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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1
STIFFENING RING DESIGN ON PV ELITE FOR EXTERNAL PRESSURE
ACTING ON THIN WALLED CYLINDRICAL MOUNDED VESSEL
1Amit Chawathe
1BE, Mechanical engineering department, Fr. C. R.I.T, Vashi, Navi Mumbai, Maharashtra, India.
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – Thin wall pressure vessels (TWPV) are widely
used in Oil & Gas industry for storage and transportation of
liquids and gases when configured as tanks. Many a times
Mounded cylindrical pressure vessels are used for storage of
LPG or Propane and are much safer. For Mounded tanksalong
with internal pressure from petrochemicals external pressure
acts as well. External pressure is compensated with increased
thickness, which becomes a costly affair to a much greater
extent if the storage tank is of high capacity. Therefore, a
stiffening ring design is done to compensate the pressure
without expenditure of extra money making it highly efficient.
Key Words: Mounded cylindrical pressure vessels, external
pressure, thickness, petrochemicals, stiffening ring.
1. INTRODUCTION
Used for storage of Liquefied gases (Mainly LPG and
Propane) at ambient temperature. Since the vessels are
installed above the highest ground watertable,thesoil cover
usually protrudes above grade as an earth mound, hence the
term “MOUNDED STORAGE”. Continuous efforts towards
improvement of safety standards led to the design of these
types of storage vessels. These are horizontal bullets
installed for bulk storage of liquefied petroleum gas (LPG).
Offering a safer method for storing highly inflammable LPG;
mounded LPG bullets arelarge,buried,horizontal cylindrical
steel tanks with dished ends. Several vessels can be located
side by side in one mound. Vessels are completely covered
with soil and only manhole/dome and other nozzles
protrude outside. Vessels have a slope of 1:200 min. for
drainage purpose.
2. ADVANTAGES OF MOUNDED BULLETS
Mounded bullets have asand cover, whichcantakeimpact
of external missile bodies. Scenario of BLEVE (boiling liquid
expanding vapour explosion) is eliminated, since no fire
possible below the bullets. Reduced fire case PSV loads as
compared to spheres. Reduced firewater requirement for
firefighting. Difficult for external agencies to identify the
mound as a storage facility. Mound cover protectsthevessels
against Heat radiation from nearby fire, Pressure wave
originating from an explosion, Impact by flying objects,
Sabotage, etc. It reduces site area due to less stringent inter
spacing requirements. Mounded bullet installation is more
space efficient than spheres.
This is because of the smaller vessel-to-vessel spacing and
due to the smaller safety distance requirement between the
mounded storage vessels and items such as control rooms,
buildings, roads etc. Mounded bullets offer the possibility of
partial or total off-site construction. Mounded bullets are
installed on sand bed foundations,which allowtheloadto be
transferred uniformly to the underlying sand. This requires
no heavy foundation work and offers uncomplicated, low
cost installation. The preferred type of foundation for a
mounded storage vessel is a continuous sand bed,
supporting the vessel over its entire length. The use of the
sand foundations allows the vessels to be installed early in
the project and also allows vessel loadings to be predicted
more accurately for vessel design. Usually the foundation
will be constructed with a slope of at least 1:200 to facilitate
draining of the vessel and the sand beneath the vessel must
have adequate elevation not less than 0.76 m to facilitate
drainage. Normally mound is provided with either earth,
sand or concombustible materials like perlite, vermiculate,
etc. for at least 700 mm thickness. As there are possibilities
for foundation settlement, the surrounding of bottomnozzle
should be filled with such material that can absorb
settlement. Provisions are provided for monitoring the
settlement of vessel in mounded storage facility. Bullets
must be coated with special corrosion inhibiting layers such
as epoxy layers and cathodic protection is critical to prevent
corrosion.
