AD-AIl12 050 DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/B 13/11 STRESS INDICES AND FLEXIBILITY FACTORS FOR 90-DEGREE PIPING ELB-ETC(U)FEB 82 A J QUEZON, G C EVERSTINE

UNCLASSIFIED OTNSROC/CMLD DC2/05 NL

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C4 DAVID W. TAYLOR NAVAL SHIPRESEARCH AND DEVELOPMENT CENTER0

U Bethesda, Maryand 20084

STRESS INDICES AND FLEXIBILITY FACTORS FOR

90-DEGREE PIPING ELBOWS WITH STRAIGHT PIPE

EXTENS IONS

cn by

oA. J. Quezon and G. C. Everstine

a% APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED.

w~ H COMPUTATION, MATHEMATICS,* AND LOGISTICS DEPARTMENT

DEPARTMENTAL REPORTLoJ

'.j U2

February 1982 DTNSRDC/CMLD-82 /05iI D-

NOWMNAD 50210 2-0)82 0 k 67(gupersedes 3000146)

MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS

DTN3RD)C

COMMANDER 0TECHNICAL DIRECTOR

01

OFFICER-IN-CHARGE OFFICER-IN-CHARGECARDEROCK 05ANNAPOLIS 0

SYSTEMSDEVELOPMENTDEPARTMENT

SHIP ERFORANCEAVIATION ANDSHIPPERORMNCE ______SURFACE EFFECTS

DEPARTMENT DEPARTMENT15 16

STRUCTURES COMPUTATION,DEPARMENTMATHEMATICS AND

DEPARMENTLOGISTICS DEPARTMENT17 18

SHIPACOUTIC PROPULSION ANDSHPACOT ICSNT AUXILIARY SYSTEMS

DEARMET 19 ( DEPARTMENT 27

SHIP MATERIALS ________CENTRAL

ENGINEERING INSTRUMENTATIONDEPARTMENT I DEPARTMENT 1

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4. TITLE (nd Subtitle) 5. TYPE OF REPORT & PERIOD COVERED~STRESS INDICES AND FLEXIBILITY FACTORS FOR90-DEGREE PIPING ELBOWS WITH STRAIGHT PIPE

EXTENSIONS 6. PERFORMING OrG. REPORT NUMBER =

7. AUTHOR(e S. CONTRACT OR GRANT NUMBER(e)

A. J. Quezon and G. C. Everstine

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA A WORK UNIT NUMBERSDavid W. Taylor Naval Ship Research Program Element 63561N

and Development Center Task Area S0348001Bethesda, Maryland 20084 Work Unit 1-2740-163

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19. KEY WORDS (Continue on reverse elde If neceeeary and Identify by bloc, number)

Piping Finite Element Flexibility FactorElbow NASTRANBend Stress Index

20. AESrACT (Continue en reveree eide if neceemay end IdentIfy by block number)

A finite element parameter study ,ms performed on a wide variety of90-degree piping elbows having straight pipe extensions to determine thesensitivity of stress indices and flexibility factors to the length of thepipe extensions. Both moment and force loadings were considered. It wasfound that stress indices are generally insensitive to the type of load(moment or force). Flexibility factors are sensitive to load type only

(Continued on reverse side)

DO . 1473 EDITION OF I NOV 66 1 OBSOLETE UNCLASSIFIEDS/N 0102-LF-014-6601

SECURITY CLAUIFICAION OF THII PAGE (Sie. Det Shtee.E)

SECURITY CLASSIFICATION OF THIS PACE (When Does Sat* .*)

