Iaetsd study and experimental analysis of linear and non linear behaviour of

STUDY AND EXPERIMENTAL ANALYSIS OF LINEAR AND NON LINEAR BEHAVIOUR OF
PIPE BEND WITH OVALITY
Balaji A#1
, Faheem Ashkar H#2
, Jahir Hussain H#3
, Elamparithi R#4
#1
Assistant Professor
#2, #3,#4
UG Scholars
Department of Mechatronics Engineering, Kongu Engineering College
Perundurai, Erode, Tamil Nadu, India-638052
1
bala2009mct@gmail.com
2
faheem.ashkar@gmail.com
3
iamjahirhussain@gmail.com
4
elamparithiramasamy@gmail.com
Abstract— the present study performed a series of
experiments using real-scale experimentation process to
evaluate the effects of load variation with respect to ovality
for various schedule numbers such as SCH 40 long radius,
SCH 40 short radius and SCH 80 short radius bends with and
without internal pressure. The experiments has been
conducted at ambient temperature within elastic limit of the
bend for under in-plane opening & in-plane closing bending
moments and also out of plane clockwise & out of plane
anticlockwise bending moments. The experiments included to
calculate the displacement as well as percentage change in
ovality in the intrados, crown and extrados regions of the
bend. The displacement in the intrados and extrados region
increased almost linearly with respect to load for both in-
plane and out of plane bending moments. This allowable limit
loads and ovality are suggested for different diameters of pipe
bends and for different pipe material. This helps in avoiding
rejection of pipes due to insufficient wall thickness. The
mathematical results and software results are compared with
experimental results to get the optimised output.
Keywords: Pipe bends, Internal Pressure, In-plane and Out of
plane bending moments.
I INTRODUCTION
Large pipelines and pipe networks are part of almost every
industrial setup today. These are most commonly found in
petroleum rigs, refineries, factories producing chemicals and
pharmaceuticals, and in power plants. In these and other industrial
applications, pipes are very often used to carry substances that, by
virtue of their pressure, temperature, physical and chemical
characteristics, can have serious negative effects on health,
property and the environment, if released into the atmosphere.
Examples of such substances include steam, oil and chlorine gas.
Failure in a piping system could cause problems, like an
unscheduled, and hence costly, plant shutdown for maintenance
or even a catastrophe, like exposing the core of a nuclear reactor.
Therefore, the integrity of pipes in industrial contexts is of
paramount importance. This integrity relies heavily on the
correctness of pipe design, which can only be achieved through a
thorough understanding of the behavior of piping components and
systems under different types of loads.
II Equations used for calculating basic parameters
The ovality of a bend section is shown in figure 1.1. The
minimum required wall thickness at the pipe bend during the
bending process does not produce a difference between the
maximum and minimum diameters greater than 8 % for internal
pressure service and 3 % for external pressure service
(Engineering Design and Analysis Ltd.,). The center line radius of
pipe bends should typically be a minimum of 3 times the nominal
pipe diameter. The codes have certain requirements for the
acceptability of finished bends. It depends upon the following
parameters
i. Thinning and Thickening.
ii. Ovality.
iii. Buckling.
Figure 1.1Bend Ovality
A Thinning and Thickening
In every bending operation the outer portion of the
bend stretched and the inner portion compressed. This leads to
thinning at the extrados and a thickening at the intrados of the
pipe bend. The thinning is defined as the ratio of the difference
between the nominal thickness and the minimum thickness to the
nominal thickness of the pipe bend. The thickening is defined as
the difference between the maximum thickness and the nominal
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64
ISBN: 378-26-138420-01

