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TECHNOWGY CONFERENCENorth Central Expressway

Texas 75206

PAPERNUMBEROTC 1569

THIS IS A PREPRINT --- SUBJECT TO CORRECTION

Oval ng o f Pipe I I nes Under Pure Bend i ng

By

J . O. Jirsa, Fook-Hoy Lee, J. C. Wilhoit, Jr. and J . E. Merwin, Rice U.

© Copyright 1972

Tecbnology Conference on behalf of the American Institute of Mining, Metallurgical, andEngineers, Inc., American Association of Petroleum Geologists, American Institute of

Engineers, American Society of Civil Engineers, American Society of Mechanical Engineers,

of Electrical and Electronics Engineers, Inc., Marine Technology Society, Society ofration Geophysicists, and Society of Naval Architects &Marine Engineers.

This paper was prepared for presentat ion at th e Fourth Annual Offshore Technology Conferencein Houston, Tex., May 1-3, 1972. Permission to copy is restricted to an abstract of notthan 300 words. Illustrations may not be copied.. Such use of an abstract should contain

acknowledgment of where and by whom the paper is presented.

BSTRACT

The inf luence of ovaling on the flexuralbehavior of pipelines stressed beyond thee la s ti c l imi t was studied. Six pipes , withdiameter ranging from 10-3/4 to 20 in. anddiameter-to-thickness ratio varying from about

30 to 80, were tested. Four of the pipes testedwere uncoated and two were coated with concrete.

Moment-curvature relationships into theplastic region of behavior were obtained

experimentally, and ovaling was measured at a l l

stages of load ing. Theore tical moment-curvatureand ovaling values were computed. Computedvalues were compared with experimental results,resulting in the conclusions that momentcurvature and ovalization curvature relation

ships can be predicted for bare p ipe undermonotonic loading, and that ovaling does no tsignificantly reduce the moment capac ity of thepipes until strains well into the plasticregion are reached.

INTRODUCTION

In this investigation th e influence o fovaling on the flexural behavior of p ipel inesstressed beyond the elastic l imit is considered.A total of six pipes were tested in flexure tosimulate bending stresses produced during laying

operations. Each pipe was tested as a simplebeam, and loads were applied to produce a regionReferences and i llu st ra t ions a t end of paper•

of pure flexure. Four of the tests were on barepipes and two on coated pipes with a f ie ld jo in tin the bending region. Theoretical ovalingvalues were computed using a strain energy

procedure and were compared with experimentalresults .

EXPERIMENTAL PROGRAM

Test Setup

The pipes were tested as simple beamssupported at the ends and loaded at two pointswithin the tes t span to produce a region of pure

flexure, as shown in Fig. 2. Both the loadingframes and the supports were assembled to enablethe frame to ro ta te freely as deflections androtat ions o f the pipe increased. Since both the

loading and supporting rods were pinned at eachend, there was no restraint to la teral movementat the supports or load points, and the intro- ,duc tion of axial forces in the pipe was avoided.

In order to hold the pipe in place and todistribute load over the su rface of the pipe, ahigh-strength gypsum mortar was cast between thepipes and the support and loading frames. Thetest setup is described in greater detail inRefs. 1 through 3.

Test Specimens

Six specimens were tested. Four wereuncoated, bare p ipes and two were coated. The

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OVALING OF PIPELINES UNDER PURE BENDING-574

coated pipes (Specimens 12A and 16B) were madeup of a steel tube core, an intermediate layerof asphaltic material, referred to hereafter asth e "somastic" interface, and an outer shell ofvery l ightly reinforced concrete. To simulatea field j oint within the pure flexure span, aband of about 36 in. of the concrete coatingand the interface material was removed at th ecenter of the pure flexure span. The properties

of the test specimens are l isted in Table 1.Stress-strain curves for the steel are shown inFigs. 2 and 3. The curves were obtained fromtests of coupons cut from the pipe. The curvesexhibited a nonlinear t ransi ti on to th e plasticrange, which had a much smaller slope than theini t ial slope.