3. DESIGN PARAMETERSFOR PRESSUREVESSEL
American Society of Mechanical Engineer's (ASME)Boiler
and Pressure Vessel Code (BPVC) Section VIII, Division2 has
been employed for the design of bullet. The parameters
considered for the design are shown in Table I.
Table -1: Design Parameters
Design Pressure (Internal) 14.5 kg/cm2
Design Pressure (External) 2 kg/cm2
Design Temperature -6 0C to +55 0C
Max. Working Pressure 15.4 kg/cm2
Operating Temperature 40 0C
Capacity 85 m3
Length 10 m
Diameter 3.5 m
Density of LPG 490 kg/m3
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 2
Design code ASME Section VIII Division 2
Wind design code IS-875
Seismic design code IS-1893 RSM
The assemblage of different components such as shells,
heads, nozzles and stiffener rings usually constructs
pressure vessels.
Fig:-1 Mounded pressure vessel with stiffening rings
3.1 Shell
Shells are the primary components that store liquids.
Cylindrical shells are widely employed as they are having
maximum section modulus and minimum induced stress
for a given diameter. Pressure vessel shells are welded
together to form a structure that has a common rotational
axis. Spherical and conical shells are also in use.
3.2 Heads
A variety of heads are used for closing the ends of
pressure vessel shells. These include hemispherical,
elliptical, torispherical,conical and flat shaped heads. Curved
configurations are stronger and allow the heads to be
lighter, thinner and less expensive than flat heads. Headsare
usually categorized by their shapes. Ellipsoidal,
hemispherical, torispherical, conical, tori-conical and flat are
the common types of heads.
3.3 Nozzle
Nozzles are necessary components of pressure vessel for
the process industries. Nozzle is a component that is welded
to the shell or heads of a pressure vessel for connecting
the vessel to inlet and outlet pipes to convey workingfluid in
and out of the vessel. In order to minimize stress
concentrations, preferred shape of nozzles are circular.
Usually the nozzle ends are flanged to allow for the
connections and to permit easydisassemblyformaintenance
or access.
3.4 Stiffener Rings
Stiffener rings are used all around the periphery of the
vessel to increase the moment of inertia at local positions,
thus increasing the resistance or strength and
reducing the thickness requirements.The material used for
stiffener rings is of comparatively low cost and it allows
economically favorable manufacturing of pressure vessels.
3.5 Loads on MoundedBullet
The analysis of mounded bullet is carried out by
considering different loads mentioned in EEMUA
Publication190:2005. Dead weight of the bullet, internal
design pressure, weight of the maximum volume of liquid
allocated to one stiffener, the pressure exerted by the
mound on top of the cylinder and domed ends, axial loads
due to changes in vessel length which are caused by
variations in pressure and temperature, pressureexertedby
the foundation and earthquake loads are considered in the
analysis.
3.6 Load Combinations
There are three load combinations considered in the
analysis for two support conditions, middle soft case and
middle hard case, as mentioned in clause A.4.2.10 of
EEMUA190: 2005.
Service (Filled with LPG in corroded condition)
Internal Design Pressure + Liquid Head + Design
Temperature + Weight of Mound.
Hydro test (Filled with water and in un-corroded (new
condition)
Hydro test pressure + Liquid Head + Weight of mound
Service (Filled with LPG in corroded condition)
Internal Design Pressure + Liquid Head +
DesignTemperature + Weight of mound + Seismic loads
The material used for the construction of different parts
of the bullet along with their tensile strengthand yield stress
values are listed in Table II
Table II Material Specification
Description Material Type of Steel Tensile
Stres
(MPa)
Yield
Stress
(Mpa)
Shells SA-516 70 Carbon
Steel
485 260
Dished
Ends
SA-516 70 Carbon
Steel
485 260
Rings SA-516 70 Carbon
Steel
485 60
Nozzles SA-350
LF2
Carbon
Steel
485 248.22
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 3
4. DESIGN CALCULATIONS FORSHELLTHICKNESS
WITHOUT STIFFENING RING
Fig:-2 Internal Pressure calculations
Fig:-3 External Pressure calculations
From the above two figures, we can note that the
minimum thickness requiredforshelltocompensateinternal
pressure is 17.14 mm i.e 18 mm nominal and the
corresponding thickness against external pressure is 21.55
mm i.e 22 mm nominal. Therefore, extra 4mm thickness is
required to compensate external pressure.Thisisavoidedby
the use of stiffening ring.
