Static and Fatigue Analysis of Pressure Vessel as per ASME Codes

Static & Fatigue Analysis of
Pressure Vessel
___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Project Report
Submitted to
Mechanical Engineering Department
U. V. Patel College of Engineering (GNU)
2018-19
Under the guidance of Submitted by
Dr. Bhavesh Patel Utsav Patel
Associate Professor (15012031061)
Mechanical Engineering Department
UVPCE – GNU

DEPARTMENT OF MECHANICAL ENGINEERING
CERTIFICATE
This is to certify that, Mr. Utsav Mahendrabhai Patel, Enrollment No.
15012031061, VIIIth
semester, pursuing B.Tech. in Mechanical
Engineering has successfully completed the project titled “Static and
Fatigue Analysis of Pressure Vessel” in the presence of the undersigned
examiners, for the academic year 2018-19.
Guided by:
………………………
Dr. Bhavesh Patel
Associate Professor
Project Coordinator: Head of Department (I/C):
……………………… ………………………
Prof. D. H. Patel Dr. C. P. Patel
Assistant Professor

Static and Fatigue Analysis of Pressure Vessel – Project Report
i
ACKNOWLEDGEMENT
In Gujarati language, one word ‘kritagya’ means that you should be thankful to person who helped
you in any way, so here is my chance to express my ‘deepest thanks’ and ‘richest gratitude’
towards personalities who helped me in my project.
Firstly, I express my deepest thanks to my guide Dr. B. P. Patel, Associate Professor, Mechanical
Engineering Dept., U. V. Patel College of Engineering, for his continuous guidance and support,
constant encouragement with ideas and cross checking of results. He showed faith in my work
and it has been a great pleasure to have him as my ‘project guide’.
I would like to thank, Dr. C. P. Patel, Head of Department (I/C), Mechanical Engineering Dept.,
U. V. Patel College of Engineering, for his cooperation and support.
Also, I am thankful to Mr. Kamlesh Chikhaliya, Executive Design Engineer, Linde Engineering,
for giving me wonderful guidance as well as for remarking my design.
I would like to thank my project coordinator, Prof. D. H. Patel, Assistant Professor, Mechanical
Engineering Dept., U. V. Patel College of Engineering, for examining my work and also for
providing necessary guidance.
I would like to thank all the members of mechanical engineering department of U. V. Patel College
of Engineering, for their unconditional support and also for providing me a friendly atmosphere.
Last but not least, I would like to thank my parent, for their constant support, encouragement and
also for always wishing best for me.

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ABSTRACT
Pressure vessels are widely used in power generating plants, industrial plants, marine applications,
space applications, etc. They often operate under extreme conditions, at high temperature and high
pressure. Hence, pressure vessels can be dangerous, and fatal accidents have occurred in the
history of their development and operation.
This makes pressure vessels highly sophisticated system. Therefore, pressure vessels should be
designed and analyzed by manufacturing industries as per different engineering authorities such
as ASME, IBR and PED. These codes provide the procedure to design the pressure vessels as per
different application requirements.
Here, pressure vessel designed as per ASME standards in order to get the design for safe working
operation. Different sections of ASME Boiler and Pressure Vessel Codes are used in order to
select the material, to determine dimensions and to design different openings. 3D model of
designed pressure vessel prepares with the help of SolidWorks modeling software.
It is very difficult to predict actual behavior of the vessel under loading, so further pressure vessel
should be analyzed by analysis software. Hence, modeled pressure vessel then analyzed for static
and fatigue loading as per ASME guideline. Analysis accomplished with ANSYS software.