Instrumentation

Each specimen was instrumented with straingauges at a number of locations over the constant moment span in the ba re pipe specimens andover the simulated joint in the coated pipes.Gauges were fastened both at the top and th ebottom surfaces and were used to determinecurvatu res. Deflections o f the pipe in thepure flexure span were also measured, andcurvatures were computed using a f ini tedifference expression. 1

To determine the oval ization of the pipe,changes in horizontal and vertical diameterswere measured at a number of sections withlarge micrometers. The change in th e diameterswere used to compute the air ratios (semimajoraxis of e li pse to corresponding radius of pipe

before testing).

Test Procedure

Load generally was applied in nominal1,OOO-lb increments. In some tests the changein curvature under a 1,OOO-lb increment was toosmall and 2,OOO-lb increments were used. Aftereach load increment applied, strain-gauge anddeflection readings were taken, and th e changesin diameter at various sections were measured.At each load stage, 20 minutes were required tocomplete th e recording of the data. The entire

test required about 5 hours to complete.

MEASURED RESULTS

Moment-Curvature Relationships

Moments were computed at a ll load stages,using measured loads applied to the pipe. Asimple finite-difference expression was used toapproximate the second derivative of thedeflection curve at a given section.

Curvatures were also determined usingstrains measured at th e extreme fibers on both

the tens ion and the compression sides of th e

OTC 1569

pipe at several sections along th e pure momentspan. The curvature i s the sum of the absolutevalues of strain at the extreme surfaces dividedby th e diameter. The curvatures computed at a l l

th e instrumented sections in the pure flexurespan were averaged to obtain a representativecurvature for th e pipe. The moment-curvaturerelationships obtained from both strains anddeflections showed excellent agreement. How-

ever, in some cases, strain-gauge readings inthe plastic region were no t reliable, and a l l

curvatures reported are based on deflectiondata. For every load stage, th e moment on thepipe and th e corresponding curvature werecalculated. Typical moment-curvature diagramsare shown in Figs. 4 through 7.

Measured Ovaling

The horizontal and vertical diameters

measured at each load stage at a number ofsections in the flexural span were used to

compute a ir ratios.I t

was assumed that duringovalization pipes that were init ial ly roundbecame ell iptical in shape, and ovalization wasdefined by the quantity air, the ratio of th esemimajor axis of the ellipse (a ) and thecorresponding radius (r) of the pipe beforetesting. Measured ovaling-curvature relationships are also plotted in Figs. 4 through 7.

COMPUTED RESULTS

A method of ana lysi s presented by Ades4was used to determine theoretical momentcurvature and ovaling-curvature relationships

for the pipes tested. By using the princ ip leof leas t work, i t i s possible to determine theshape of the c ross -sec tion of the tube as afunction of i ts longitudinal curvature and also,after the shape is found, to determine th ebending moment carried by the tube. Duringovalization, i t is assumed that tubes that areinit ial ly round become e l li p ti c al in shape,that the circumferential deformation isinextentional, and th at l in es originally normalto the middle surface remain so after loading.

By virtue of th e principle of leas t work,

the total internal strain energy must be aminimum at a stationary point. For a given

radius of curvature , P , the ovalization air is

varied until minimum internal strain energy is

reached. The program used to determine momentcurvature and ovaling-curvature relationships isdescribed in d eta il in Ref. 5.

EFFECT OF OVALING ON RESPONSE

Effect of Ovaling on Moment CapaCity

Moment-curvature relationships werecomputed for the six pipes tested and compared

with measured values. First, the moment-

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1569 J . O. JIRSA, FOOK-HOY LEE, J. C. WILHOIT, JR. and J. E. MERWIN1-575

curvature relationship was computed consideringth e pipe maintained i ts original shape. Second,the pipe was allowed to oval and become ell ipt i-cal in shape, and th e moment-curvature relationship was obtained as previously described.Computed moment-curvature relationships areshown in Figs. 4 through 7. In a l l cases, th emoment carried by the ovalized pipe was somewhat less than that carried by th e pipe with no

ovaling. However, for most cases the differences were small. In general, local bucklingfailure occurred before large reductions inmoment capacity were observed. Therefore, i tcan be concluded that ovaling has l i t t l einfluence on the moment capacity carried by th epipe.

