Ansys Pipe Stress

][NClLUDES TJHIE 1-12 x 3 LN2 TRANSFER L][NE

ANALYSIS RESULTS

D-ZERO Engineering Note 3740S10-EN-162

Jeff Wendlandt

(Revised by CH Kurita)

May 311988

APprovedH~I

PIPE STRESS ANALYSIS PAGE 2

-INTRODUCTION

The analysis of pipe stress due to thermal contraction and expansion can be accomplished in numerous ways This report examines the analysis methods available to us and provides the reasons for the methods we chose to use It then describes the results of the 1-12 x 3 vacuum-jacketed LN2 transfer line The LN2 line also serves as an example for an analysis using the method chosen A brief discussion of the 4 x 6 N2 exhaust line follows these items

METHOD COMPARISON AND SELECTION

The methods compared include the Grinnell and Tube Turns Chart methods Grinnell Moment method commercial software for PCs and ANSYS

The chart methods have been used for many years with success but are very tedious and time consuming This type of analysis has limitations For instance the particular geometry being analyzed might not fit into the charts available in the handbook To analyze a given geometry assumptions are made which lead to uncertainties in the results From the past experience with chart methods it was decided that a better approach was needed

Information on pipe stress software advertised in magazines was acquired originally by Brian Fitzpatrick The information received included written material and demonstration disks Several demonstration disks were working programs One working program AUTOPIPE was available for us to compare our results with the other analysis methods AUTOPIPE proved to be easy to use and provided a detailed analysis The geometry is quickly entered and conforms to various codes including B311 and B313 Letter sized sheets can be printed out which reveal the results in an organized manner The software packages have these stated advantages but are expensive The initial purchase prices range from $150000 to $600000 with the average at $450000 (not including user fees)

At the same time an analysis was performed on ANSYS ANSYS offers much more power and is less expensive than the software programs because the pipe module is already available as a part of the existing

-) ANSYS package in use at the laboratory The PC software however is much easier to use than ANSYS even though ANSYS provides a pipe module


_ for easy geometry input The LN2 transfer line was analyzed first by the Grinnell chart method and later done on ANSYS The ANSYS solution provided much lower bending stress results The values were lower by a factor of two in some instances We questioned whether or not the stress intensification factor( SIF ) of the short radius elbows was included in the ANSYS calculations because the SIF value of 26 is close to the factor the ANSYS values differed from the chart values After later investigation the SIF used in ANSYS was found to be 23 because the default radius for a short radius (sr) elbow is incorrectly 1 x 00 The actual radius of sr elbows is 1 x NOM DIA This radius is a term in the SIF calculations and leads to the discrepancy CODE B313 equations for the SIF calculations are shown in TABLE 1 This flaw in ANSYS is easily corrected by inserting the numerical elbow radius instead of sr

In order to compare the results of each analysis method a simple 6 x 6 L shaped pipe run was examined The 1-12 sch-l0s 304 SS pipe with a short radius elbow was analyzed under the condition that it is rigidly fixed at both ends and cooled down from 300K to 77K The results are as follows

MEIHOD MAX BENDING STRESS Grinnell Moment 13664 psi ( A Parker) Grinnell Chart 20075 psi Tube Turns Chart 14769 psi ( A Parker) ANSYS 12737 psi AUTOPIPE 9638 psi

From this comparison several conclusions were drawn The Grinnell Chart method is too conservative and both chart methods are inefficient and limited AUTOPIPE and other PC programs are efficient but too expensive Therefore ANSYS is our best alternative because it already exists here and is inexpensive to operate

1middot1Z X 3 LNZ TRANSFER LINE ANALYSIS RESULTS

The analysis included in this report contains the maximum bending stresses (which are located at the elbows) the forces at the anchor points and the displacements at the nodes The initial analysis began with a dimensioned piping layout sketch An acceptable solution was determined


1 by locating vacuum break placements The vacuum breaks act as rigid anchors and restrain displacements which then redistribute stresses Originally the solution was checked with the use of the Grinnell Piping Handbook The 1-12 x 3 pipe is 304 SS sch-IOs pipe with short radius elbows and a single welding tee The thermal contraction upon cooling from 300K to 77K results in the majority of the stresses produced additionally gravity was added to this analysis although it did not produce any sizable changes in the results The thermal contraction shown in code B311 is 385100ft or 14387 X 10-5inin-K [laquo385inI00ft)12inft)1 (300K-77K)] The dimensions and locations of middotthe anchor points are shown in FIGURE I The bending stresses and anchor forces are shown in FIGURE 2 The allowable code stress(Sa) is 25500 psi and should never be exceeded by the computed stress (Se) Computed stress consists of the bending stress(Sb) and the torsional stress(St) Se= (Sb2 + 4St2 )12 The torsional stresses are insignificant contributors to the computed stress At the element with the maximum bending stress of 17840 psi the maximum torsional stress is 49 psi

The ANSYS model is composed of elements an~ nodes The pipe elements are made of two nodes and share these nodes with two adjacent elements Some nodes are Ieftover during the geometry construction and are not associated with any elements FIGURE 3 gives locations of the nodes and FIGURE 4 gives the element numbers formed in the creation of the ANSYS model TABLE 2 shows the displacements of these nodes The maximum displacements and associated nodes are shown at the bottom of this table This concludes the summary of the results