(Block 20 continued)

for short pipe extensions. Flexibility factors for moments generally exceedthose for forces. Stress indices are sensitive to length of pipe extensiononly for A< 0.35, where X is the bend characteristic parameter. Flexibilityfactors are sensitive to length of pipe extension over the entire range ofelbow parameters considered. The "critical length" of straight pipeextension (defined as the minimum length of pipe for which the elbow stressindex is insensitive to further increases in pipe length) was found to beabout three pipe diameters for A< 0.35 and one diameter for A>0.35. Acomparison of the finite element results to those of a torus program calledELBOW indicated that ELBOW is generally not adequate for predicting stressindices and flexibility factors for 90-degree elbows with straight pipe

a r

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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAELE'Uhm DaM SMtm1i0

limb

TABLE OF CONTENTS

Page

LIST OF FIGURES . . . . . . ................................... iii ***** j

ADISTR ATIVESIFRMO ...... ............................... .. . .. 1v

ASOPET OF ....STUDY......................... ......... ... .. . ... .... 6

APPROSACH V INOMAIN............................. 1

PNTSONTATION AND........ DICSSO OF ..RESULTS..........15..

CEFNLUIONS ......................................... 19

RCOENDATIONSY... o.......... oo .. .... .. .o ... -... o.... o....24

APPROACH oT........... .oo........ -........ .. .o . . .. o . .. ... o....25

APPENDIX - TABLES OF FINITE ELEMENT RESULTS FOR 90-DEGREE ELBOWSWITH STRAIGHT PIPE EXTENSIONS .... .o........... ... 27

REFERENCES ...... ..... o.. .o.. ~o...... o........... o.... ...... 51.

LIST OF FIGURES

I - Pictorial Representation of Nondimensional Elbow Geometric Data .... 9

2 - Geometry and Configuration of Piping Elbow .. oo... o.... ......... 12

3 - Typical Finite Element Model of Piping Elbow o.o.oo..... .o..o...... 14

4 - Sensitivity of Stress Index to Length of Pipe Extension ... oo..... 17

5 - Sensitivity of Flexibility Factors to Length of Pipe

6 - Sensitivity of Flexibility Factors to Length of Pipe

Ex e s ost/ .4 . o ~ o o o.. . . o o ~ . o o o . * o. . 2

LIST OF FIGURES (Continued)

Page

7 - Comparison of Finite Element and ELBOW Flexibility Factors ......... 23

LIST OF TABLES

1 - Dimensions of Piping Elbows ........................................ 7

2 - Nondimensional Elbow Geometric Data ................................ 8

3 - Stress Indices For Elbows Having Equal Length StraightPipe Extensions of Length Three Diameters .......................... 18

4 - Flexibility Factors for Elbows Having Equal Length StraightPipe Extensions of Length Three Diameters .......................... 22

iv

ABSTRACT

A finite element parameter study was performed ona wide variety of 90-degree piping elbows havingstraight pipe extensions to determine the sensitivityof stress indices and flexibility factors to thelength of the pipe extensions. Both moment and forceloadings were considered. It was found that stressindices are generally insensitive to the type of load(moment or force). Flexibility factors are sensitiveto load type only for short pipe extensions.Flexibility factors for moments generally exceed thosefor forces. Stress indices are sensitive to length of

pipe extension only for X < 0.35, where X is the bendcharacteristic parameter. Flexibility factors aresensitive to length of pipe extension over the entirerange of elbow parameters considered. The "criticallength" of straight pipe extension (defined as theminimum length of pipe for which the elbow stressindex is insensitive to further increases in pipelength) was found to be about three pipe diameters forX < 0.35 and one diameter for X > 0.35. A comparisonof the finite element results to those of a torusprogram called ELBOW indicated that ELBOW is generallynot adequate for predicting stress indices andflexibility factors for 90-degree elbows with straightpipe extensions.

ADMINISTRATIVE INFORMATION

This work was sponsored by the Naval Sea Systems Command in Program

Element/Task Area 63561N/S0348001, Task 21302, Work Unit 1-2740-163.

Naval Sea Systems Command cognizant program manager is Dr. F. Ventriglio

(NAVSEA 05R).