thickness divided by the nominal thickness of the pipe bend. The
percentage change in thinning and thickening is calculated by
using the formula as shown in the equation 2.1 and 2.2
(Veerappan A and Shanmugam S, 2012). Because of uncertainties
introduced by the pipe-manufacturing method, it is not possible to
exactly predetermine the degree of thinning.
------- (2.1)
------- (2.2)
Where,
Tnom =Nominal Thickness of the Bend (mm).
Tmax =Maximum Thickness of the Bend (mm).
Tmin =Minimum Thickness of the Bend (mm).
B Ovality
During the bending operation the cross section of the
bend assumes to be an oval shape whose major axis is
perpendicular to the plane of bend. The degree of ovality is
determined by the difference between the major and minor axes
divided by the nominal diameter of the pipe. When the bend is
subjected to internal pressure, it tries to reround the cross section
by creating secondary stress in hoop direction. The percentage
change in ovality is calculated using the equation 2.3 (Veerappan
A and Shanmugam S, 2012).
-------- (2.3)
Where,
Dmax =Maximum Outside Diameter of the Bend (mm).
Dmin =Minimum Outside Diameter of the Bend (mm).
Dnom =Nominal Outside Diameter of the Bend (mm).
III STANDARD PARAMETERS
The specification such as bend dimensions and
chemical compositions of the bend section were taken from
ASME B36.10 catalogue for 1inch diameter bend. The bends are
classified into the following categories.
1) SCH40 (Wall Thickness-3.4mm)
The outer diameter of the bend is kept constant and the bore size
will be varied according to the schedule number of bend. In
schedule number itself the bends are classified into two
categories.
1) Long Radius Bend.
2) Short Radius Bend.
In our investigation three types of specimens has been
used according their availability.
1) SCH40 – Long Radius Bend.
2) SCH40 – Short Radius Bend.
3) SCH80 – Short Radius Bend
In each section a straight pipe of six inch length has been attached
at the both side of the bend section.
The standard parameters and chemical composition of
the pipe is given in the table 3.1 and 3.2 which is taken from
ASME B36.10 and ASTM A106 Grade B catalogue.
Table 3.1 Standard Parameters
Description Parameters
Pipe Standard ASTM 106 Grade B
Schedule Number (SCH) 40 and 80
Pipe Size 25 mm
Outside Diameter (D) 33.4 mm
Inside Diameter 26.6 mm and 24.4mm
Wall Thickness (t) 3.4 mm and 4.5mm
Tensile Strength(min) 413MPa
Yield Strength(min) 241MPa
Table 3.2 Chemical Compositions
Composition Percentage
Carbon(max) 0.30
Manganese 0.29 to 1.06
Phosphorous(max) 0.025
Sulfur(max) 0.025
Silicon(min) 0.10
IV EXPERIMENTATION SETUP
` The diagrammatical model of the experimentation setup
is shown in figure 4.1 for testing the elbow under in-plane
bending mode. One end of the pipe end is clamped at the ground
and other end is kept free for applying the in-plane moment load.
A long rod is attached at the end of the free end for applying the
in-plane load easily. The length of the straight pipe EB and GH is
equal to six times the diameter of the bend section. In-plane
bending mode can be created when the load applied in vertical
direction on the beam BA. When the load applied in vertically
upward direction, the bend section is subjected to in-plane
opening mode and vertically downward direction, the bend
section is subjected to in-plane closing mode. And out-of-plane
bending mode is created by applying the load in horizontal
direction on the beam. Spring balance and load cell is used to
measure the magnitude of the applying load which is placed at the
free end of the rod. Dial gauges are used to measure the deflection
in the bend section by fixing it in the intrados, crown and extrados
regions. The maximum elastic bending moment that can be
applied in the test specimen is calculated by using the formula
given below which is taken from ASME BPVC, Section III is
shown in the equation 4.1.
Figure 4.1 Diagrammatical Model of Set-up [Karmanos et al.]
Maximum bending moment (Mi (max)) = ------ (4.1)
Where,
z = Section Modulus.
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ISBN: 378-26-138420-01

Sm = Allowable Stress Value.
= Bend Factor (Rt/r2
)
Long Radius SCH40 Bend =613.54N-m
=1067.64N (108.8kg)
Short Radius SCH40 Bend =468.25.1N-m
=814.91N (83.09kg)
Short Radius SCH80 Bend =675.40N-m
=1175.43N (119.81kg)
The Pro/E model and photographic view of the setup is
shown in the figure 4.1 and 4.2 which is shown in different views.
By rotating the hand wheel the desired load is applied to the
corresponding bend section.
FRONT VIEW SIDE VIEW
TOP VIEW
Figure 4.2 CREO Elements Model
SIDE VIEW
FRONT VIEW
TOP VIEW
Figure 4.3 Photographic View of the Setup
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ISBN: 378-26-138420-01

Figure 4.4 Isometric View of CREO Elements Model
Figure 4.5 Isometric View of the Setup
The bend section which is to be tested is fixed in the
base frame. One end of the long rod is attached to the bend
section and other side of the rod is clamped in the plate which
moves up and down for applying the in-plane bending modes. The
movement of the plate can be attained by rotating the hand wheel.
Spring balance is placed in the bottom of the vertical frame when
the bend is subjected to in-plane opening mode and it is placed in
the top of the vertical frame when the bend is subjected to in-
plane closing mode. Two supports which are resting on the base
frame for applying out of plane bending in clockwise and
anticlockwise modes. Dial gauges are used to measure the
deflection in the bend section by fixing it in the intrados, crown
and extrados regions. During experimentation the load is applied
in the incremented manner up to maximum bending moment that
can be applied to bend section. For each mode three sets of
reading has been taken and then it is averaged. In this
experimental setup the readings are taken without any internal
pressure like water, oil, steam etc.
V RESULTS AND DISCUSSION
V.I ANALYSIS RESULTS
Using Finite Element Analysis (FEA) method, ansys
12.1 were performed with solid element type. The following
values of material properties were used in present calculations
E = 193 GPa, Poisson’s ratio of γ = 0.3 and the limiting stress of
σ= 193 MPa. The FEA models were subjected to internal
pressure, in-plane bending and out of plane bending mode.
Internal pressures were applied as a distributed load to the inner
surface of the FEA model.
Figure 5.1.1 Cross Section of the Pipe bend with attached to
straight pipe
Figure 5.1.2 Pipe bend with attached to straight pipe
Figure 5.1.3 In plane bending mode (closing)
Figure 5.1.4 Stress Distribution of the pipe bend in In-plane
bending mode (closing)
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ISBN: 378-26-138420-01