iii
INDEX
Sr. No. Contents Page No.
Acknowledgement i
Abstract ii
Index iii
List of Figures iv
List of Tables iv
Notations v
1 Introduction 1-4
1.1 Types of Pressure Vessels 1
1.2 Causes of Pressure Vessel Failure 1
1.3 Factors to be Considered for Designing of Pressure Vessel 1
1.4 Loads Acting on Pressure Vessel 2
1.5 Accidents Occurs in the History of Pressure Vessel 2
1.6 Problem Formulation 3
2 Design of Pressure Vessel 5-13
2.1 Selection of Material 5
2.2 Selection of Welding Material & Welding Process 6
2.3 Design of Vessel Shell 6
2.4 Design of Vessel Head 7
2.5 Design of Openings and Reinforcement 8
2.6 Design and Selection of Flanges 11
2.7 Design of Support 12
3 Modeling of Pressure Vessel 14-15
4 Upgradation in Model 16-17
5 Hydrostatic Test Analysis 18-20
5.1 ASME Guideline for Hydrostatic Test Analysis 18
5.2 Hydrostatic Test Analysis in ANSYS 18
6 Fatigue Analysis 21-22
6.1 ASME Guideline for Fatigue Analysis 21
6.2 Fatigue Analysis in ANSYS 22
7 Conclusion 23
Appendix 24
Bibliography 31

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LIST OF FIGURES
Fig. No. Figure Name Page No.
1.1.1 Vertical Pressure Vessel 1
1.5.1 Bhopal gas factory vessel failure 2
1.6.1 Configuration of Pressure Vessel 4
2.4.1 Skirt length as per Section UW 8
2.5.1 External Reinforcement 9
2.7.1 Design of Skirt Base 13
3.1.1 Model of Pressure Vessel 14
3.1.2 Dimensions of Pressure Vessel 15
4.1.1 Modified Model of Pressure Vessel 17
5.2.1 Equivalent (von-mises) Stress 19
5.2.2 Total Deformation 20
5.2.3 Stress Linearization 20
6.2.1 Fatigue Life 22
LIST OF TABLES
Table No. Table Name Page No.
2.1.1 Selection of Material from ASME Section II/Part D 17
2.1.2 Allowable stress values for selected material 20
2.7.1 Design of Skirt Base 20
4.1.1 Different analysis results with different modification in model 28
5.2.1 Result of stress linearization 29
6.1.1 Fatigue Screening Criteria for Method A 30

v
NOTATIONS
Following notations are used in the design of pressure vessel:
Symbol
D
R
L
P
T
CA
E
Dn
Dhh
Dmh
Disb
tsb
S
ST
SY
Tmax
Tmin
ρ
µ
ts
th
tn
te
Rn
Dp
tw
thh
Rhh
Rmh
tmh
tf
O
Ps
PHS
W
Pm
Pb
Meaning
Inside Diameter of shell
Inside Radius of the shell
Length of the shell
Design Pressure Gauge Absorption
Design Temperature Absorption
Corrosion Allowance
Longitudinal Joint Efficiency
Diameter of Inlet & Outlet Nozzle
Diameter of Handhole
Diameter of Manhole
Inside Diameter of Skirt
Thickness of skirt
Maximum Allowable Stress
Minimum Tensile Strength
Minimum Yield Strength
Maximum Temperature Limit
Minimum Temperature Limit
Density
Poisson’s Ratio
Thickness of Vessel Shell
Thickness of Vessel Head
Thickness of nozzle
Thickness of Reinforcement
Inside radius of the Nozzle
Outer diameter of Reinforcing Element
Weld Size at nozzles
Thickness of handhole opening
Inside radius of the handhole
Inside radius of the manhole
Thickness of manhole opening
Thickness of flange
Outer diameter of flange
Static Pressure
Hydrostatic Pressure
Dead Weight
Membrane Stress
Bending Stress
Unit
mm
mm
mm
N/mm2
℃
mm
-
mm
mm
mm
mm
mm
N/mm2
N/mm2
N/mm2
℃
℃
kg/m3
-
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
MPa
MPa
N
MPa
MPa