INTRODUCTION

Common practice in the design of shipboard piping systems is to

compute stresses and flexibilities for piping elbows using elementary beam

theory for straight beams and applying correction factors called stress

no,1

indices and flexibility factors. The correction factors are generally

calculated by assuming that the elbow behaves as if it were part of a complete

torus, for which analytical solutions for stresses and flexibilities are

available. This approach thus accounts for the bend radius, the pipe

diameter, the wall thickness, the material properties, and the internal

pressure (a nonlinear effect when combined with other loads). However,

the approach ignores such considerations as the bend angle and end

conditions, which can include flanges, straight pipe extensions, or other

elbows.

Since the inclusion of these considerations rules out the use of analytic

solutions, the only way to compute stresses and flexibilities in such cases

is to use an approximate numerical approach such as the finite element method.

The finite element method is well-established in general and has, in

particular, been verified as suitable for predicting the static behavior of

piping elbows and tees [1-3i.

The overall aim of this work is to determine the flexibilities and

stresses in piping elbows and bends in the configurations commonly used on

naval ships. This report addresses in particular the end condition proilem

by analyzing in some detail 90-degree elbows with straight pipe extensions

of various 'Fngths.

The general approach is to analyze a selection of elbows of a variety

sufficient (1) to determine the sensitivity of the elbow stress indices and

flexibility factors to the length of straight pipe extensions, and (2) to

determine the minimum length of straight pipe extension (Lhe "critical

length") for which the stress indices are considered insensitive to further

increases in pipe length.

* A complete listing of references is given on page 51.

2

The volume of data generated by these analyses is sufficiently complex

that only preliminary conclusions will be drawn from the data at this time.

A follow-up report will present a more complete analysis of the data presented

here and develop usable design equations, formulas, or curves.

DEFINITIONS

The stress index c for an elbow is defined [4,5] as the ratio of the

maximum stress intensity for the elbow to the maximum bending stress in a

straight pipe having the same cross section. The stress intensity S is

defined as twice the maximum shear stress in the elbow for a given loading

condition. Thus the maximum stress intensity is the maximum of

s: = 11 - 21 = {(a- a )z + 4T2}Ix y XY

s2 - 1l - 031 = I(G. + Gy) + S 1/2S3 = 102 - 031 = I(ax + Gy) - S1[12

for any arbitrary orientation of an applied moment vector M, where, for the

two-dimensional state of stress that occurs in thin-walled piping elbows,

0, = maximum principal stress

02 = minimum principal stress

03 = 0 (the third principal stress in 3-D elasticity)

x, c a normal stresses in longitudinal and circumferential directions

T - shear stressxy

The calculation of Smax (the maximum of S1, $29 and S3) requires a search

over all possible orientations of the moment vector M. Hence, the stress

index c is given by

3t

max /no m (2)

where a is the nominal stress for the corresponding straight pipe asnom

predicted by elementary beam theory:

0 = M/Z (3)nora

where Z is the section modulus.

For internal pressure loading,

c= max/nom (4)

where a is the maximum stress in the elbow subjected to internal pressure.max

The nominal stress a is taken as the maximum stress occurring in anom

cylindrical pressure vessel due to an internal pressure load:

o nm =pr/t (5)nom, f

where p is the applied internal pressure, r is the mean pipe radius, and t is

the wall thickness.

The flexibility factor k for a piping component (e.g., an elbow) is

defined as the ratio of a relative rotation of that component to a nominal

rotation:

k 6 ab /nom (6)

where eab rotation of end "a" of the piping component relative to end "b"

of that component due to a moment loading M, and in the direction

of M

0nom A nak rotation of an equal length of straight pipe due to the

moment M

4!

For elbows, the nominal rotation is computed using beam theory, in which case

e no .- ML/EI (7)norm

for inplane and out-of-plane moments, and

eo- ML/GJ (8)nom

for torsional moments, where

M - applied moment load

L = arc length of centerline of elbow

E - Young's modulus of material

G = shear modulus of material

I = moment of inertia of cross section

J = torsional constant of cross section kequal to the polar moment of

inertia for circular cross sections)

For 90-degree elbows, L=TR/2 , where R is the bend radius.