PIPING ANALYSIS USING ANSYS

U sing the LN2 transfer line as an example I present a procedure for piping analysis using ANSYS The reader is assumed to have access to the ANSYS 43 version user manual and any applicable V AX user guides The ANSYS USERS GUIDE written by Mark Leininger used as a reference in this report is helpful for any ANSYS user Any analysis begins with a dimensioned piping layout sketch After this vacuum breaks externalinternal bellows and flexhose can be located on the piping layout to reach acceptable stress levels The model is created and entered into ANSYS To use ANSYS the user must be setup to do so This can be accomplished in the login file or by typing LIB[LIBANSYS]SETUPCOM after login


There are two modes used in ANSYS These are the interactive and

batch modes The interactive mode is entered by typing ANSYS_INTER after the $ prompt The budget code (dch) and the user defined file name excluding the file extension(DAT) is then entered The user is now in the interactive mode This mode allows the user to input and analyze a model at the terminal Frequently plots are made on the screen to get the proper view arrangements The interactive mode is helpful when a specific stress or displacement is desired instead of extra information The batch mode is entered by typing ANSYS_BA TCH The budget code previously defined file name including the file extension approximate CPU time and several questions answered NO follow After this the job is put in queue for analysis Upon completion files are created including the solution file and a file that extracts the geometry stresses displacements and forces from the solution file and lists them in a readable manner This latter file (nameLIS) can be printed out on a line printer and the results can then be viewed The listing file provides a documentation of the stresses for later use

The analysis of the LN2 transfer line began with the creation of a file named N2LINE26DAT A file (name26DAT) contains the pipe data and geometry and is created outside of ANSYS If the input data needs to be changed the outside file(name26DAT) is just edited The complete file(N2LINEDAT) includes the analysis commands and postprocessing to extract the results and is appended to this report N2LINE26DA T only includes the pipe data and geometry and its end is indicated on the appended file A step by step procedure is now presented for a batch job

1 Create name26DAT file using an editor

2 Type ANSYS_INTER

3 Enter budget code ( dch )

4 Enter file name with no extension ( name)

5 Type liNT

-Begin-inp prompt is then displayed

6 Type INPUT26 (ANSYS reads file 26)

7 Check the information scrolling by the screen

8 Enter FINI to leave PREP7

) 9 Enter IEOF to leave ANSYS_INTER


10 Edit name26DAT adding additional

retrieval information and correcting any errors

11 Rename the name26DAT to nameDAT

12 Type ANSYS_BATCH after the $ prompt

13 Enter budget code

14 Enter CPU time [ 5 minutes]

15 Answer NO to the next 3 questions

16 After completion of the job type the listing

file name LIS on the screen to check the

results

17 Print the listing file on your line printer

The commands listed in the appended file are now explained andor given the locations of the explanations in the ANSYS manual

PREP7

This command places the user in the preprocessing module for model input A brief summary of the module is found starting on page 321

TIT 1-112 X 3 LIQUID NITROGEN TRANSFER LINE

An explanation is found on page 3112 of the ANSYS Users Manual

MPTEMP175144200294 MPDAT AEXII304E6299E6294E6283E6

These two commands construct a temperature table for the Youngs Modulus The first field in MPTEMP and the third in MPDATA are the beginning slot location in the temperature table The slot locations must be the same The data for the temperature table was found in TABLE C-6 of the ASME B311 CODE A more detailed explanation of these commands is found on pages 3331 and 3332 The valid material properties are found on page 3431


- ALPXII4387Emiddot5 DENSI2899

These both are material properties that also can be placed in the temperature table but were not for this example They are shown on page 3431

TREF300 TUNIF77

These commands specify the reference and uniform temperatures of the pipe The commands are found on pages 3321 and 33157

The following commands used in the geometry input are found in the PIPE MODULE section 3324

PSPECI1510S

This command is found on page 33241 and defines the pipe material and dimensions

BRANCH1

Defines the beginning point of a new stretch of pipe and is explained on page 33242

RUN middot18 RUN 295 BEND 15

These two commands are used to define straight runs of pipe and elbows The straight runs of pipe are formed in incremental lengths from a beginning point The elbows are formed between two previously defined straight pipes The bend radius must be specified in order to get the correct SIPs The defaults and explanations of these commands are explained on pages 33243 and 33244 The first RUN command forms nodes 1 and 2 while the second forms node 3 The BEND command forms nodes 4 -7 The next RUN command creates node 8 This pattern continues throughout the piping layout


BRANCH30 RUN -435 TEE

This series of commands place a welding tee at node 30 The RUNs previously executed have formed the nodes 30 and 3~ The RUN listed to the right forms node 36 The TEE command forms nodes 37-39 The TEE command is located on page 33243

By knowing these patterns the nodes are located on the piping layout before the the files are created The organization this provides is beneficial in locating tees and anchor points

DlALL through D70ALL

This command specifies zero displacements for these nodes These nodes are then the anchor points On page 33161 the D command is explained in detail

