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A Study on the Effect of Cross Section

Approximation on the Behaviour of Pipe Bends

with Ovality and ThinningT. Christo Michael AR. Veerappan

*S. Shanmugam

Department of Mechanical Engineering, National Institute of Technology, Tiruchirappalli – 620 015, Tamilnadu, INDIA.*Corresponding author email: [email protected]

Abstract — The effect of cross section approximation on the

behaviour of pipe bends with shape imperfections under internal

pressure was performed numerically. Two cross sections namely

elliptical and semi oval were taken for analysis. FE analyses were

performed on these cross sections. The hoop stress induced due to

internal fluid pressure load was obtained for the models . On

comparison, the stress induced in the elliptic and semi oval

sections differed by a large amount. Five cross sections from firstoff trial report which is the actual cross section at the bend

section were analysed and the stress induced was compared with

the elliptic and semi oval cross sections. The results confirmed

that approximation in cross section produces considerable effect

on the induced stresses. The effect of bend radius and the

combined effect of ovality and thinning/thickening on the stress

developed were studied for the assumed (elliptic and semi oval)

cross sections and compared

Keywords- Axisymmetric, Bend angle, Bend radius, Ovality, Pipe

bend, Thinning.

I. I NTRODUCTION

Pipe bends are critical components in piping systems andgenerally are the most economical means of changingdirections while providing flexibility and end reactions to

piping systems within the allowable limits [1]. The bendsection may be a potential source of damage during service,

due to internal pressure and other loads, particularly in thecases where significant ovality and wall thickness variation(thinning/thickening) exist, which are introduced during themanufacturing process[2 - 4]. The acceptability of pipe bendsdepends on the magnitude of these shape imperfections [5].

For numerical investigation when ovality is considered, thecross section of the pipe bend is often assumed to be perfectly

oval or elliptical [6 - 9] as shown in Fig. 1(a). Distortion incold bend tubes is usually limited to the outer half of the bend

where flattening occurs and the distortion can be described bya semi-oval/semi-round section [10] as shown in Fig. 1(b).

Both the aforesaid shapes do not represent the true crosssection of pipe bend but are only approximated. In industriesgenerally the contour of the pipe bend cross sections arecaptured in their first off trial test (FOT) to study and acceptthe pipe bends with ovality and thinning/thickening. The

contours reveal that the cross section is neither elliptical nor semi oval. Nevertheless, as literatures propose, elliptical andsemi oval cross sections are employed to analyse the pipe bend analytically and numerically.

Analyses in pipe bends rely on the assumptions of constantwall thickness along the contour of the pipe’s cross section

and no initial ovality [11]. However, the majority of short-radius curved pipes are made using a forming process, and, asa result, have variable wall thickness along the contour of the pipe’s cross section. The pipe wall is thinner than nominal onthe convex side and is thicker on the concave one [11].Bending of a curved pipe is accompanied by the flatteningforces. They transform initial circular cross sections of a pipeinto oval cross sections [12]. Ovality is a main defect in all

pipe bending techniques [13].

The current study aims at determining the effect of shapeapproximation in cross section on induced stresses in pipe

bend by comparing the stress induced in elliptical and semi

oval cross sections of pipe bend with each other and withthose obtained from actual cross section taken from FOTreports. The effect of ovality and thinning/thickening isstudied for the assumed cross sections. Studying the combinedeffect of ovality and thinning/thickening is more significant inthe stress analysis than studying the shape imperfectionsindividually as the real geometry of pipe bend has both theirregularities.

Previous study has shown that when internal pressure is the

predominant load, in a 90° pipe bend, without consideringinitial ovality and variable wall thickness, 2D axisymmetric

models provide accurate stress results compared with thoseobtained from 3D models [14]. The determination of the effect

of ovality and thinning on the performance of 2D and 3D pipe bends was done and it was observed that they producecomparable results [15]. Hence 2D models have been used todetermine the effect of shape approximation on the inducedstresses in the present analysis. The effect of bend radius onthe induced stress was also studied for the elliptic and semielliptic sections by considering four different bend radii

namely 101.6 mm, 152.4 mm, 203.2 mm and 304.8 mm.