The critical length of pipe extension for an elbow is defined here as the

minimum length of straight pipe extension for which the stress index is

considered insensitive to further increases in pipe length. This

sensitivity results from the reduced ability of the elbow to ovalize due

to the presence of straight pipes and flanges. At some length of pipe

extension (the critical length), additional end effects due to the restriction

of ovalization no longer occur.

The bend characteristic parameter X, a dimensionless parameter widely

used in elbow design, is defined as

- tR/r2 1V-2 (9)

5

where t - wall thickness

R - bend radius

r - mean pipe radius

V - Poisson's ratio of material

The nondimensional bend radius Y is defined as

y - R/r (10)

The internal pressure loading parameter i is defined as

= pR2 /Ert (11)

where p is the internal pressure.

SCOPE OF STUDY

Table I summarizes the piping elbows of interest to naval piping

designers. (The data in this table were compiled by Mr. L.M. Kaldor of the

Machinery Stress Analysis Branch (Code 2744) of the David W. Taylor Naval Ship

R&D Center, Annapolis, Maryland.) Included are elbows of 19 nominal pipe

sizes, four bend radii, and three materials. The data in the table represent

a total of 204 different elbows, a number which must be reduced if the

parameter study is to be reasonably manageable.

The information in Table 1 can also be displayed in nondimensional form

Table 2) by dividing all length dimensions by the mean pipe radius r for each

elbow. A graphical display is more useful still. Since the two key

geometrical parameters defining an elbow are its nondimensional wall thickness

and bend radius, we can use these two parameters to construct a figure (Figure

1) which locates all elbows of interest. In Figure 1, a dot is entered for

6

TABLE 1 - DIMENSIONS OF PIPING ELBOWS

Nominal Min. Wall Thickness (in.) Bend Radius (in.)Pipe Outside -

Size Diameter CA715 CA719 In625 SR LR 3D 5D(NPS) (in.) 700 psi 1050 psi 1050 psi

1/4 .540 .065 .106 .012* - - - 1.253/8 .675 .072 .110 .014* - 1.8751/2 .840 .072 .115 .018* - 1.5 1.5 2.53/4 1.050 .083 .121 .022* - 1.125 2.25 3.75

1 1.315 .095 .129 .028* 1 1.5 3 51 1/4 1.660 .095 .139 .035* 1.25 1.875 3.75 6.251 1/2 1.900 .109 .146 .040* 1.5 2.25 4.5 7.52 2.375 .120 .160 .050* 2 3 6 102 1/2 2.875 .134 .175 .060* 2.5 3.75 7.5 12.53 3.500 .165 .193 .073 3 4.5 9 153 1/2 4.000 .180 .208 .083 3.5 5.25 10.5 17.54 4.500 .203 .222 .093 4 6 12 205 5.563 .220 .253 .115 5 7.5 15 256 6.625 .259 .285 .137 6 9 18 308 8.625 .340 .343 .179 8 12 24 4010 10.750 .380 .405 .223 10 15 30 5012 12.750 .454 .464 .264 12 18 36 6014 14.000 .473 .501 .290 14 21 42 7016 16.000 .534 .559 .331 16 24 48 80

Poisson's ratio .294 .294 .309Young's modulus 22.E6 22.E6 30.E6 psi

* Thickness may be greater due to welding considerations.

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each of the 204 elbows in Tables I and 2. The figure is useful because it

indicates the ranges of interest for the geometrical parameters t/r and R/r.

The collection of dots in Figure I has also been enclosed by a dashed

polygon. We expect that the range of behavior (stresses and flexibilities) of

elbows can be deduced by studying primarily elbows lying on the periphery of

the polygon. Moreover, the elbows actually analyzed would not have to be real

elbows appearing in Tables 1 and 2, but merely a suitable collection of elbows

defined by parameter pairs (t/r and R/r) lying on the polygon in Figure 1.