The D command marks the end of the N2LINE26DAT Use ANSYS_INTER with the IINPUT26 command ( see page 6 ) to input the data The geometry and nodes are checked to ensure that ANSYS has all of the information necessary to execute a run At this time the elements and nodes can be plotted to get the proper picture by using the SHOW command With the terminal used in this example SHOW9600240 was entered because a VT240 terminal with a 9600 baud rate was used The NOSHOW command writes the plots to a file if a hardcopy is desired These commands are shown on page P34 The NIEW command and other plot commands located in APPENDIX P( page P35 and on) can then be used to arrange the plot Once everything is found to be correct ANSYS is exited and the file is edited and must then be renamed without the two digit integer The commands added to the N2LINE26DAT file are now shown

ITERll

This command indicates the number of iterations performed in the analysis For pipe analysis only one iteration needs to be performed This command is found on page 33152

ACEL 1

The ACEL command produces the effect of gravity and is found on page


33158 The acceleration is one g in the Z direction which results in a gravity effect in the -Z direction

KRFl

This command calculates and prints the reaction and nodal forces in the LIS file It is found on page 33156

AFWR 1

It causes the analysis file to be written and is shown on page 33272

VIEWl-l-ll ANG LE160 EPLOT

These commands are used to get a recognizable plot The view command specifies a point that determines a line of viewing from that point to the OrIgm The angle command rotates the picture about the viewing axis and lt~

is not always needed These commands are listed on page P35 The EPLOT command produces an element plot and is discussed as well as other pREP7 plot commands on pages 3381 and 3382

FINI INPUT 27 FINI

The first FINI leaves PREP7 and the INPUT command reads the analysis file 27 The last FINI leaves the solution phase If the analysis is to be done interactively the EXE command shown on page 3112 is placed before the INPUT27 The batch execution does not need this command The retrieval of information or post processing follows

POST1

A brief summary of the POST 1 section is found on page 611

SETll

It causes the solution file to be read and this command IS found on page

PAGE 1 0 PIPE STRESS ANALYSIS

6123

PRSTR

This command prints the stresses selected before the issue of the SET command The batch mode selects a list of stresses to be printed out upon the execution of the PRSTR command To select a stress in the interactive mode it must be done before the SET command with the issue of the STRESS command For example the bending stress at node I(SEE FIG 4161 of the ANSYS manual) for a straight section of pipe is selected by entering STRESSSBI1614 Field 1 is for a unique label defined by the user Field 2 is for the stiffness type [16-straightpipe 17 -tee 18-elbow ] Field 3 is the item number which defines the post data item out of the items available for that stiffness type The STRESS command is explained on page 6121 The post data items available for the element types are found on 4162 4172 and 4182

VIEWmiddotmiddot ANGLE60 PLDISP

These commands are the same ones that were shown earlier The PLDISP command is a POST 1 plot command that plots the displaced elements due to the contraction The1 overlays the displaced and non-displaced elements on the plot This plot accompanies the appended file The POST1 plot commands are discussed on pages 6130 to 6132

FIN I

This leaves POST1 and concludes the analysis of the piping system To get a hardcopy of the plots created by the plot commands

ANSYS_HARDCOPY _FILE21 is entered after the dollar sign prompt After which name21DAT is entered for the file name as well as a CPU time of 5 minutes The plot is then placed in queue

In the process of analyzing the piping system many files are created These filos are given some explanation in appendix C File 12 is the solution file File 16 contains the geometry information File 18 retains the history of the input File 21 contains the plots and file 26 is the file created outside of ANSYS to be input These files become a part of the users directory after a run has been completed Once file12 is created any


post information available can be viewed on the screen by activating ANSYS_INTER once again and entering POSTt

4 x 6 N2 EXHAUST LINE

Two different analyses were performed on the piping line each modeling a different solution Both solutions lower the stresses to an acceptable level Vertically hanging flexhose at these nodes on the internal pipe or horizontal external bellows on the straight pipe below these nodes are the two solutions considered The external bellows solution is desirable but due to limitations in the movement of the circled nodes this solution is not completely acceptable at this time The flexhose solution doesnt require movement in these nodes but the flexhose are contained In

the inner pipes which is not as desirable as an external bellows solution A suitable solution is still being sought

PIPE STRESS ANALYSIS PAGE 1 2

REFERENCES

ANSYS USERS MANUAL Swanson Analysis Systems 1987 Chemical Plant and Petroleum Refinery Piping [ B313] ASME 1984 Leininger Mark ANSYS USERS GUIDE Fermilab Computing

Department July1986

ACKNOWLEDGMENTS

I wish to thank Tony Parker Bob Wands and Kay Weber for their help

---~--- -____-_ _-------------- shy

1-12 X 3 LIQUID NITROGEN TRANSFER LINE LAYOUT AND DIMENSIONS

CC T 765

DROA3

37475

x -VACUUM BREAKS ( ANCHOR POINTS)

z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

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an C ~

L

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18

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Figure 1 V

1-12 X 3 LIQUID NITROGEN TRANSFER LINE NODES 46

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x -VACUUM BREAKS ( ANCHOR POINTS )