5. DESIGN CALCULATIONS FORSHELLTHICKNESS
WITH STIFFENING RING
Fig:-4 Internal pressure calculations
Fig:-5 External pressure calculations
After the application of stiffening ring, we can see that the
external required thickness has reached below 15 mm,
thereby making the internal pressure thickness governing.
The stiffening ring cross section used in this case is as
follows:
Fig:-5 External pressure calculations
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 4
6. RESULTS
Table III Steel Requirement
Description Shell Thk
(governing)
Steel Plate required
(in Kgs)
Total Wt.
saved (kg)
Without
Stiffner
22mm 15666
With Stiffner 18mm 12817 2849
In our case the weight of stiffenering ring each is 1000 Kg.
Therefore with the use of 2 Stiffening rings we can manage
to save upto 850 kg Steel. For heavy capacity mounded
vessels, where the weight of mound is also quite significant,
there could be high amount of steel that would be saved.
REFERENCES
[1] ASME Boiler & Pressure Vessel Code Section VIII 2
Division: Alternative Rules for Construction of Pressure
Vessels, Pressure Vessels Division, American Society of
Mechanical Engineers, New York. 2007.
[2] Barge, V.H., S.S. Gawade and V. Patil (2013) Thermal-
Structural Analysis & Optimization of Pressure Vessel using
Finite Element Analysis. International Journal of Advanced
Engineering Research and Studies. 4. 104-106.
[3] Bednar, H.H. (1986) Pressure Vessel DesignHandbook,2
Edition, Krieger Publishing Company, Malabar, FL, USA.
[4] Block, D.L., M.F. Card and M.M. Mikulas (1965) Buckling
of Eccentrically Stiffened Orthotropic Cylinders, Langley
Research Center, National Aeronautics and Space
Administration, Washington. D. C. USA.
[5] Borovkov, A.I. and D.S. Mikhaluk (2002) Finite Element
Stress Analysis and Multi-Parameter Optimizationofa High-
Pressure Vessel. Proceedings of International ANSYS
conference, Canonsburg, PA, USA. April.
[6] Braestrupe, M.W. (2005) Design and Installation of
Marine Pipelines.
1st Edititon. Blackwell Science Ltd, OX, UK
[7] Deng, Y.C. and G. Chen (2010) Carrying Capacity of
Pressure Vessels Under Hydrostatic Pressure. Tech Science
Press. 4. 65-75
[8] Guide for the Design, Construction and use of Mounded
Horizontal Cylindrical VesselsforPressurisedStorageofLPG
at ambient temperatures, Publication 190, EEMUA, Beech
Street, London. 2005.
[9] Heckman, D. (1998) Finite Element Analysis of Pressure
Vessels. Summer Internship programme, Monterey Bay
Aquarium Research Institute, CA, USA.
[10] Khan, S.M.A. (2010) Stress Distributions in a Horizontal
Pressure Vessel and the Saddle Supports. International
Journal of Pressure Vessels and Piping. 87. 239-244.
[11] Stefanovic, R. and Y. Noman (2012) DesignandAnalysis
of Buried Liquid PetroleumGasStorageBulletsSupported on
Multiple Saddles. Journal of Pressure Vessel Technology.
134. 035001.1-6.
[12] Xue, L., G.E.O. Widera, and Zhifu Sang (2008) Burst
Pressure Prediction of Cylindrical Shell Intersection.Journal
of Pressure Vessel Technology. 130. 1-5.