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1. Introduction
A pressure vessel is a container designed to hold gases or liquids at a pressure substantially
different from the ambient pressure [1]
. Pressure vessels are used for either transmitting fluid or
for storing fluid. Storage vessels are widely used in industrial plants for storing chemical at below
or higher than the atmospheric pressure. Pressure vessels can be dangerous, and fatal accidents
have occurred in the history of their development and operation. Hence pressure vessels should
be designed and analysed as per standards.
1.1 Types of Pressure Vessels
According to configuration pressure vessels can be classified as follows:
1. Horizontal Pressure Vessel
2. Vertical Pressure Vessel
3. Spherical Pressure Vessel
Fig. 1.1.1 Vertical Pressure Vessel
1.2 Causes of Pressure Vessel Failure
Generally, failure of pressure vessels occurred due to one of the following reasons:
 Improper Selection Material is the major part of the defect in the vessel.
 Incorrect design or incorrect design data and also, the inaccurate or incorrect design methods
causes of failure.
 Poor quality control and improper fabrication procedures including welding are fabrication
problems.
 Failure due to corrosion fatigue.
 Due to environmental problems.
1.3 Factors to be Considered for Designing of Pressure Vessel
Following factors should be considered for designing of pressure vessel:
 Maximum allowable working pressure or design pressure is the main factor for pressure vessel
design. Pressure in the vessel should not exceed the maximum allowable pressure otherwise
it fails.

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 Allowable working temperature range or design temperature is also an important factor for
pressure vessel design, if temperature varies beyond temperature limits then it tends to alter
the properties of material.
 Factor of safety
 Corrosion allowance is the amount of material in vessel that is available for corrosion without
affecting the pressure containing integrity.
1.4 Loads Acting on Pressure Vessel [2]
In working condition, pressure vessels are subjected to following loads:
 Internal or external design pressure
 Weight of the vessel and normal contents under operating or test conditions (this includes
additional pressure due to static head of liquids)
 Superimposed static reactions from weight of attached equipment, such as motors, machinery,
other vessels, piping, linings, and insulation
 The attachments of internals and vessel supports such as lugs, rings, skirts, saddles, and legs
 Cyclic and dynamic reactions due to pressure or thermal variations or from equipment
mounted on a vessel, and mechanical loadings
 Impact reactions such as those due to fluid shock
 Temperature gradients and differential thermal expansion
1.5 Accidents Occurs in the History of Pressure Vessel [3]
Following are some cases of pressure vessels failure:
 Bhopal gas Leakage; December 2, 1984; 25000 killed, 600000 injured.
 Feyzin Explosion; January 4, 1966; 18 killed, 81 injured.
 Texas city; March 23, 2005; 15 killed, 150 injured.
Fig. 1.5.1 Bhopal gas factory vessel failure

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1.6 Problem Formulation
This problem given by vendors. Vendors provided problem definition and required data for
designing. Problem definition is as follows:
 Design a pressure vessel used as an adsorber in chemical plant and analyze it for static and
fatigue loading in order to get safe operation. Configuration of pressure vessel is as shown in
fig. 1.6.1 and primary data for design is given below:
 Equipment : Adsorber
 Orientation : Vertical
 Total Shell Length : 4800 mm or 188.98 in
 Vessel Inside Diameter : 1400 mm or 55.12 in
 Design Pressure Gauge Adsorption : 9.316 N/mm2
or 93.1632 psi
 Design Temperature Adsorption : 65 ℃
 Corrosion Allowance : 3 mm
 Longitudinal Joint Efficiency : 1
 Weight of filling : 5500 kg
 Excepted life time : 20 Years
 Shell/Dished End Material : Carbon Steel (SA516 Gr. 70)
 Diameter of Inlet & Outlet Nozzle : 152.4 mm or 6 in
 Diameter of Handhole : 203.2 mm or 8 in
 Diameter of Manhole : 609.6 mm or 24 in
 Type of Support : Skirt Support
 Inside Diameter of Skirt : 1435 mm
 Thickness of skirt : 20 mm
 Base Bolting : 1600 BCD/12 × M30