- NODES 8

z

y 12x

Figure 3

1-12 X 3 LIQUID NITROGEN TRANSFER LINE ELEMENTS

29

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bull - NODES

z 5

y x 7

1

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Figure 4

----

ASME CODE FOR PRESSURE PIPING ANSIASME B313-1984 EDITION CHEMICAL PLANT AND PETROLEUM REFINERY PIPING TABLE D-l

APPENDIX D FLEXIBILITY AND STRESS INTENSIFICATION

FACTORS Notes to Table D-l appear on p 207

TABLE D-l FLEXIBIUTY FACTOR k AND STRESS INTENSIFICATION FACTOR i

Stress Intensification FactouFlexibility Flexiblflty

CharacteristicFactor Description k b SketdI

T

Welding elbowU l69 or 1amp5 075 09 r pipe bend h hZ ) ---r shyt2~l h V

__ Rl - bend

radius

Closely spaced miter bend12l cot 6 fs s lt rz (1 + tan 6) 2 r 2z

SinltJle miter bendl2 or 152 09 09 1 cot 8 fwidely spaced miter bend hl h 2 h21l 2s rl (1 + tan 8) r2

~

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TABLE 1

tHUIHI~IAKY IIAIA - VNAUHIlIUlllU USE IgtIBTRIIlUIION OR DUPL1CATION IS PROHIBITED ALL RI~ITS RESEHVED FOR SUPPORT CALL MARK LEININGER PHONE (312) 840-4 ) TWX

) 1-112 X l LIQUID NITROGEN TRANSFER LINE 80959 MAY 181988 CP 5380 )

--- t DISPLACEMENT 80LUTION TIME - OOOOOOE+OO LOAD 8TEP- ITERATIONshy CUM ITER NODE UX UY UZ ROTX ROTY ROll

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0106087 0100783 0104652 0-106360

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( 12 -0663526pound-01 OOOOOOOE+OO 0225838 16 0232365pound-01 0641586 -119763 -t

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( 26 -0 223638E-02 -0 327385E-Ol O (27 -0 442232E-02 -0 330519E-Ol O 28 -0middot482334E-o~ -o-304oo1E-01--o-692069E-o1 O 30 0750909E-Ol -0 634371E-o1 -0

( 32 0923824E-ol -0 188193E-01 -0 (33 0958342E-ol -0 223627E-Ol -0 34 middot0middot956997E-ol--- middot-0-267539E-01middot 35 OOOOOOOE+OO OOOOOOOE+OO 00

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l ( DISPLACEMENT SOLUTION TIME - OOOOOOE+OO LOAD STEP- ITERATION 1 CUM ITERshyNODE -UX UY UZ ROTX ROTY ROTZ

t l69 0734721E-01 0141071 -0 755202E-01 0217799E-02 -0 224104E-02 -0301198E-02 70 ---middot-OoOOOOOE+OO --o-oooOooE+OO---OrOOOooOE+OOmiddot---O-OOOOOOE+OO middot-0middotOOOOOOE+00---middot0 OOOOOOE+00 ----- shy

72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~

( 73 -0 157880E-01 0730249E-01 -o151339E-01 0132495E-02 -0 143373E-02 -0 158209E-02 (74 -0 156880E-01 0689719E-01 -0 132987E-01 0103755E-02 -0 124774E-02 -0 126971E-02 _----_- -__----__--- shy

MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02

INTEGEk STORAGEREOUIREMENTS FOR BACK SUBSTITUTION CP- 5490 TIME- 909603 FIXED DATA 762 TEMPORARY DATA - 902 TOTAL- 1664CTvCn A~T _ t11 TCnCAcv _ bull ~e tl1 - It~tT ofI

TABLE 2

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IPREP7 ITIT 1-12 X 3 LIqUID NITROGEN TRANSFER LINE MPTEMP175144200294

r~PDATAEX11304E6299E6294E6283E6 LPXll4387E-5 DENS 1 2899 TREF300 TUNIF77 PSPECl1 510S BRANCHl RUN-18RUN295 BEND 15 RUN72 BEND I 15 RUN3745 RUN20425 BEND 15RUN88 BEND 15RUN 11-22 75 BEND 15 RUN-33 RUNlO10 BEND 15 RUN33BRANCH 30 RUN-435 TEE

ARUN175 BEND 15 RUN 140 RUN765 BEND 15BRANCH 40 RUN 10 TEE RUN-30 BEND15RUN 35 BEND 15RUN30 BEND 15 RUN II 23 BENDl5DlALL D8ALL D24ALL D35ALL D46ALL D 70 AL__l___ END OF N2LINE26DAT ITERl1 ACELl KRFl

r--AFWR 1 IVIEWl-l-ll IANGLEl60 EPLOT FINI IINPUT27

FINI fPOSTl SET1l PRSTR

I(VIEW 1 -I -I 1 IANGLEI60 PLOISPl FIN

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ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x