Also shown in Figure I are several curves of constant X, the bend

characteristic parameter, assuming a Poisson's ratio of 0.3, which is typical

for the materials listed in Table 1. These curves are useful fcr observing

the range of X represented by the elbows in Table I and for verifying the

extent to which certain elbow behavior depends only on A, as predicted by the

idealized theory for tori.

This study will therefore concentrate on elbows defined by the periphery

of the polygon in Figure 1. In addition, only 90-degree elbows with straight

pipe extensions will be considered. Elbows with other bend angles and end

conditions will be studied in future efforts.

For moment and force loadings, the internal pressure in the pipe is

assumed to be zero throughout this report. To assume otherwise introduces

a nonlinear effect which would greatly complicate the analyses. However,

because the nonzero pressure case is of considerable interest, it will be

pursued in future work.

APPROACH

Elbows defined by the parameter pairs t/r and R/r were chosen primarily

10

from the periphery of the polygon in Figure 1. For each elbow chosen, finite

element analyses were performed by the NASTRAN structural analysis computer

program in order to compute flexibility factors and stress indices for various

lengths of straight pipe extension varying from near zero to three or four

pipe diameters.

The elbow configuration modeled consists of a 90-degree elbow with

straight pipe extensions attached to each end of the elbow, as shown in Figure

2. The end of one pipe extension was fixed. The end of the other pipe

extension was terminated with a rigid flange. Applied loads consisted of

internal pressure as well as the six possible forces and moments applied to

the flange at the free end. For this study, internal pressure loads are not

combined with either force or moment loads.

The finite element results were also compared to results obtained by a

fast-running computer program called ELBOW (61 which is used by some piping

designers. Program ELBOW uses analytical methods to compute flexibility

factors and stress indices for elbows idealized as endless toroidal sections.

For zero internal pressure (ip=0), ELBOW's calculation of the flexibility

factor depends only on the bend characteristic parameter A.

For flexibility factors only, the finite element results were also

compared to flexibility factors computed according to the current ASME code

[71, which, for zero internal pressure, uses the relation

k = 1.65/h (12)

where

h - tR/r2 (13)

and a k calculated to be less than unity is taken as unity.

11

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0

4) Cho

'-44

00

12

For internal pressure loading, the finite element results for the stress

index c were also compared to the frequently used analytical expression

c = (2y - 1)/(2y - 2) (14)

presented in the Kellogg book [51, where Y is the nondimensional bend radius

(R/r). Since for our elbows Y ranges from about 1.5 to 11, Equation (14)

indicates that the internal pressure stress index should be between I and 2.

A typical finite element model of an elbow and the two straight pipe

extensions is shown in Figure 3. By symmetry, only half of the circumference

of the elbow cross section need be modeled. The elbow and pipe extensions

were modeled using NASTRAN's two-dimensional quadrilateral QUAD2 plate element

with aspect ratios averaging near unity in the elbow region and about two near

the ends of the pipe extensions. All models used 12 elements in the

circumferential direction.

To compute flexibility factors, the average rotations of the cross

sections at each end of the elbow were required. These averages were obtained

in each cross section of interest by defining in that cross section an

imaginary center point which was connected to the points on the circumference

by beam elements flexible enough not to contribute significantly to the

stiffness of the model.

A special purpose finite element data generator was written to automate

completely the preparation of the NASTRAN input data decks so that the

specification of only a few parameters was required to analyze a particular

case.

Poisson's ratio was fixed at 0.3 for all analyses to eliminate the

material constants as parameters in the study. This assumption has an

insignificant effect on the solutions obtained, since stresses and

13

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000

00,0

0100

-4

14J

flexibilities are very insensitive to small changes in Poisson's ratio.