[13] Yogesh, K. and M.S.R. Lakshmi (2012) Design and Finite
Element Analysis of Mounded Bullet. Journal of Exclusive
Management Science. 1. 1-14.

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Stiffening Ring Design on PV Elite for External Pressure Acting on Thin Walled Cylindrical Mounded Vessel

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1 STIFFENING RING DESIGN ON PV ELITE FOR EXTERNAL PRESSURE ACTING ON THIN WALLED CYLINDRICAL MOUNDED VESSEL 1Amit Chawathe 1BE, Mechanical engineering department, Fr. C. R.I.T, Vashi, Navi Mumbai, Maharashtra, India. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract – Thin wall pressure vessels (TWPV) are widely used in Oil & Gas industry for storage and transportation of liquids and gases when configured as tanks. Many a times Mounded cylindrical pressure vessels are used for storage of LPG or Propane and are much safer. For Mounded tanksalong with internal pressure from petrochemicals external pressure acts as well. External pressure is compensated with increased thickness, which becomes a costly affair to a much greater extent if the storage tank is of high capacity. Therefore, a stiffening ring design is done to compensate the pressure without expenditure of extra money making it highly efficient. Key Words: Mounded cylindrical pressure vessels, external pressure, thickness, petrochemicals, stiffening ring. 1. INTRODUCTION Used for storage of Liquefied gases (Mainly LPG and Propane) at ambient temperature. Since the vessels are installed above the highest ground watertable,thesoil cover usually protrudes above grade as an earth mound, hence the term “MOUNDED STORAGE”. Continuous efforts towards improvement of safety standards led to the design of these types of storage vessels. These are horizontal bullets installed for bulk storage of liquefied petroleum gas (LPG). Offering a safer method for storing highly inflammable LPG; mounded LPG bullets arelarge,buried,horizontal cylindrical steel tanks with dished ends. Several vessels can be located side by side in one mound. Vessels are completely covered with soil and only manhole/dome and other nozzles protrude outside. Vessels have a slope of 1:200 min. for drainage purpose. 2. ADVANTAGES OF MOUNDED BULLETS Mounded bullets have asand cover, whichcantakeimpact of external missile bodies. Scenario of BLEVE (boiling liquid expanding vapour explosion) is eliminated, since no fire possible below the bullets. Reduced fire case PSV loads as compared to spheres. Reduced firewater requirement for firefighting. Difficult for external agencies to identify the mound as a storage facility. Mound cover protectsthevessels against Heat radiation from nearby fire, Pressure wave originating from an explosion, Impact by flying objects, Sabotage, etc. It reduces site area due to less stringent inter spacing requirements. Mounded bullet installation is more space efficient than spheres. This is because of the smaller vessel-to-vessel spacing and due to the smaller safety distance requirement between the mounded storage vessels and items such as control rooms, buildings, roads etc. Mounded bullets offer the possibility of partial or total off-site construction. Mounded bullets are installed on sand bed foundations,which allowtheloadto be transferred uniformly to the underlying sand. This requires no heavy foundation work and offers uncomplicated, low cost installation. The preferred type of foundation for a mounded storage vessel is a continuous sand bed, supporting the vessel over its entire length. The use of the sand foundations allows the vessels to be installed early in the project and also allows vessel loadings to be predicted more accurately for vessel design. Usually the foundation will be constructed with a slope of at least 1:200 to facilitate draining of the vessel and the sand beneath the vessel must have adequate elevation not less than 0.76 m to facilitate drainage. Normally mound is provided with either earth, sand or concombustible materials like perlite, vermiculate, etc. for at least 700 mm thickness. As there are possibilities for foundation settlement, the surrounding of bottomnozzle should be filled with such material that can absorb settlement. Provisions are provided for monitoring the settlement of vessel in mounded storage facility. Bullets must be coated with special corrosion inhibiting layers such as epoxy layers and cathodic protection is critical to prevent corrosion. 