1 1 - 1 2 X QUID NITROGEN TRANSFER LINE

APPENDIX A r 1 In the analysis performed on the LN2 transfer line the inner pipe is

supported by the outer pipe only at the anchor points In the final detailed

design G-IO spiders which act as guides and supports will be included If

the final design in any way hinders movement of the inner pipe another

analysis will be performed The design is modified until an acceptable

solution is reached The detailing work has not been performed at this

time

-- -~------------------

r

APPENDIXB

The allowable stress of 25500 psi is calculated by using table A-I and

section 30235 of the ANSIIASME B313 1984 edition The information is

enclosed within this appendix

ANSIASME 8313-1984 EDITION ASME CODE FOR PRESSURE PIPING 1 i 30234 30235 CHEMICAL PLANT AND PETROLEUM REFINERY PIPING

TABLE 30233C TABLE 30233D INCREASED CASTING QUALITY FACTORS Ec ACCEPTANCE LEVELS FOR CASTINGS

Supplementary Examination Factor Material Acceptance Acceptable in Accordance with Note(s) Ec Examined Applicable level Discontinshy

(Thickness) Standard (or Class) uities (1) 085 (2)(al or (2Hbl 085 Steel (J)(a) or (3Hb) 095 (to 1 ingt ASTM E 4461 1 Types A S C III and (V(al or (2)(bl 090 (25mm) m and (3)(a) or (3)(b) 100 (2)(a) or (2)(b) and (3)(a) orO)(b) LOO Steel

(over 1 in to ASTM E 446 1 2 Types A S C NOTES 2 in) (2S (1) Machine all surfaces to a finish of 250 in arithmetic average to Slmm)

roughness height per ANSI B461 thus increasing the effectiveshySteel

ness of surface examination (over 2 in t STM E 1861 2 Categories A B C

) 11 t-~-lIe all surfaces of each casting (magnetic material 4112 in)

oJ by the magnetic particle method if n~-lfce with ASTM E 709 or E 138 Judge acceptability ir __ dance with MSS (51 mm

SP-53 using reference photos in ASTM E 125 to 114 mm) (bJ Examine all surfaces of each casting by the liquid penetrant Steel method in accordance with ASTM E 16S Judge acceptability (over 4112 in ASTM E 2801 2 Categories A S C of flaws and weld repairs in accordance with Table 1 of MSS to 12 inJ SP-53 using ASTM E 12S as a reference for surface flaws (114 mm to

(3) (a) Fully examine each casting ultrasonically in accordance with 305 mm) ASTM E 114 accepting a casting only if there is no evidence

Aluminum amp ASTM E lSS1 Shown in reference of depth of defects in excess of S of wall thickness

Magnesium radiographs(b) Fully radiograph each casting in accordance with ASTM E 142 Judge in accordance with the stated acceptance levels in Copper Ni-Cu ASTM E 2721 2 Codes A Ba Bb

Table 302330 Bronze ASTM E 310 1 2 Codes A and B These standards have been approved by ANSI as American National

NOT8 (0Standards (ll These standards have been approved by ANSI as American Nashy

tional Standards J which may be used for certain types of welds if addishytional examination is performed beyond that required by the product specification ~5 S + 025 s0 (1 a)

30235 limits of Calculated Stresses Due to Susshy In the above equation tained Loads and Displacement Strains Sf = basic allowable stress at minimum metal temshy

(a) Internal Pressure Stresses Stresses due to internal perature expected during the displacement pressure shall be considered safe when the wall thickshy cycle under analysis [See Note (2) of Appenshyness of the piping eomponent and its means of stiffenshy dix A 30224 and 3023] ing meet the requirements of 304 Sh = basic allowable stress at maximum metal temshy

(b) External Pressure Stresses Stresses due to extershy perature expected during the displacement nal pressure shall be considered safe when the wall cycle under analysis [See Note (2) of Appenshythickness of the piping component and its means of dix A 30224 and 3023] stiffening meet the requirements of 304 f = stress-range reduction factor for displacement

(c) Longitudinal Stresses SL The sum of longitudishy cycle conditions 2 for the total number of cyshynal stresses due to pressure weight and other sustained cles over the expected life (from Table loadings SL shall not exceed S in 30235(d) The 30235) Expected life J means the total numshythickness of pipe used in calculating SL shall be the ber of years the system is expected to be in nominal thickness Tminus mechanical corrosion and erosion allowance c

2Applies to essentially noncorroded piping Corrosion can sharply (d) Allowable Displacement Stress Range SA The decrease cyclic life therefore corrosion resistant materials should be

allowable displacement stress range (see 31923) for considered where a large number of major stress cycles is anticipatedo the computed displacement stress range Sf (see The designer is cautioned that the fatigue life of materials operated 31944) shall be in the creep range may be reduced

16

ANSIASME B313-984 EDITION ASME CODE FOR PRESSURE PIPING TABLE AmiddotI CHEMICAL PLANT AND PETROLEUM REFINERY PIPING (

TABLE A-I (CONTo) ALLOWABLE STRESSES IN TENSION FOR METALS (1)

Numbers in Parentheses Refer to Stress Table Notes Which Appear at the Beginning of this Appendix Specifications ASTM Unless Otherwise Indicated

Min Min P Tensile Yield Min Min

No Factor Strength Strength Temp Temp Material Spec No (5) Grade Class E ksi ksi Not~ (6) to 100 200 300 400 500 600

Stainless Steel (4) (Contd) Electric Fusion Welded Pipe and TII~s (2) (CDnid)

