Memorandum No. 5, " Stress Report for Class, 6-inch and Larger Gate Valves (ECE No. 8).

~ ..

Yours very truly, h-t'

'ECR/mr E. C. Rodabaugh

Enclosures:

1(1) Requested but Not Received Documente . .

-(2) Table of Centents and Certification Sheet, Valve Stress Report.

(3) Responses (by Bechtel) to 11/8,9/84 Meeting Questions:

(4) Bechtel Data'to Check i-factors (5) Bonney Forge Sweepolet 1-factors t

cc:~ Dave Terao Melanie Miller -

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$2 19ects/c) t A Fitt f ur*rf Seist's/c /}nctly s/C, A rW Por>r,o {&y Yenoo , 7<el-m .l ]

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(1)' C ett tYo3. /0 ond 11 ' f. --he rev reared o f Feb. l'fr meels.fn er;>a ' Wes/.ej house,

]El [C ott Nr. / 9, feckle/ ~ famp S fra. X'/Afof, us; o n e, j, /, ,, _ (;,,,,,g,J , _ g con <ffefe copy of /k S,0ec. edes /ven uired et h _ Jon. . 'PC,,,res.ry. fa a '

Tiern(5)Io! /Als feller'v:ffr respec/ /* - h? Mos. / 1 aos/ 2 2 .

U ) te R Mo. 1, .S/ rex 6porf'ose As+1C Ca r Cress') Valves, ues Aren.*th ed estaeaf-

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hk ITokle of C.nfe.*Is : wtd ' many x,ide 4ceaf pyas.. 4 .fo Lis . A co a h /s' suas f er nithed

  • f ' flg Jan. '![ '"'Ch'*y * . Se c Ife*n . f t) *f .hB" l'll*

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& 7~C : S , Mksq$ WO lt MkrTYjd - 25$3 f:S l Eo<1, Z, E.c2 4 EM,1/se/11 2 eoger TABLE OF CONTENTS

"# ' M'#' "' # ' ' '

,7 VOLUME I

// /s/ / 5 i m s s ,; 4.ss e  !

n b Kapadon Volvn f

section Number .Tooic l Introduction i j

Valve Cross-Reference I

Certification of Compliance 1 Revision Page -

2 References ,

3 Materials Stress Tables - The calculations included in this volume are grouped by section number which are ordered by valve size. .

VOLUME II -

4

  1. Assembly and Detail Drawings 5 Design Conditions and Basic Operating toads Body (Shape Rules, Primary and Secondary Stresses) g.

6 7 Body (Fatigue and Cyclic Analysis)'

8 Main Flange and Main Flange Bolting

.9 Bonnet 10 Disc ,

11 Seat Ring o 12 Guide 13 .Back Seat 14- Stem 15 ' Stem-Disc-Connection-16 Torque Arm and Key 17 Gland, G1and' studs and Gland Follower 18 Yoke

);

19 Natural Freqeency and critical Deflections

-20 . Yoke-to-Bonnet: add Yoke-to-Operator Bolting' -

Q .

. Westinghouse Electric Corporation

SUBJECT:

Electro Mechanical Division PAGE: 'ii!

( -

i.

. , ti

I

t g,fMENT.5UBMITTAL u ..Ousc. rew i ine FORM _ _ , _

PAR l

8 A L-

_ 6 04o5 _ R I

OM TO I

iSTINGHOUSE ELECTRIC CORPORATION WEMD PAR No. 0 0 e PAoE 10F CHESWICk,PA.15024l JCLEAR ENERGY SYSTEMS 3X 355 I I ISSUE DATE O ,

TTSOURGH. PENNSYLVANIA 15230 rTn: W. H. Black WB-0-151 ENo.tTR.No. AE-VE-2078  :

E. D. Webster I I J

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couro=Luf @ @r. o. @

anv414arv Valvoc ri.sEn AcTioNasi scovinto av TNis "" " * / ' 8 * @ @ '. . ** * ***.r . i uusTcecouri.trs gpggp l- _,_{.

ShPPLILA SERIAL no. O & SJPPLIE R C RCER h0. @

hl SEQUENCE CODE (Use proper Codo) APPROVAL STATUS CODE 3MITTAL CODE A= FOR APPROVAL. O=6hCINAL SUSMITTAd Pl0 WCCNVENT R=RESUCMITTAL OUE TJSCohTAENTS RESUEMtTT AL RECulRED I = FOR INFORMATION (Use Proper Code)

V=RE5UBMnTTAL DUE T ) SUPPL 1ERCHANGES ", C vA [OR INFORAATION M-PSUSMITT AL DUE TO 00CWENTOUALITY (Use Pro;er Code)

TEM P.O. IT EM DRAWINO NO./ SPEC. N0' CESCRIPTION / TITLg EN GIN E E RIN G PROCCOURE NO. g g - CCuMENTS N T. NO. .g 9

, n 1 A EM-5161 9d. 0 StressReporf6"+CheckVal tes 2 . A [EM-54dh) 93 O h"+GateValves .