4
Fig. 1.6.1 Configuration of Pressure Vessel

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2. Design of Pressure Vessel
Pressure vessel designed as per ASME BPVC Section VIII/Division II (1998 ASME) [2]. In
which, “Subsection A/Part UG – General Requirement for All Methods of Construction and All
Materials” considered for selection of material as well as to calculate the design data.
2.1 Selection of Material
From part UG, UG – 4 (which describes general requirement for the selection of material) says
that, “Material subjected to internal pressure, those specifications should be obtained from section
II. Also, material permitted by the applicable part of Section VIII/Subsection C”. Since given
pressure vessel will be manufactured from plate, UG – 5 describes material requirement for plate,
strip or sheet. But UG – 5 refers same as UG – 4.
Selected material for pressure vessel is: SA 516 Gr. 70 [Low Alloy Steel, Plate]
This material is present in Table UCS – 23. So, this material can be used for manufacturing of
pressure vessel. From UCS – 6 (for Steel Plates), allowable stresses of these materials given in
Table – 1A of Section II/Part D for different temperature ranges.
From ASME BPVC Section II/Part D Table – 1A (2015) [4], following properties are obtained
for selected material SA516 Gr.70 (Plate) (Refer Table 2.1.1),
 Minimum Tensile Strength, ST = 70 ksi or 482.63 N/mm2
 Minimum Yield Strength, SY = 38 ksi or 262.00 N/mm2
 Minimum Temperature Limit, Tmin = -20 ℉ or -28.89 ℃
 Maximum Temperature Limit, Tmax = 1000 ℉ or 537.78 ℃
Other special notes from Table – 1A, G10, S1, T2 are not applicable for given application.
For Allowable Stress:
From Table – 1A, maximum allowable stress is different for different temperature ranges. Here,
working temperature is 65 ℃ (or 149 ℉). Hence, as per working temperature range,
 Maximum Allowable Stress, S = 20 ksi or 137.89 N/mm2
Also, from Mandatory Appendix 1/Table 1-100(Refer Table 2.1.2),
 For cast ferrous material,
S = .
× 𝑆T (for room temperature and below)
=
.
.
× 𝑆T × 𝑅T (for above room temperature)
Where,
RT = ratio of tensile strength at average temperature to tensile strength at room
temperature (obtained from trend curve).
Note: Given working temperature is not too much higher than room temperature hence first
equation can be used. Also, there is no change in material strength up to 500 ℉.

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S = .
× 𝑆T
= .
S = 20 ksi or 137.89 N/mm2
 Allowable stress, S = 20 ksi or 137.89 N/mm2
Also, from Section II/Table PRD,
 Poisson’s Ratio = 0.30
 Density, 𝜌 = 0.282 lb/in3
or 7805.73 kg/m3
2.2 Selection of Welding Material & Welding Process
UG – 9 which describes welding materials says that welding material and processes comply with
Section II/Part C.
From ASME BPVC Section II/Part C (2015) [5], following are some specifications for welding
material and processes,
 SFA 5.1/ SFA 5.1M (Welding Specification for Carbon Steel electrodes for SMAW)
 SFA 5.17/SFA 5.17M (For Submerged Arc Welding)
 SFA 5.18/SFA 5.18M (For Gas Shielded Arc Welding)
 SFA 5.20/SFA 5.20M (For Flux Cored Arc Welding)
 SFA 5.25/SFA 5.25M (For Electroslag Welding)
 SFA 5.26/SFA 5.26M (For Electro Gas Welding)
2.3 Design of Vessel Shell:
UG – 27 of Design Section gives required thickness of Vessel Shell. So, from UG – 27,
For Cylindrical Shell,
1. As per circumferential stress (Longitudinal Joints)
If P < 0.385SE, then
𝑡s = .
2. As per longitudinal stress (Circumferential Joints)
If P < 1.25SE, then
𝑡s = .
As longitudinal joints efficiency is given and also data satisfies condition P < 0.385SE. Hence,
thickness of vessel shell is given by,