2SCr-20Ni Pip~ A 312 8 TP3l0 080 75 30 (28) (35) (39) -3251160 Z5Cr-ZONi Pipe A 312 8 TP310 080 75 30 (28) (29) (35) (39) -325 160 16Cr-12Ni-ZMo Pipe A 312 8 TP316 080 75 30 (27) (28) -325 160 16Cr-12Ni-2Mo Pipe A 312 8 TP316H 080 75 30 (27) -325 160

-0 Pipe A312 8 TP316L 080 70 25 -325 133 18Cr-13Ni-3Mo Pipe A 312 8 TP317 080 75 30 (27) (28) -325 160 18Cr-10Ni-Ti Pipe A 312 8 TP321 080 75 30 (28) -325 100 18Cr-l0Ni-Ti Pipe A 312 8 TP321H 080 75 30 -325 160

18Cr-10Ni-Cb Pipe A 312 8 TP347 080 75 30 (28) -425 160 18Cr-10Ni-Cb Pipe A 312 8 TP347H 080 75 30 -325 160 18Cr-10Ni-Cb Pipe A 312 8 TP348 080 75 30 (28) -325 160 18Cr-10Ni-Cb Pipe A 312 8 TP348H 080 75 30 -325 160

_18Cr-aNi Pipe A 312 8 TP304 085 75 30 (27) (28) -425 170 18Cr-aNi Pipe A 312 8 TP304H 085 75 30 (27) -325 170 18Cr-aNi Pipe A 312 8 TP304L 085 70 25 -425 142 23Cr-12Ni Pipe A 312 8 TP309 085 75 30 (28) (35) (39) -3251 170

25Cr-ZONi Pipe A 312 8 TP310 085 75 30 (28) (35) (39) -3251 170 25Cr-ZONi Pipe A 31Z 8 TP310 085 75 30 (28) (29) (35) (39) -3251 170 16Cr-12Ni-ZMo Pipe A 312 8 TP316 085 75 30 (27) (28) -325 170 16Cr-12Ni-2Mo Pipe A 312 8 TP316H 085 75 30 (27) -325 170

16Cr-12Ni-2Mo Pipe A 312 8 TP316L 085 70 25 -325 142 18Cr-13Ni-3Mo Pipe A 312 8 TP317 085 75 30 (27) (28) -325 170 18Cr-10Ni-Ti Pipe A 312 8 TP321 085 75 30 (28) -325 170 18Cr-l0Ni-Ti Pipe A 312 8 TP321H 085 75 30 -325 170

18Cr-l0Ni-Cb Pipe A 312 8 TP347 085 75 30 (28) -425 170 18Cr-10Ni-Cb Pipe A 312 8 TP347H 085 75 30 -325 170 18Cr-l0Ni-Cb Pipe A 312 8 TP348 085 75 30 (28) -325 170 18Cr-l0Ni-Cb Pipe A 312 8 TP348H 085 75 30 -325 170

Type 304 A 240 A 358 8 304 2 085 75 30 (21) (28) (31) (36) -4251 170 Type 304L A 240 A 358 8 304L 2 085 70 25 (36l -425 142 Type 316 A 240 A 358 8 316 2 085 75 30 (27) (28) (311 (36) -3251 170 Type 310L A 240 A 358 8 316L 2 085 70 25 (36) -325 142

Type 347 A 240 A 358 8 347 2 085 75 30 (28) (30) (36) -42 170 Type 321 A 240 A 358 8 321 2 085 75 30 (28) (30) (36) -32 170 Type 309S A 240 A 358 8 309S 2 085 75 30 (28) (311 (35) (36) -32 170 Type 310S A 240 A 358 8 3l0S 2 085 75 30 (l8) (311 (35) (36) -32 170

Type 310S A 240 A 358 8 310S 2 085 75 30 (28) (29) (311 (35) (36) -32 170 Type 348 A 240 A 358 8 348 2 085 75 30 (28) (30) (36) -32 170 Type 304 A 240 A 358 8 304 5 090 75 30 (271 (28) (31) (36) 180 Type 304L A 240 A 358 8 304l 5 090 70 25 (36) -425 150

Type 310 A 240 A 358 8 )16 5 090 75 30 (27) (28) (31) (36) -3251 180 Type 316L A 240 A 35a 8 310l 5 090 70 25 U6J -325 150 Type 347 A 240 A 358 8 347 5 090 75 30 (28) DO) (Jo) ~2511a0 Type 321 A 240 A 358 8 321 5 0lt10 75 30 (28) (JO) Do) -325 180

144

J

1- rtf

ANSIASME B313-1984 EDITION ASME CODE FOR PRESSURE IIPING TABLE A-I CHEMICAL PLANT AND PETROLEUM REFINERY PIPING

TABLE A-I (CONTDgt ALLOWABLE STRESSES IN TENSION FOR METALS (l)

Numbers in Parentheses Refer to Stress Table Notes Which Appear at the Beginning of this Appendix Specifications ASTM Unless