I I Aldo for G.O. L P.O. belod- M)Q G.O. 4T-68563-ARG-AR1 - P.O. 546- 1CJ-191614-Bfl Ifk G.O. AT-6856'-ARO-AR1 - P.O. 546- ICJ-191604-an 90 __

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b.O. As (4512 P.o. Sh, Nd-MIW -BN Yb -

6.o. AD 6E61o ... --$o dVI, -N G 19/a03 - Bel .-

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c, Ca s T Rie u T.80 N 6TT81N AL EN GINCCRING COMMENTS ,

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{IS CERTIFIES THAT STRESS REPORTS EM #5161Ml AND EH #5405-1

[oE5BloRos.2 EA MAV P.C. BLDG. 2

.VitWtv FtK REQUIREMENTS 0F SECTION III, DIV.1, OF THE ASME PURCH. SYSTEMS M. BONFIGLIO R olN AT " K. DELUSE

)ILER AND PRESSURE VESSEL CODE. PARA's NA-3350 AND NB-35'0D AND ,, oyer uldt-its 1Ht UESIGN AND OPERATING CONDITION STATED IN QUIPMEff '[eUYER rRoJECT ucats!

R. DELISSIO

'ECIFICATIONS G-678852-2 AND G-678853-2. D. CAVADA OPC AEEFILE:[/.

220/(lgf72 22"l$i/Cll2

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. 1FI LIO j N .hf hhdi,3, hko ,

'I I URCHASING AU'THORIZATION *

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sofortnation contained herein does involve e change in price. delivery ci i ,r ms I

sdIon 2tsons.you are not to proceed en accordance vath PAR but pursue the ACKNOWLEDGMENT

{ RETURN tit.tEOt ATELY) ,

one os currently defined by the order and immediately notify the buydt.

his PAR confere. Owine Ove eiiio o.ie Isaia ocknowledge .eceipt end ecceptane's of this PAR by signing and letarning one copy to Fettinghouse **'"

tectric Corporetion at the abon ad*ets.vnthen 15 days from date of iNi PAR.

tARK for esrentson ef SW O w 7 .- ,

stONATune

/2lTlg f Esc /. 3 C NlC l,

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  • r Sahids/ e Fett 4 JER //so/rt VoyHe 2l> ayes Request for additional information by NRC at the MEB meeting on November 8 and 9, 1984 at the VEGP jobsite.

OUESTION i Demonstrate the means by which the specification dictates the minimum wall thickness for the steam line to the turbine-driven auxiliary feedwater pump.

RESPONSE

Piping wall schedules as called out in the material classification sheets are based on the minimum wall calculations for the indicated pressure temperature design conditions.

The piping fabricator is required by specification (X4AQO1, Paragraph 13'2.3.3) to measure the wall thickness on-all pipe and fittings and determine -,

acceptability based on the minimum wall thickness as

. specified in appendix D. " Butt Weld End Preparations and -

Transitions". A copy of X4AQO1, Paragraph 13.2.3.3' is attached.

OUESTION 11 What_value was assigned to the adjustment factor f in stress calculations and justify the use of the value?

RESPONSE .

A stress adjustment factor, f of 1.0 was considered in the stress calculation for the transient from cold startup to hot standby. The number ofEcycles for this occurrence g is significantly less than 7000. .This condition envelopes all other: conditions.

For example, table 3.9.N.1-llin-the.VEGP-FSAR-3 (attached). defines the number of_ loading and unloading operations between 15 and 100 percent of full. power as 13,200. The f factor:for this cyclic condition is.o.9.

In consideration of the_small temperature range (554?F-545'F perEW 1etter GP-2932),-the expansion-stresses are significantly lower than 90 percent 1of'the stress allowable.

QUESTION iii 1

-Provide a' copy ofLpurchase orders'for an elbow:and'a tee:

fitting"in--the steam line to;the auxiliarycfeedwater turbine-driven pump.

Oll2t

.+

RESPONSE

A copy of the purchase order is not available for these items since these are purchased by the piping fabricator and not by Bechtel.

OUESTION iv What che dus are performed to ensure pressure design -

requiretents are satisfied for the 4 inch branch connection to the main steam li'ne.

RESPONSE

~

Bechtel reviews and verifies the vendor branch connection' calculations in accordance with paragraph 9.1.2F of specification X4AQO1 (copy attached).

OUESTION v

- What is.value of the factor i utilized in the stress -

calculations? Provide sufficient information to allow

. reviewer to verify value of.i.

RESPONSE

_ Stress intensification factors for the' steam line between the main steam line and the turbine-driven pump are shown-in the AssumptionsSection IV,oof the stress calculation folders.

Stress intensification factors for standard ~ fittings such as elbows, tees, and reducers are calculated and; applied' by-the ME-101' computer program (Linear ~ Elastic Analysis o of Piping Systems). The SIF are calculated in accordance with ASME1Section-III,l Division.1:- subsection;NC, Fig.