AR. Veerappan et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 2, Issue No. 2, 132 - 138

ISSN: 2230-7818 @ 2011 http://www.ijaest.iserp.org. All rights Reserved. 32

mailto:[email protected]






Fig. 1 Assumed pipe bend sections for the analysis

II DEFINITIONS

Percent ovality C0, thinning Ct, and thickening Cth , are definedas follows [16 – 18]:

1002minmax

minmax

D D

D D

oC (1)

100

min

t

t t

t C (2)

100

max

t

t t

thC (3)

III ASSUMPTIONS

The following assumptions are made in the analysis: Linear

behaviour, homogeneous isotropic material, and steady staticstate loading. The effects of the following are not consideredin the present evaluation: Bourdon’s effect, external pressure,external forces, external moments, centrifugal forces due tochange of fluid flow direction, effects of friction between the pipe inside fluid and the pipe bend inner surface, fluid

turbulence, interfaces between the straight pipe and pipe bend,tolerances and deviations of the straight pipe before

fabricating into pipe bend and pipe bend surface roughness [5,6].

IV INPUT DATA

The parameters considered for analysing the assumed cross

sections (elliptic and semi elliptic) is given below.

Pipe Parameters Specification Material ASME SA234 WPB [19]

Internal Pressure 10 MPa Outside Diameter 114.3 mm

Nominal Thickness 8.56 mm

Bend Radii 101.6, 152.4, 203.2 and 304.8

mm Percent Ovality 0% to 20% in steps of 5%

Percent Thinning/Thickening 0% to 20% in steps of 5% V ANALYSIS AND COMPARISON BETWEEN

ELLIPTIC AND SEMI ELLIPTIC CROSS SECTIONS

The elliptic cross section of a typical bend is assumed to become a perfect ellipse after bending as shown in Fig. 1(a).The major axis of the elliptical shape of pipe bend is assumedto be perpendicular to the plane of bending of the pipe bend.

The minor axis of the elliptical shape of pipe bend is assumed

to be in the plane of pipe bend. The pipe bend is assumed to besmooth, without ripples. The assumed semi elliptic crosssection is shown in Fig. 1(b).

5.1 Stress Analysis

The finite element method is a numerical analysis techniqueused by engineers, scientists, and mathematicians to obtainsolutions to the differential equations that describe, or approximately describe a wide variety of physical and non- physical problems. During the last three decades considerableadvances have been made in the applications of numericaltechniques to analyze pressure vessel and piping problems.Among the numerical procedures, finite element methods arethe most frequently used [20].

5.1 Methodology

In this paper linear static analyses were carried out using thecommercial FE program ANSYS v12. A scripting language,APDL (ANSYS Parametric Design Language) [21], was usedto automate the common tasks and build the model in terms of parameters. By exploiting symmetry one half of the problemwas modelled for the 2D models. The axisymmetric modelwas meshed with PLANE183 [22] quadrilateral elements. TheFE models, after supplying necessary boundary and loading

conditions, were solved. The required output results were

(a) Elliptic section(b) Semi elliptic section


ISSN: 2230-7818 @ 2011 http://www.ijaest.iserp.org. All rights Reserved. Page 133



obtained, using APDL commands and directly written into an

excel file.

5.2 Pre-Processing

The 2D axisymmetric cross sections were modelled usingPLANE183 element with axisymmetry option. PLANE183 isa higher order 2-D element. It has quadratic displacement behavior and is well suited to modeling irregular meshes. Thiselement is defined by 8 nodes having two degrees of freedomat each node: translations in the nodal x and y directions. Theelement may be used as a plane element (plane stress, plane

strain and generalized plane strain) or as an axisymmetricelement.

Material properties namely modulus of elasticity andPoisson’s ratio were specified to the models. The

axisymmetric model was generated using mapped meshingensuring proper aspect ratio. The total number of elements for the axisymmetric model is chosen as 60 with 3 elementsacross the thickness of the pipe cross section to develop themesh model. Symmetry boundary condition was supplied tothe models. Internal fluid pressure load was applied to theinner surface of the models.

5.3 FE Analysis

(a) Elliptic cross section

(b) Semi ellipticFig. 2 Meshed models with constraints and load

The models were solved to obtain the required results. The programmes using APDL were written to create the models

with various combinations of ovality and thinning/thickeningfrom 0% to 20 % in steps of 5%, constraint the models as

aforementioned, apply the internal pressure load and solve the

problem.