Otherwise Indicated

Min Min Pshy Tensile Yield Min Min No Factor StmgthStrngth Temp Temp

Material Spec No (5) Grade pound ksi ksi Notes (6) to 100 200 300 400 500 600

Stainless Steel (4) (Conld) Welded Fittings

laCr-aNi 18Cr-8Ni 18Cr-8Ni

A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7

nCr-l2Ni A 403 a WP309 100 75 30 Ob) (28) (2) (35) r-shy shy 200

bull ~3 8 WP310 100 75 30 ObI (28) (2) (35) -325 200 25Cr-20Ni 403 8 WP310 100 75 30 (lb) (28) (29) (2) (35) -325 200 18Cr-10Ni-Cb-Ta A 403 8 WP347 100 75 30 (lb) (28) (30) (2) -425 200 18Cr-10Ni-Cb-Ta A 403 8 WP347H 100 75 30 (lb) (28) (30) (32) -325 200

IbCr-12Ni-2Mo A 403 8 WP31b 100 75 30 UbI (27) (28) (1) (32) -325 200 IbCr-12Ni-2Mo A 403 8 WP316H 100 75 30 (lb) (27) (3) (32) -325 200 IbCr-12Ni-2Mo A 403 8 WP31bL 100 70 25 nb) (32) -325 Ib7 laCr-13Ni-3Mo A 403 8 WP317 100 75 30 Cl6) (271 (28) (3l (32) -325 200

18Cr-10Ni-Ti A 403 8 WP321 100 75 30 (lb) (28) (30) (32) -325 200 18Cr-10Ni-Ti A 403 8 WP321H 100 75 30 Ub) (3D) (32) -325 200 18ir~~b A 403 8 WP34a 100 75 30 (l6) (28) (30) (2) -325 200

~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170

18Cr-8Ni A 403 8 WP304H 085 75 30 (16) (27) CH) (32) -325 170 18Cr-8Ni A 403 8 WP304L 085 70 25 (6) (32) -425 141 23Cr-12Ni A 403 8 WP309 085 75 )0 lt1b) (28) (32) 05) -325 170 25Cr-20Ni A 403 8 WP310 085 75 30 (6) (28) (32) (35) -325 170

25Cr-20Ni A 403 8 WP310 085 75 )0 (l6) (28) (29) (2) (35) -325 170 18Cr-8Ni-Cb A 403 8 WP347 085 75 30 (lb) (28) ()O) (2) -425 170 18Cr-eNi-Cb IbCr-12 Ni-2 Mo

A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170

IbCr-12Ni-2Mo A 401 8 WP316H 085 75 30 (6) (27) (31) (32) -325 170 IbCr-12Ni-2Mo A 403 8 WP316L 085 70 25 lt1b) (32) -325 141 18Cr-13Ni--3Mo A 403 8 WP317 085 75 30 (lo) (27) (28) (J II (32) -325 170 18Cr-10Ni--Ti A 403 8 WP321 085 75 30 (lb) (28) (30) (32) -325 170

18Cr-10Ni-Ti A 403 8 WP321H 085 75 30 Ub) (0) q2) -325 170 18Cr-10Ni-Cb A 403 8 WP348 085 75 30 Ub) (28) (30) (2) -325 170

18Cr-8Ni A 403 8 WP304 080 75 30 Ubi (27) (28) (311 em -425 160 leCr-8Ni A 403 8 WP304H 080 75 30 Ub) (27) (311 (2) -325 1b0 18Cr-aNi A 403 8 WP304L 080 70 25 (lb) (2) -425 133 23Cr-12Ni A 403 8 WP309 080 75 30 (lb) (28) (32) OS) -325 100

25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO

25Cr-20Ni A 403 8 WP310 080 75 30 Ub) (28) (29) (2) (5) -325 IbO 18Cr-8Ni-Cb A 403 8 WP347 080 75 30 UbI (28) (0) (32) -425 IbO 18Cr-8Ni-Cb A 403 8 WP347H 080 75 30 (1b) (30) (32) -325 1amp0

1ampCr-12Ni-2Mo A 403 8 WP31b 080 75 30 Ob) (27) (28) (31) (2) -325 160 IbCr-12Ni-2Mo A 403 8 WP31bH 080 75 30 (lb) (27) (1) (2) -325 1amp0 IbCr-12Ni-2Mo A 40) 8 WPHbL 080 70 25 (lampl D21 - 3Z5 13)

18Cr-1 IN-3Mo A 403 8 WP31] 080 75 )0 (Ibl 127) (28) D 11 021 middot)25 1amp0

J

152

ACKNOWLEDGEMENTS

The information provided by Dave Howe of Rosemount Roger Koopman

of Process Sales and Lew Novekoff of Lesman Instrument Company is

greatly appreciated


-INTRODUCTION

The analysis of pipe stress due to thermal contraction and expansion can be accomplished in numerous ways This report examines the analysis methods available to us and provides the reasons for the methods we chose to use It then describes the results of the 1-12 x 3 vacuum-jacketed LN2 transfer line The LN2 line also serves as an example for an analysis using the method chosen A brief discussion of the 4 x 6 N2 exhaust line follows these items

METHOD COMPARISON AND SELECTION

The methods compared include the Grinnell and Tube Turns Chart methods Grinnell Moment method commercial software for PCs and ANSYS