NC-3673.2-(b)-1.

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       .~-   .                                                                                    Enc /. 5 Ect? k rEN, Y'W" 2 pages STRESS'INTENSlFICATION FACTORS FOR SWEEPOLETS RECOMMENDED USE:

f t The values in Table 1 are intended to be used in making t piping system stress analyses in accordance with all ANSI Piping Codes pnd other Codes which use stress intensification factors. NOMENCLATURE: r = mean radius of branch pipe R = mean radius of run pipe g * , h'" . ,

                                       .              t = nominst wall thickness of branch pipe T = nominalwallthickness of run pipe                             -

M = applied bending moment as shown below:

                                                                                  " 88 hM bin 9 -@j    .      .
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Meb 's N Mav g..-] u,, 0.5 Interpolate between: r/R = 0.5, i = [0.17 (R/ r/R = 1.0,i = 0.45 (R/T)]'#8 (t/T) (F.).t. (F.)0.25] (t/T) (F.) (F.) 1.0 1.0 1.0 M.,

                                      .M     .,M    ,.

0.40 (R/T) 8'8 (F ) (F.)

                                     .M         M M.,, M.,                          T.0                                                            .
                                    'M,,. M ., M,,                 or, for r/R R 0.5,                                                                                      -' --

M,.. M M.,. 0.5 (R/T)tra (r/R) (F.) but not less than 1.5 (2) See norienclature sketch for def;nition of subscripts. to These factors are to be used in accordance with USAS B31.1.0-

                   - 1967,'Parr119.6'4 pxcept tlist for ** Branch (Lee s)"                                          ; es) F, = F = 1.0, for flush or'dre'ssed lasert welds.*

F. = 1.0, for as-welded Insert welde .  ;. F, = 10.5 + r/R) but not less than 1.0, for as-wefded Insert welds. - q

                                         . g _ g(f., M P .4. (f.,, M P -                                                    Is= 1 + 0.05 (r-3), but not less than 1.0.

d

                                                                   . , gag
                                                                                                                      ,(*fThe minimusn values of I depend upon the type of Oltth butt weld .                       .;

' and similarly for the other Codes based en the strese Intensl8 cation . between sweepolet and branch pipe. F or D stands for flush or - factor cor. cept. , dressed; A-W stands for es. welded. : EXAMPLE #1 C ' EXAMPLE #2

                .. Calculate the stress intensir: cation facier for an out-of-                                          ' Calculate the stress Intensification factor for an in-plane
                 - plane bending shoment appiiod to the branc.5 of a 12" x 6*,'                                           moment on the branch of the hehder. described in Ex.

standard weight, carbort steel Sweepolet' header. The ample #1. l '

                , insert weld and the girth weld between Sgreepolet and ~                                                     r/R = 0.5,1 = [0.17 (R/T)** + 0.25) (t/T) (F.) (Fs) 1 branch pipe are dressed. '                                                  -
                                                                                                     =

l = (0.17 (6.187/0.375)*'8 + 0.25] (0.280/0.375) (1.0) (1,000) - r = (6.625-0.280)/2 = 3.172* - '

                                                                                                                           ' I = 1.018
                           =                    5)/2 = 6.W :                                                                  r/R = 1 D, f = 0.45 (R/T)** (t/T) (F.) (Fs)                    .   .

T = 0.378* ' . .. . I = 0.45 (6.187/0.375)** (0.280/0.375) (1.0) (1,000) ?

                                                                                                      ~

Fa= 1'+ 0.05 (3.172-3) = 1.0086 - . i = 2.196 = ' ' >

                  ..From Table 1, the stresis Intensification factor' for an out- :                                     Linter) olating for r/R '= 3.172/6.187 = 0.513 yleids?

cf-plane moment on the branch (Mus) is: <

                                                                                                        ,"                   - Q= 1.04. -                                                 ~'

fue = 0.45(R/T)(r/R)'* (t/T)(F.)(Fs) .

                     . lu, = 0.45 (6.187/0.375)** (3.172/6.187)'8 (0.280/0.375) (1.0) (1.000) -

fe = 1.57 , gp

                , The research program conducted by Bonnsy locluded the.:                                               'In the case of Example.#2, (le,,) calculated = 1.05 vs.

ifatigue testing of a number of 12" x 6*, standard weight, ,(f.,,): esp 'unlal = 0.45. Therefore,-for the examples ,

                 . carbon steel headers with welds dressed. The average                                                   elled, the strese Inten menelan factors calculated by the-
                 " value el.1 determined.experimentaNy for en out-of plane                                                appropriate equatione in the above table are about 259fi bending moment en the branch was (lue) avg. = 1.22.f                                                   higher than the average ag-P _ "", determined values.1 While the degree of conservatlem in Tables 1,' 2 and S le verleble, for Example #14 .-                                             1      .
                                                                                                                                                                                                             ~

f (lu.) calculated = 1.57 vs. (lue) experimental = 1.22. : , . g) e

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