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𝑡s = .
Where,
ts = minimum thickness required of shell, (in)
P = internal design pressure, (psi)
S = maximum allowable stress, (psi)
R = inside radius of the shell, (in)
E = longitudinal joint efficiency
𝑡s =
. × .
× . × .
𝑡s = 1.9406 𝑖𝑛
𝑡s = 49.2925 𝑚𝑚
𝑡s = 49.2925 + 𝐶𝐴 [Considering the Corrosion Allowance (CA=3 mm)]
𝑡s = 52.2925 𝑚𝑚
𝑡s ≈ 54 𝑚𝑚
 Thickness of Vessel Shell, ts = 54 mm
Note: Stiffening rings are not required because pressure vessel is not subjected to external
pressure.
2.4 Design of Vessel Head
UG – 32 describes the design consideration for “Formed Heads, and Sections, Pressure on
Concave Side”. It says design consideration are different for different types of heads. Type of
heads or shape of heads should be selected based on type of application. Following are the types
of head:
i. Ellipsoidal Head
ii. Torispherical Head
iii. Hemispherical Head
iv. Tori conical Head
v. Conical Head
 Selected type of Head: Semi Ellipsoidal Head (2:1)
For Ellipsoidal head,
1. Thickness of Head
From UG – 32, the required thickness of a dished head of semi ellipsoidal form (for 2:1
elliptical head), shall be determined by,
𝑡h = .
Where,
th = minimum thickness required of head, (in)

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D = inside diameter of the shell, (in)
𝑡h =
. × .
× × . × .
𝑡h = 1.8746 𝑖𝑛
𝑡h = 47.6148 𝑚𝑚
𝑡h = 47.6148 + 𝐶𝐴 [Considering the Corrosion Allowance (CA=3 mm)]
𝑡h = 50.6148 𝑚𝑚
𝑡h ≈ 52 𝑚𝑚
 Thickness of Vessel Head, th = 54 mm
2. Skirt Length
As per UG – 32 (l), all formed heads, thicker than the shell and concave to pressure, intended
for butt welded attachment, shall have a skirt length sufficient to meet the requirement of fig.
UW – 13.1 (refer fig. 2.4.1).
Fig. 2.4.1 Skirt length as per Section UW
 Since, 𝒕h ≤ 𝒕s, skirt length is not required.
2.5 Design of Openings and Reinforcement
From UG – 36, which describes design consideration for openings in pressure vessel,
a) Shape of Opening:
For cylindrical shell vessel, shape of opening can be circular, elliptical, or obround.
 Selected shape of opening: Circular

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b) Size of opening:
1. Pressure vessels having inside diameter 1520 mm or less should be designed by section
UG – 36 to UG – 43.
2. In this case, properly reinforced openings in formed heads and cylindrical shells are not
limited in size.
For opening in an end closure (in heads), which is larger than one half the inside diameter of
shell, then reducer section is required.
 In this case, reducer section is not required, because any openings in the end closure is not
greater than half of the inside diameter of shell.
1. Selection of reinforcement for nozzles and handhole
 Selected Reinforcement type: External Reinforcement
Fig. 2.5.1 External Reinforcement
 From UG – 40 (limits of reinforcement), the outside diameter of reinforcement should be
equal to or grater than twice the inside diameter of nozzle (means Dp ≥ 2Dn).
 There is no consideration provided for thickness of reinforcement (te).
2. Design of Inlet and Outlet Nozzle
From Appendix L/L – 7.2, Thickness of the nozzle is given by,
𝑡n = .
× 𝑅n
Where,
tn = thickness of nozzle, (in)
Rn = inside radius of the shell, (in)

10
𝑡n =
. ×
× . × .
𝑡n = 0.2112 𝑖𝑛
𝑡n = 5.3656 𝑚𝑚
𝑡n = 5.3656 + 𝐶𝐴 [Considering the Corrosion Allowance (CA=3 mm)]
𝑡n = 8.365 𝑚𝑚
𝑡n ≈ 10 𝑚𝑚
 Thickness of inlet and outlet nozzle, tn = 10 mm
 Thickness of Reinforcement, Assume te = 15 mm
 Outer diameter of Reinforcing Element, Dp = 14 in = 355.6 mm
 Weld Size, tw = 𝟎. 𝟕 × 𝒕e = 10.5 mm
3. Design of Handhole Opening
From Appendix L/L – 7.2, Thickness of the handhole is given by,
𝑡hh = .
× 𝑅hh
Where,
thh = thickness of handhole opening, (in)
Rhh = inside radius of the handhole, (in)
𝑡hh =
. ×
× . × .
𝑡hh = 0.2817 𝑖𝑛
𝑡hh = 7.1542 𝑚𝑚
𝑡hh = 7.1542 + 𝐶𝐴 [Considering the Corrosion Allowance (CA=3 mm)]
𝑡hh = 10.1542 𝑚𝑚
𝑡hh ≈ 12 𝑚𝑚
 Thickness of Handhole Opening, thh = 12 mm
 Thickness of Reinforcement, Assume te = 20 mm
 Outer diameter of Reinforcing Element, Dp = 18 in = 457.2 mm
 Weld Size, tw = 𝟎. 𝟕 × 𝒕e = 14 mm
4. Design of Manhole Opening
From Appendix L/L – 7.2, Thickness of the manhole opening is given by,