The chart methods have been used for many years with success but are very tedious and time consuming This type of analysis has limitations For instance the particular geometry being analyzed might not fit into the charts available in the handbook To analyze a given geometry assumptions are made which lead to uncertainties in the results From the past experience with chart methods it was decided that a better approach was needed

Information on pipe stress software advertised in magazines was acquired originally by Brian Fitzpatrick The information received included written material and demonstration disks Several demonstration disks were working programs One working program AUTOPIPE was available for us to compare our results with the other analysis methods AUTOPIPE proved to be easy to use and provided a detailed analysis The geometry is quickly entered and conforms to various codes including B311 and B313 Letter sized sheets can be printed out which reveal the results in an organized manner The software packages have these stated advantages but are expensive The initial purchase prices range from $150000 to $600000 with the average at $450000 (not including user fees)

At the same time an analysis was performed on ANSYS ANSYS offers much more power and is less expensive than the software programs because the pipe module is already available as a part of the existing

-) ANSYS package in use at the laboratory The PC software however is much easier to use than ANSYS even though ANSYS provides a pipe module


















2 Type ANSYS_INTER



5 Type liNT
















results



PREP7









TREF300 TUNIF77



PSPECI1510S


BRANCH1











ITERll


ACEL 1




KRFl


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FINI INPUT 27 FINI


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SETll



6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

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Figure 1 V


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- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







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radius



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TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated


















2 Type ANSYS_INTER



5 Type liNT
















results



PREP7









TREF300 TUNIF77



PSPECI1510S


BRANCH1











ITERll


ACEL 1




KRFl


AFWR 1





FINI INPUT 27 FINI


POST1


SETll



6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated











results



PREP7









TREF300 TUNIF77



PSPECI1510S


BRANCH1











ITERll


ACEL 1




KRFl


AFWR 1





FINI INPUT 27 FINI


POST1


SETll



6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







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__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated




TREF300 TUNIF77



PSPECI1510S


BRANCH1











ITERll


ACEL 1




KRFl


AFWR 1





FINI INPUT 27 FINI


POST1


SETll



6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







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__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated








ITERll


ACEL 1




KRFl


AFWR 1





FINI INPUT 27 FINI


POST1


SETll



6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated



KRFl


AFWR 1





FINI INPUT 27 FINI


POST1


SETll



6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated

0 PIPE STRESS ANALYSIS

6123

PRSTR




FIN I










REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated







REFERENCES


Department July1986

ACKNOWLEDGMENTS


---~--- -____-_ _-------------- shy


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated


CC T 765

DROA3

37475


z 72

PLATFORM

JUMPERY x

T

SEC

JUMPER

+33

an C ~

L

~10

18

~ 295

Figure 1 V


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated


~)


- NODES 8

z

y 12x

Figure 3


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated


29

8


bull - NODES

z 5

y x 7

1

3

4

Figure 4

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated

----







T


__ Rl - bend

radius



~

)

TABLE 1




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated




-0785001pound-01 -0 729399E-Ol

0106087 0100783 0104652 0-106360












C 53 -0198923 O 184976-0 115296 fmiddot54 -0191491 0177527 -0118146 -~7----o~694----O-1-62449----o-1-1221-7 58 -0170122 0159984 -0 1


64 -0 678540E-01 0253599 -0158933 ( 67 0728159E-Ol 0150943 -0 822340E-01 (68 0754061pound-01 0145924 -0 788463E-01

( (

[~ (






72 -0 131267E-01 0762805E-01 -0 174912E-01 0149378E-02 -0 182792E-02 -0 188259E-02 ~


MAXIMUMS ( NODE 49 16 18 21 50 64

VALUE -0631709 0641586 -120360 0701399E-02 0819035E-02 -0 438934E-02


TABLE 2

bull

l







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated







--J

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated

o ) --

ANSYS-- 43

MAY 18 1988

80554

PLOT NO 2

POST1 DISPL

STEP= 1

ITER= 1

ORIG

XV=-1

YV=-1

ZV=1

DIST=321

XF=809

YF=9S2

ZF=251

ANGL=6O

DMAX= 136

DSCA=236

Z x








time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated







time

-- -~------------------

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated

r

APPENDIXB


























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated























16


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated


















144

J

1- rtf




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated




Otherwise Indicated





A 403 A 403 A 403

8 8 a

WP304 WP304H WP304l

l00 100 100

75 75 70

30 30 25

(l2) (lb) (27) (28) (31) (32) Ub) (27) (31) (32) (lb) (32)

-42~-325 -425

200 200 Ib7





~ A 403 a WP304 085 75 30 (l6) (271 (28) (31) (32) -425 170



A 403 A 403

8 8

WP347H WP316

085 085

75 75

)0 30

(l6) (28) (30) (32) (lb) (271 (28) en) (32)

-325 -325

170 170




25Cr-20Ni A 403 8 WP310 080 75 30 ltlb) (28) (32) (35) -325 IbO




J

152

ACKNOWLEDGEMENTS



greatly appreciated

ACKNOWLEDGEMENTS



greatly appreciated

Ansys Pipe Stress

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