3. DESIGN PARAMETERSFOR PRESSUREVESSEL American Society of Mechanical Engineer's (ASME)Boiler and Pressure Vessel Code (BPVC) Section VIII, Division2 has been employed for the design of bullet. The parameters considered for the design are shown in Table I. Table -1: Design Parameters Design Pressure (Internal) 14.5 kg/cm2 Design Pressure (External) 2 kg/cm2 Design Temperature -6 0C to +55 0C Max. Working Pressure 15.4 kg/cm2 Operating Temperature 40 0C Capacity 85 m3 Length 10 m Diameter 3.5 m Density of LPG 490 kg/m3
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 2 Design code ASME Section VIII Division 2 Wind design code IS-875 Seismic design code IS-1893 RSM The assemblage of different components such as shells, heads, nozzles and stiffener rings usually constructs pressure vessels. Fig:-1 Mounded pressure vessel with stiffening rings 3.1 Shell Shells are the primary components that store liquids. Cylindrical shells are widely employed as they are having maximum section modulus and minimum induced stress for a given diameter. Pressure vessel shells are welded together to form a structure that has a common rotational axis. Spherical and conical shells are also in use. 3.2 Heads A variety of heads are used for closing the ends of pressure vessel shells. These include hemispherical, elliptical, torispherical,conical and flat shaped heads. Curved configurations are stronger and allow the heads to be lighter, thinner and less expensive than flat heads. Headsare usually categorized by their shapes. Ellipsoidal, hemispherical, torispherical, conical, tori-conical and flat are the common types of heads. 3.3 Nozzle Nozzles are necessary components of pressure vessel for the process industries. Nozzle is a component that is welded to the shell or heads of a pressure vessel for connecting the vessel to inlet and outlet pipes to convey workingfluid in and out of the vessel. In order to minimize stress concentrations, preferred shape of nozzles are circular. Usually the nozzle ends are flanged to allow for the connections and to permit easydisassemblyformaintenance or access. 3.4 Stiffener Rings Stiffener rings are used all around the periphery of the vessel to increase the moment of inertia at local positions, thus increasing the resistance or strength and reducing the thickness requirements.The material used for stiffener rings is of comparatively low cost and it allows economically favorable manufacturing of pressure vessels. 3.5 Loads on MoundedBullet The analysis of mounded bullet is carried out by considering different loads mentioned in EEMUA Publication190:2005. Dead weight of the bullet, internal design pressure, weight of the maximum volume of liquid allocated to one stiffener, the pressure exerted by the mound on top of the cylinder and domed ends, axial loads due to changes in vessel length which are caused by variations in pressure and temperature, pressureexertedby the foundation and earthquake loads are considered in the analysis. 3.6 Load Combinations There are three load combinations considered in the analysis for two support conditions, middle soft case and middle hard case, as mentioned in clause A.4.2.10 of EEMUA190: 2005. Service (Filled with LPG in corroded condition) Internal Design Pressure + Liquid Head + Design Temperature + Weight of Mound. Hydro test (Filled with water and in un-corroded (new condition) Hydro test pressure + Liquid Head + Weight of mound Service (Filled with LPG in corroded condition) Internal Design Pressure + Liquid Head + DesignTemperature + Weight of mound + Seismic loads The material used for the construction of different parts of the bullet along with their tensile strengthand yield stress values are listed in Table II Table II Material Specification Description Material Type of Steel Tensile Stres (MPa) Yield Stress (Mpa) Shells SA-516 70 Carbon Steel 485 260 Dished Ends SA-516 70 Carbon Steel 485 260 Rings SA-516 70 Carbon Steel 485 60 Nozzles SA-350 LF2 Carbon Steel 485 248.22