PRESENTATION AND DISCUSSION OF RESULTS

Finite element analyses were performed for 21 elbows with straight pipe

extensions of various lengths. The geometric data for these 21 elbows are

plotted in Figure 1. In most cases, the pipe extensions placed at each end of

the elbow were of equal length. For each of the 21 elbows, the number of

analyses performed (in order to vary the length of pipe extensions) ranged

from six to 13, the average being about 7.5. The total number of analyses

performed was 157. The stress index and flexibility factor results for all

these analyses are tabulated in detail in the Appendix.

Although our original purpose in performing these calculations was to

derive usable design equations, formulas, and curves, the complexity of the

resulting data (tabulated in the Appendix) makes this a formidable task.

This report, which is therefore a little less ambitious, will instead

summarize some of the key results indicated by the data. All observations

in this section are based on data in the Appendix.

We first consider the influence of the type of loading (moment or

force) on the results. The applied forces were chosen so as to yield the

same bending moment at the elbow middle, where stresses are generally the

greatest. The tables in the Appendix show that stress indices depend

very little on whether the applied load is a force or moment, particularly

when the pipe extensions are long. The flexibility factors are only slightly

more sensitive than the stress indices to load type for elbows with long pipe

extensions. However, flexibility factors are quite sensitive to load type for

elbows with short pipe extensions. Flexibility factors due to moment loadings

15

generally exceed those due to force loadings.

In retrospect, this independence of stress index with load type can

perhaps be explained by noting that the index depends only on the solution in

the middle of the elbow, which is always (for 90-degree elbows) sufficiently

far from the ends so as not to be significantly affected by the load type.

The elbow flexibility, in contrast, depends on the solution over the entire

length of the elbow and hence might be expected to be more sensitive than

stress index to load type.

A second question which arises is: How sensitive are stresses and

flexibilities to the length of pipe extensions? A related question is: How

long do the pipe extensions have to be in order for elbow stresses and

flexibilities to be independent of further changes in length? In Figure

4 the dependence of stress index on length of straight pipe extension (equal

at both ends) is plotted for various elbows. Figure 4 indicates that stress

indices are very sensitive to length of pipe extension for small X and

insensitive for large X. It appears that the transition from sensitivity to

insensitivity occurs near X - 0.35. Figure 4 also indicates that the critical

length of straight pipe extensions, based on stress indices, is about three

pipe diameters for X < 0.35 and one pipe diameter for X > 0.35.

Table 3 summarizes the stress index results for the 21 elbows with equal

length pipe extensions three diameters long. The actual stress indices, which

are generally greatest with long (rather than short) pipe extensions, are

grossly over-predicted in general by the idealized program ELBOW. For

internal pressure loading, the classical relation, Equation (14), is

excellent.

Flexibility factors for moment loadings exhibit a sensitivity to length

16

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170

TABLE 3 - STRESS INDICES FOR ELBOWS HAVING EQUAL LENGTH STRAIGHTPIPE EXTENSIONS OF LENGTH THREE DIAMETERS

NASTRAN Internal PressureELBOW

Moment Force NASTRAN Kellogg

1 .063 1.50 10.2 10.0 14.5 1.93 2.002 .126 1.50 6.55 6.41 9.28 1.89 2.003 .126 3.00 7.13 6.96 8.56 1.23 1.254 .204 1.50 4.61 4.52 6.82 1.82 2.005 .204 4.88 5.39 5.21 5.98 1.12 1.136 .210 5.00 5.31 5.18 5.87 1.12 1.137 .283 1.50 3.62 3.68 5.53 1.77 2.008 .283 6.75 4.39 4.26 4.70 1.08 1.099 .335 8.00 3.90 3.81 4.14 1.07 1.07