Figure 5.1.5 Out of Plane bending model
Figure 5.1.6 Out of Plane bending (clockwise)
Figure 5.1.7 Stress Distribution of the pipe bend in Out of plane
bending mode (clockwise)
The same procedure was performed for in plane
opening mode and out of plane anticlockwise mode and the graph
was plotted for displacement and deflections. These values are
compared with experimental setup values.
V.II EXPERIMENTAL RESULTS
A In plane Closing Bending Mode:
The maximum displacements results in intrados, crown
and extrados regions as well as the percentage change in ovality
of the bend during Inplane Closing Bending Mode is shown in
table. The readings are taken as five sets and the average values
are shown in the following table.
Table 5.2.1 Displacement and percentage change in ovality
B Out of Plane Clockwise Mode:
The maximum displacements results in intrados, crown
and extrados regions as well as the percentage change in ovality
of the bend during Out of Plane Clockwise mode is shown in
table. The readings are taken as five sets and the average values
are shown in the following table.
Table 5.2.2 Displacement and percentage change in ovality
The same procedure was performed for inplane opening
mode and out of plane anticlockwise mode and the graph was
plotted for displacement and deflections.
VI GRAPHS AND DISCUSSIONS
The displacement variation for analysis results were
compared with experimental results, it shows the approximately
same variation and percentage change in ovality for various
schedule number of pipe bends are plotted as below.
S.
No
Schedule
Number
Maximum Displacement (mm)
Percentage change
in Ovality
Intrados
Region
Crown
Region
Extrados
Region
Zero
Load
(kg)
Maximum
Load (kg)
1
40-Long
Radius
1.69 0.92 1.48 4.310 3.070
2
40-Short
Radius
0.74 0.151 0.62 1.417 0.299
3
80-Short
Radius
0.75 0.258 0.99 3.333 1.856
S.
No
Schedule
Number
Maximum Displacement (mm)
Percentage change
in Ovality
Intrados
Region
Crown
Region
Extrados
Region
Zero
Load
(kg)
Maximum
Load (kg)
1
40-Long
Radius
0.79 0.56 0.74 4.32 2.09
2
40-Short
Radius
0.54 0.05 0.35 0.35 0.299
3
80-Short
Radius
0.65 0.154 0.59 0.59 1.57
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ISBN: 378-26-138420-01

Graph 6.1 Displacement Variations for Analysis Results
Graph 6.2 Displacement Variations for Experimental Results
Graph 6.3 Percentage Change in Ovality for SCH 40 radius pipe
bends in experimental values.
VII CONCLUSIONS
The experimental results and analytical results show
inplane bending moment has more deflections compared to out of
plane bending moment. Percentage variation in ovality during
inplane closing mode and out of plane clockwise mode from zero
to maximum loading is increased from schedule 40 long radius to
schedule 40 short radius that is from 28.77 to 72.89 but
decreased from schedule 40 short radius to schedule 80 short
radius that is from 72.89 to 44.31 . For inplane opening mode
and out of plane anticlockwise mode the percentage variation in
ovality behaves the same manner as that of out of plane clockwise
mode. The experimental results describe that maximum
displacement occurs in the intrados region and hence the intrados
region exhibit more flexible property than the extrados region.
When the schedule number is increased rigidity of the bend
material is increased as well as the percentage variation in ovality
is also increased.
The present work can be extended to include the effect
of internal pressure on the pipe bend with in-plane and out of
plane bending moment, temperature effects involved, material
microstructure analysis to control geometrical irregularities due to
ovality. The influence of initial ovality in pipe bends is considered
to be one of the major factors in reducing the percentage ovality
which demands analysis of the behavior to avoid geometrical
irregularities. The temperature effects involved in the pipe bends
while introducing internal pressure needs to be analyzed to find
the exact reason for geometrical irregularities in pipe bends due to
ovality. The material microstructure analysis can help to predict
the behavior of various materials at elevated temperature and
pressure to predict the grain size changes when loading is done on
a pipe bend.
VIII REFERNCES
1. Veerappan AR, Shanmugam.S and T.Christo Michael.,
‘Effect of ovality and variable wall thickness on collapse
loads in pipe bends subjected to in-plane bending closing
moment’, Engineering Fracture mechanics, Vol.7, pp.138-
148,2012.
2. Veerappan A and Soundrapandian S., ‘The Accepting of
Pipe Bends With Ovality and Thinning Using Finite
Element Method’, Journal of Pressure Vessel Technology,
Vol .132(3), pp.031204, 2010.
3. Chattopadhyay J., ‘The effect of internal pressure on in-
plane collapse moment of elbows’, Nuclear Engineering
and Design, Vol .212, pp.133- 144, 2002.
4. Weib E., 'Linear and nonlinear finite-element analyses
of pipe bends', International Journal of Pressure Vessels
and Piping, Vol .67(2), pp.211-217.1996.
69
ISBN: 378-26-138420-01

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