Fig. 3 Flow chart for the APDL program

The hoop stress values obtained at intrados and extradossections of the two cross sections of pipe bend were writteninto an excel file.

yes

Yes

Model

Constraints

Load

Solution

Input diameter, thickness, bendradius and material properties

Ovalit = 0

Thinning = 0

If

Ovality ≤ 20

If

Thinning ≤ 20

no

No

Hoop stress at intradosand extrados written as an

Excel file

Stop

Thinnin + 5

Ovality + 5

Ct = 10Co = 10

R = 152.4 mm

Ct = 10Co = 10

R = 152.4 mm





Fig. 2 shows the meshed model of elliptic (Fig. 2(a)) and semi

elliptic (Fig. 2(b)) cross sections with boundary conditions andinternal pressure load.

5.4 The Computer Program

A program was written in APDL to create the models, analyzeand get the results into a separate file which is then plotted asgraphs for all different problems. Fig. 3 shows the flowchart

of the program.The program prompts the user to enter the pipe diameter, bendradius, thickness, internal pressure and material properties. On

giving the required input, the program creates the models insequence keeping ovality constant at 0% and varyingthinning/thickening from 0% to 20 % in steps of 5%, appliesthe internal pressure load and solves the problem. Hoop stressvalues at intrados and extrados sections are obtained andwritten into an Excel file. The ovality is then incremented insteps of 5% up to 20% repeating all the other steps. The procedure is repeated for other bend radii.

5.5 Interpretation of Stress Analysis Results

0

5

10

15

20

25

30

0 5 10 15 20

Ovality, %

H o o p s t r e s s d i f f e r e n c e ,

%

Fig. 4 Percent difference in hoop stress between elliptic and

semi elliptic sections at the intrados for R = 101.6 mm

0

2

4

6

8

10

12

14

16

0 5 10 15 20

Ovality, %


%


semi elliptic sections at the extrados for R = 101.6 mm

Fig. 4 shows the absolute percentage difference in the hoop

stress values at the intrados between elliptic and semi ellipticmodels for bend radius 101.6 mm. It can be observed that this

difference increases with increase in ovality. For constantovality, increase in thinning also causes an increase in thisdifference. At the extrados section (Fig. 5), the difference isless compared to the intrados section but still large inmagnitude, the minimum and maximum being 9.62% and

14.75% respectively.

0

5

10

15

20

25

30

35

0 5 10 15 20

Ovality, %


%



0

5

10

15

20

25

0 5 10 15 20Ovality, %


%



As the bend radius is increased to 152.4 mm, at the intrados,

the difference increases with increase in thinning for 5%ovality alone. As ovality is increased beyond 5%, thedifference decreases with increase in thinning keeping ovalityconstant (Fig. 6). At the extrados, increase in ovality keepingthinning constant causes an increase in the difference percentage (Fig. 7). The maximum and minimum percentagedifference at the intrados are 28.77% and 6.99% respectivelywhile it is 21.76% and 1.53% respectively at the extrados.As the bend radius is increased to 203.2 mm, 5% ovality produces a decrease in the difference with increase in thinningat the intrados (Fig. 8) and extrados (Fig. 9). As ovality is





increased to 10% and beyond, increase in thinning causes an

increase in the percentage difference in hoop stress betweenelliptic and semi elliptic cross sections. The maximum

difference is as high as 38.28% at the intrados and 28.53% atthe extrados while the minimum difference at these sectionsare 2.23% and 7.26% respectively, both occurring at 20%thinning and 5% ovality.

0

5

10

15

20

25

30

35

4045

0 5 10 15 20Ovality, %


%



0

5

10

15

20

25

30

0 5 10 15 20Ovality, %


%



The percent difference in hoop stress increases with increasein bend radius. Figures 10 and 11 show the percent variationin the hoop stress values between elliptic and semi ellipticcross sections at the intrados and extrados respectively for bend radius of 304.8 mm. The maximum difference isobserved at this bend radius. At the intrados, the difference isas high as 55.01% while at the extrados it is 38.37%.

For all bend radii, the models with 0% ovality and thinningvarying from 0% to 20% yield the same hoop stress for boththe cross sections considered, since for these combinations of ovality and thinning, both the assumed cross sections becomethe same i.e. circular with thinning, hence validating themodeling and analysis procedure used.