10 .346 1.50 3.39 3.45 4.88 1.74 2.0011 .451 10.8 3.10 3.02 3.29 1.04 1.0512 .451 1.80 2.77 2.83 3.94 1.56 1.6313 .600 3.00 2.43 2.32 2.93 1.25 1.2514 .700 3.Ou 2.12 2.04 2.61 1.25 1.2515 .973 10.2 1.67 1.71 2.00 1.05 1.0516 .975 3.00 1.76 1.80 2.13 1.26 1.2517 1.50 9.49 1.47 1.45 1.71 1.06 1.0618 1.50 3.90 1.119 1.54 1.75 1.19 1.1719 2.39 8.00 1.27 1.25 1.52 1.07 1.0720 2.39 5.15 1.32 1.37 1.52 1.14 1.1221 3.01 5.75 1.28 1.33 1.45 1.12 1.11

18

of straight pipe extension similar to that of the stress indices, except that

the transition from sensitivity (small X) to insensitivity (large X) occurs at

about X - 1.0. For flexibility factors calculated from force loadings, there

is no clear region of insensitivity. Two plots illustrating this sensitivity

are shown in Figures 5 and 6. These two figures indicate that elbows become

stiffer as the pipe extensions shorten, probably because the flanges inhibit

ovalization of the cross section.

Table 4 summarizes the flexibility factor results for the 21 elbows with

equal length pipe extensions three diameters long. There is considerable

variation between inplane and out-of-plane flexibility factors, neither of

which are predicted very well in general by the idealized approach used in the

ELBOW program; it does not distinguish between inplane and out-of-plane

moments in calculating the flexibility factor. The data listed in Table 4 are

also shown graphically in Figure 7.

CONCLUSIONS

The following conclusions apply to 90-degree piping elbows with straight

pipe extensions terminated by rigid flanges.

Stress indices are generally insensitive to whether the applied load is

a force or a staticaily equivalent moment. For elbows with long pipe

extensions at each end, flexibility factors are only slightly more sensitive

than the stress indices to load type. However, flexibility factors are quite

sensitive to load type when the pipe extensions are short. Flexibility

factors for moment loadings generally exceed those for force loadings.

Stress indices are very sensitive to length of pipe extension for

A < 0.35, where A is the bend characteristic parameter, and generally

19

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210

TABLE 4 - FLEXIBILITY FACTORS FOR ELBOWS HAVING EQUAL LENGTH STRAIGHT

PIPE EXTENSIONS OF LENGTH THREE DIAMETERS

NASTRAN (Moment) NASTRAN (Force)y ELBOW ASME

Inplane Out-of-Plane Inplane Out-of-Plane Code

1 .063 1.50 21.8 9.84 20.9 10.1 27.5 27.5

2 .126 1.50 11.3 5.44 10.8 5.47 13.8 13.7

3 .126 3.00 11.3 5.86 10.7 5.85 13.8 13.7

4 .204 1.50 6.98 3.62 6.63 3.58 8.49 8.48

5 .204 4.88 7.18 4.09 6.63 3.94 8.49 8.48

6 .210 5.00 7.03 4.02 6.54 3.91 8.27 8.24

7 .283 1.50 5.04 2.79 4.76 2.71 6.09 6.11

8 .283 6.75 5.28 3.23 4.80 3.04 6.09 6.11

9 .335 8.00 4.47 2.85 4.05 2.67 5.09 5.16

10 .346 1.50 4.14 2.41 3.89 2.31 4.92 5.00

11 .451 10.8 3.32 2.31 2.95 2.09 3.69 3.84

12 .451 1.80 3.19 2.05 2.91 1.92 3.69 3.84

13 .600 3.00 2.48 1.82 2.27 1.70 2.71 2.88

14 .700 3.00 2.15 1.67 1.97 1.55 2.32 2.47

15 .973 10.2 1.65 1.48 1.47 1.33 1.73 1.78

16 .975 3.00 1.69 1.46 1.59 1.37 1.73 1.77

17 1.50 9.49 1.30 1.31 1.15 1.16 1.32 1.15

18 1.50 3.90 1.35 1.31 1.23 1.20 1.32 1.15

19 2.39 8.00 1.14 1.23 1.02 1.10 1.13 1.00

20 2.39 5.15 1.17 1.24 1.07 1.13 1.13 1.00

21 3.01 5.75 1.14 1.23 1.00 1.08 1.08 1.00

22

1-4 0

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239

insensitive for X > 0.35. The critical length of straight pipe extension

(defined as the minimum length of pipe for which the stress index is

insensitive to further increases in pipe length) is about one pipe diameter

for X < 0.35 and three diameters for X > 0.35.