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 3 4. DESIGN CALCULATIONS FORSHELLTHICKNESS WITHOUT STIFFENING RING Fig:-2 Internal Pressure calculations Fig:-3 External Pressure calculations From the above two figures, we can note that the minimum thickness requiredforshelltocompensateinternal pressure is 17.14 mm i.e 18 mm nominal and the corresponding thickness against external pressure is 21.55 mm i.e 22 mm nominal. Therefore, extra 4mm thickness is required to compensate external pressure.Thisisavoidedby the use of stiffening ring. 5. DESIGN CALCULATIONS FORSHELLTHICKNESS WITH STIFFENING RING Fig:-4 Internal pressure calculations Fig:-5 External pressure calculations After the application of stiffening ring, we can see that the external required thickness has reached below 15 mm, thereby making the internal pressure thickness governing. The stiffening ring cross section used in this case is as follows: Fig:-5 External pressure calculations
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 4 6. RESULTS Table III Steel Requirement Description Shell Thk (governing) Steel Plate required (in Kgs) Total Wt. saved (kg) Without Stiffner 22mm 15666 With Stiffner 18mm 12817 2849 In our case the weight of stiffenering ring each is 1000 Kg. Therefore with the use of 2 Stiffening rings we can manage to save upto 850 kg Steel. For heavy capacity mounded vessels, where the weight of mound is also quite significant, there could be high amount of steel that would be saved. REFERENCES [1] ASME Boiler & Pressure Vessel Code Section VIII 2 Division: Alternative Rules for Construction of Pressure Vessels, Pressure Vessels Division, American Society of Mechanical Engineers, New York. 2007. [2] Barge, V.H., S.S. Gawade and V. Patil (2013) Thermal- Structural Analysis & Optimization of Pressure Vessel using Finite Element Analysis. International Journal of Advanced Engineering Research and Studies. 4. 104-106. [3] Bednar, H.H. (1986) Pressure Vessel DesignHandbook,2 Edition, Krieger Publishing Company, Malabar, FL, USA. [4] Block, D.L., M.F. Card and M.M. Mikulas (1965) Buckling of Eccentrically Stiffened Orthotropic Cylinders, Langley Research Center, National Aeronautics and Space Administration, Washington. D. C. USA. [5] Borovkov, A.I. and D.S. Mikhaluk (2002) Finite Element Stress Analysis and Multi-Parameter Optimizationofa High- Pressure Vessel. Proceedings of International ANSYS conference, Canonsburg, PA, USA. April. [6] Braestrupe, M.W. (2005) Design and Installation of Marine Pipelines. 1st Edititon. Blackwell Science Ltd, OX, UK [7] Deng, Y.C. and G. Chen (2010) Carrying Capacity of Pressure Vessels Under Hydrostatic Pressure. Tech Science Press. 4. 65-75 [8] Guide for the Design, Construction and use of Mounded Horizontal Cylindrical VesselsforPressurisedStorageofLPG at ambient temperatures, Publication 190, EEMUA, Beech Street, London. 2005. [9] Heckman, D. (1998) Finite Element Analysis of Pressure Vessels. Summer Internship programme, Monterey Bay Aquarium Research Institute, CA, USA. [10] Khan, S.M.A. (2010) Stress Distributions in a Horizontal Pressure Vessel and the Saddle Supports. International Journal of Pressure Vessels and Piping. 87. 239-244. [11] Stefanovic, R. and Y. Noman (2012) DesignandAnalysis of Buried Liquid PetroleumGasStorageBulletsSupported on Multiple Saddles. Journal of Pressure Vessel Technology. 134. 035001.1-6. [12] Xue, L., G.E.O. Widera, and Zhifu Sang (2008) Burst Pressure Prediction of Cylindrical Shell Intersection.Journal of Pressure Vessel Technology. 130. 1-5. [13] Yogesh, K. and M.S.R. Lakshmi (2012) Design and Finite Element Analysis of Mounded Bullet. Journal of Exclusive Management Science. 1. 1-14.