Moment-Gurvature Relationships for Bare Pipes

The comparison between measured and computed moment-curvature relationships is shownin Figs. 4 through 7. The agreement between themeasured and computed was generally good in theini t ial stages of loading for a ll the specimens.After yielding, the computed and measuredcurves compared very closely except for SpecimenlOB, which showed greater measured moments withincreasing curvature. This i s due to the steelstress-strain relationship used in the analysis.The analytical function used in the analysisdescribes a material with a monotonically decreasing modulus in the plastic region. Thes teel s t ress-s t ra in curve for Specimen lOB, Fig.2 showed strain hardening at a strain of about0.0085. As a result, the measured moment ishigher than computed for large strains.

Although th e steel stress-strain characteris t ics of other pipes also indicated somestrain hardening, the pipes failed in bucklingbefore strains reached the strain hardeningregion.

Ovaling-Gurvature Relationships

The measured and computed oValing

curvature relationships are compared in Figs.4 through 7 for th e bare pipes and in Figs.8 and 9 for the coated pipes. The agreementbetween the measured and computed curves was

satisfactory for a ll the specimens. Theapparent excess s tr ength o f Specimen lOB wasa tt ributed to th e steel, which exhibited anincrease in stiffness at large strains. In a llth e other tests, buckling failure with largeair ratios occurred at curvatures that wereconsiderably lower than that recorded forSpecimen lOB. However, i t appears that computations based on Ades' method satisfactorilypredic ts oval ization of pipes under purebending. I t does not appear that the concretecoating has any significant effect on ovaling

at the field joint.

SUMMARY AND CONCLUSIONS

In this repo rt t he effects of oValing onthe behavior of pipes under pure bending wasreported. The inf luence of concrete-coat ingon oValing at the joint was also studied.Theoretical moment-curvature and ovalingcurvature relationships obtained using a strainenergy procedure were compared with experimental

results.

Based on th e test results obtained, thefollowing conclusions were reached.

1. Moment-curvature and ovaling-curvaturerelationships computed using the s train-energyapproach suggested by Ades1 satisfactorilypredicted the measured response for bare pipesunder monotonic loading.

2. Ovaling did not significantly reduceth e moment capac ity of the pipes unti l strainswell into the plastic region were reached.

3. The concrete coating had l i t t l e effecton the ovaling characteristics of the pipe atth e simulated f ie ld j oi nt .

ACKNOWLEDGMENT

The authors would like to aclmowledge th efollowing companies for their sponsorship ofthis work: Atlantic Pipe Line Co., ColumbiaGas System Service Corp., Chevron Oil FieldResearch Co., Esso Production Research Co.,Gulf Research and Development Co., J. Ray·

McDermott and Co., Inc., Mobil Pipe Line Co.,Shell Pipe Line Co., Southern Natural Gas Co.,Texas Eastern Transmission Corp. , Trunkline GasCo. and United Gas Pipe Line Co.

REFERENCES

1. Jirsa, J. 0., Wilhoit, J. C. , Jr . , Aguirre,M. and Mogbo, N. C.: "Ef fect o f ConcreteCoating on the Rigidity of 12 3/4 In. LinePipe", Paper OTC 1072 presented at 1st Offshore Technology Conference, Houston, May18-21, 1969, 2, 47-58.

2. Lee, Fook-Hoy: "Buckling and Ovaling ofPipe-Line", MS Thesis, Rice U. (May, 1971).3. Mogbo, N. C., Jirsa, J. O. and Wilhoit, J.

C. , Jr. : "Effective Stiffness of ConcreteCoated Line Pipe", ASME Paper 7l-Pet-26presented at the Petroleum MechanicalEngineering Conference, Houston (Sept.,

1971).4. Ades, Clifford S.: "Bending Strength of

Tubing in th e Plastic Range", J. Aeronautical Sciences (Aug., 1957) 605=610.

5. Wilhoit, J. C., Jr. and Merwin, J. E.: "TheEffect of Axial Tension on Moment Carrying

Capacity of Line Pipe Stressed Beyond the

Elastic Limit", Paper OTe 1355 presented

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I-576OVALING OF PIPELINESUNDER PURE BENDING OTO 156

at 3rd Offshore TechnolofgConference,

Houston,April 19-21, 1971, ~, 293-296.