For elbows loaded by internal pressure only, the stress indices are

insensitive to the length of straight pipe extension. The theoretical

predictions by the classical relation given in the Kellogg book for this case

are excellent.

Flexibility factors exhibit a sensitivity to length of straight pipe

extension over the entire range of elbow parameters considered. Flexibility

factors for out-of-plane loading differ considerably from those for inplane

loading.

The fast-running computer program ELBOW, which idealizes elbows as

sections of tori, is generally not adequate for predicting stress indices or

flexibility factors for 90-degree elbows with straight pipe extensions.

RECOMMENDATIONS

Although a large quantity of useful data has been compiled in this

report, the report is viewed as interim, since the information is not in a

form to be easily used by a piping system designer. We therefore recommend

that the data presented here be analyzed fuither to obtain usable design

equations, formulas, or curves for 90-degree elbows with straight pipe

extensions.

Since not all elbows used in naval designs are 90-degree elbows, we

recommend that other bend angles (e.g., 45 degrees) be investigated. Also,

future parametric studies would be less expensive if a more restrictive

24

selection of elbows is made.

The presence of an internal pressure preload is known to have a

significant effect on momen; stress indices and flexibility factors. A finite

element procedure for this combined loading case, which is mathematically

nonlinear, needs to be formulated and validated. Following such validation,

the various parametric studies discussed above (for which the internal

pressure is zero) should be repeated for several typical nonzero pressure

levels.

ACKNOWLEDGMENTS

We acknowledge with pleasure the fruitful discussions held with Mr.

L.M. Kaldor and Dr. Y.P. Lu of the Machinery Silencing Division (Code 274).

25

APPENDIX

Tables of Finite Element Results for 90-DegreeElbows with Straight Pipe Extensions

27

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REFERENCES

1. Marcus, M.S., and G.C. Everstine, "Finite Element Analysis of PipeElbows," Report CMLD-79/15, David W. Taylor Naval Ship Research andDevelopment Center, Bethesda, Maryland (Feb 1980).

2. Quezon, A.J., G.C. Everstine, and M.E. Golden, "Finite ElementAnalysis of Piping Tees," Report CMLD-80/11, David W. Taylor Naval ShipResearch and Development Center, Bethesda, Maryland (June 1980).

3. Quezon, A.J., and G.C. Everstine, "Comparison of Finite ElementAnalyses of a Piping Tee Using NASTRAN and CORTES/SA," Ninth NASTRAN Users'Colloquium, NASA CP-2151, Washington, D.C., pp. 224-242 (Oct 1980).

4. Dodge, W.G., and S.E. Moore, "Stress Indices and Flexibility Factorsfor Moment Loadings on Elbows and Curved Pipe," Report ORNL-TM-3658, Oak RidgeNational Laboratory, Oak Ridge, Tennessee (March 1972).

5. The M.W. Kellogg Company, Design of Piping Systems, Second Edition,John Wiley and Sons, Inc., New York (1964).

6. Dodge, W.G., and S.E. Moore, "ELBOW: A Fortran Program for theCalculation of Stresses, Stress Indices, and Flexibility Factors for Elbowsand Curved Pipe," Report ORNL-TM-4098, Oak Ridge National Laboratory, OakRidge, Tennessee (Apr 1973).

7. American Society of Mechanical Engineers, "ASME Boiler and PressureVessel Code. Section III, Rules for Construction of Nuclear Power PlantComponents" (1980 edition).

51

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