It has been observed that the common assumptions of elliptic

and semi elliptic cross sections found in literature do not givecomparable results. The difference between the results is very

high and therefore unacceptable. The general observation isthat at the intrados, up to R = 203.2 mm, the semi ellipticmodels yielded higher values than the elliptic models while for R = 304.8 mm, the elliptic models gave higher hoop stressvalues than semi elliptic models. At the extrados, the elliptic

cross section gives higher values for most of the combinationsof bend radius, ovality and thinning.

0

10

20

30

40

50

60

0 5 10 15 20

Ovality, %

H o

o p s t r e s s d i f f e r e n c e ,

%



0

5

10

15

2025

30

35

40

0 5 10 15 20Ovality, %


%



VI REAL CROSS SECTION ANALYSIS ANDCOMPARISON

The pipe manufacturing industries always accept or reject pipe bends based on the magnitude of shape imperfections obtainedfrom the first off trial reports. The pipe after bending is cut atthe bend section, the impression at this section is taken on agraph paper, thinning and ovality measurements are madefrom these impressions and based on the magnitude of theseimperfections the pipe bend is accepted or rejected. Hence itwould be realistic to analyse real time pipe bend cross sections





obtained from these reports for the stresses induced. Five cross

section impressions as shown in Fig. 12 were taken for theanalyses. The details of these bend sections is given in table 1.

Table 1 Details of the actual cross sections considered for

analysis

Id

No.

Diameter,

mm

Thickness,

mm

Bend

Radius,

mm

Thinning,

%

Ovality,

%

A

51 5.0

31.75 17.31 1.28B 38.00 8.75 4.58

C 51.00 15.19 4.26

D 95.25 13.09 8.64

E 121.00 20.4 5.57

Id No. A Id No. B

Id. No. C Id No. D

Id No. EFig. 12 Scanned image of the actual cross sections considered

for analysis

The FOT reports of these cross sections were first scanned andthe image was converted into an AutoCAD drawing file. Necessary corrections were made to the image in AutoCADand the drawing was saved and converted into IGES file and

imported into ANSYS and necessary corrections in the modelwas done. The ANSYS models were meshed with PLANE183elements and solved after applying necessary constraints andinternal pressure load. The hoop stress induced at intrados and

extrados sections were extracted. The elliptic and semi elliptic

models were also modelled to the dimensions of the actualcross section and solved to obtain the hoop stress induced. Fig.

13 shows the steps involved in the creation of the actualmodel.

(a) Scanned image (Id No. E) (b) AutoCAD image

(c) Actual cross section imported into ANSYS, meshed,constrained and internal pressure applied

Fig. 13 Steps involved in creation of the actual cross section

Table 2 Percentage difference in hoop stress between actualand assumed cross sections

Id

No.

Comparison Between Actual

and Elliptic Cross Sections, %

Comparison Between Actual

and Semi Elliptic Cross

Sections, % Intrados Extrados Intrados Extrados

A 75.08 32.51 70.95 29.46

B 72.00 21.07 86.29 33.98

C 22.02 9.75 36.38 23.03

D 22.72 25.14 7.27 45.94E 37.89 48.17 56.35 57.74

The actual cross section was compared with elliptic and semielliptic sections for the hoop stress induced due to internalfluid pressure load. Table 2 gives the absolute percentagedifference in the stress values between actual cross section andassumed cross sections. It can be seen that the difference islarge. It was observed that the stress induced in the actualcross section was higher than the assumed sections for Id No.A, B and C while for Id. No. D and E, it was lower than theassumed sections.





VII CONCLUSIONS

Stress analysis carried out for the assumed and actual pipe bend cross sections show that they are not comparable. Theactual cross sections taken from FOT reports gave resultsmuch different from the assumed sections. Therefore the pipe bend analysis needs to be necessarily carried out with actualcross section models to obtain its actual performance which

will lead to a better design and will also improve the procedure involved in accepting/rejecting pipe bends based on

the shape imperfection. Higher bend radii can cause a greater difference in the stresses induced between elliptic and semielliptic sections.

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NOMENCLATURE

Co : percent ovalityCt : percent thinningCth : percent thickening

D : pipe outside diameter, mmDmax : maximum outside pipe diameter, mmDmin : minimum outside pipe diameter, mmt : nominal thickness of pipe bend, mmtmax : maximum pipe thickness, mm

tmin : minimum pipe thickness, mmR : bend radius to neutral axis, mm



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