TABLE 1 - PROPERTIES OF TEST SPECIMENS

Coati ngThi ckness

Speci men Di am in. Thi ckness, i n. Concrete, in. Somastic, in.

10a 10. 75 0. 233 0 0

10b 10. 75 0. 350 0 0

16a 16. 00 0, 260 0 0

20a 20. 00 0. 255 0 0

12a 12. 80 0. 260 1. 45 0. 5

Test Spans, f t.Shear F1exure

6 6

6 6

9 9

9 9

9 9

16b 16. 10 0. 260 1. 70 0, 5 9 9

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—.;: --— --- ~++-—J_j

IIII

~

11

R 0

--- -1.1- — -Li- ---

1 Shear SDan t Pure Momenf Sean t ‘Shonr ~nrtn

120

Fig. 1 - Schematic representation of test set “up.

or0002 0.004 0$003 000E? 0.010

St rain (i n-per-i n)

50.20a

“j40--

~ 30.-

; 20.G ,0.

0

Ov0.002 0.004 13.(j06 0.008 O.Ojo

Strain (in-per-in)”

Fig. 3 - Stress strain curves.

Fig. 2 - Stress strain curves.

----- noovalinga/r

i -.fiI Lu

r..-1 —---- ---—--

‘“M- 0ovoling

.’ t

@

--- -.

- . 100 1’,

, , 1 . s;

, ’ r ,, ) t ; ’~.

& I ,- - - - -~- 80

/

,,t

.&.alr .1$

/’ .’/“,’ ‘

— Measured

------- Computed

xBuckling Failure

--Ho

-1.08

--1.06

-1.04

--1.02

Fig. 4 - Moment-curvature and oval ization-curvaturerelationships, Specimen 10a.

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c)--.

,,— Measured

a “\ --—-- Computed a/r‘. ,’

----C180 .-

’160 ,.-

----- -1.4---—---- ‘----------.-~ ~--iiO-&Olingz = ------------------- -

-----

E120 -‘\,Ovaling,

~\ .’ s“ -1.3

gloo -- ,>:

,/’ ‘.80 .-,

z/’ “. 4.2

,,~~ 60 . .!-- ,/’

40-

20-0

100 200 300 400 500 600 700 800 900

Curvature, x 10-4per ft .

Fig. 5 - Moment-curvature and oval izat ion-curvaturerelationships, Specimen 10b.

250.<

“7x+. 200”c

g ,50-

Z

F [oo-

$

50.

.- ===.=-----------

— Meosured-------- –--—Computed

0XBuckling Failure

20 40 6’0 80 100 120 140 160

-

-.

Curvature, x 10-4 per ft.

Fig. 6 - Moment-curvature and oval izati on-curvaturerelationships, Specimen 16a.

500.+“y --------. -------- noovalingx --------------------- - ----

---400. -

- -ovoling

‘Z‘1.08

2 /’

0 3oo- /’

25— Measured -1.06

/’/’ ----- Computed

E,

/ ~Buckling~ 200 ..

,,” Failure,/

e ::

~-~ -- 1.04

/./“

, ‘,,.~ ;

I 00 -.,.

/’ 1.02‘.

----

020 40

t[40

ti;;atur~~x I02 jer f’tzo

Fig. 7 - Moment-curvature and oval ization-curvaturerelationships, Specimen 20a.

U I1,05

1.04I

/“1.03 - //’

/— Measured

1.02 ------ Computed)@uckling Failure

1.01 .-

4s0 8’0 120 I&o 2bo 240 280 320


I .012 -

1,010 -

I.00B -

1.006 -

1.004 -

1.002t

— Measure

----–– Comwte

X Buckling Foiiu

@

---, r ‘,

0,:\, /

.---

1/ ,2a 4b 6b 8’0 160 12.0 140 160 Iba2ba


Fig. 8 - Oval izati on-curvature relationship,Specimen 12a,

Fig. 9 - Oval izati on-curvature relationship,Specimen 16b.

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