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𝑡mh = .
× 𝑅mh
Where,
tmh = thickness of manhole opening, (in)
Rmh= inside radius of the manhole, (in)
𝑡mh =
. ×
× . × .
𝑡mh = 0.8450 𝑖𝑛
𝑡mh = 21.4626 𝑚𝑚
𝑡mh = 21.4626 + 𝐶𝐴 [Considering the Corrosion Allowance (CA=3 mm)]
𝑡mh = 24.4626 𝑚𝑚
𝑡mh ≈ 25 𝑚𝑚
 Thickness of Manhole Opening, tmh = 25 mm
5. Inspection of Openings
From UG – 46, all pressure vessels for use with compressed air shall be provided with suitable
manhole, handhole or other inspection openings for examination and cleaning.
As per (f)(3), all pressure vessels over 36 in. inner diameter shall have a manhole or at least
two handholes.
As per (g)(1) & (2), a circular manhole shall be not less than 15 in. diameter and a handhole
opening shall be not less than 2 in. × 3 in.
 So, all the required consideration for openings are satisfied.
2.6 Design and Selection of Flanges
According to UG – 44, which describes Flanges and Pipe Fittings design consideration says that
selection of flanges depends on pressure-temperature characteristics.
Selection of flanges should be as per ASME B16.
From ASME B16.5 (2003) [6],
 From Table 1A (4), Selected Material is: CA 516 Gr.70
 From Table 2-1.1:
For Working Temperature = 65 ℃
For Working Pressure = 93.16 bar
Selected Class = Class 600 [T = 100 ℃ & P = 93.2 bar]
Class 900 [T = 100 ℃ & P = 139.8 bar]

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Selection of Nominal Pipe Size (NPS):
1. Welding neck flanges for inlet and outlet nozzle:
From Table 18, for Class 900, the dimensions of the flanges are not specified and can be
manufactured as per purchaser requirement. But ranges in between NPS 5 to NPS 6.
2. Blind flange for handhole:
From Table 18, for Class 600/NPS 8,
Outer diameter of flange, O = 420 mm
Thickness of flange, tf = 55.6 mm
3. Blind flange for manhole:
From Table 18, for Class 600/NPS 24,
Outer diameter of flange, O = 940 mm
Thickness of flange, tf = 101.6 mm
2.7 Design of Support
Following are type of supports used in pressure vessels:
i. Leg support
ii. Saddle support
iii. Skirt support
Following are the design data for vessel support:
 Selected Support Type: Skirt Support
 Selected Material: SA 516 Gr.70
 Inside Diameter of Skirt, Disb = 1435 mm
 Thickness of skirt, tsb = 20 mm
 Bolting: 1600 BCD/12 × M30
 Bolting Material: IS 2062 Gr. A (Structural Steel)
 Base Design: As per EIL Standard: 7-12-0004 [7] (Refer Fig. 2.7.1 and Table 2.7.1)
 Holes: For inlet nozzle (6 in.)
For inspection opening (6 in.)

13
Fig. 2.7.1 Design of Skirt Base

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3. Modeling of Pressure Vessel
Model of pressure vessel prepared by modeling software Solidworks 2017. Model of pressure
vessel is prepared as per obtained design data. Hence, this model is ready to use for further
analysis. Model of pressure vessel is shown in fig. 3.1.1 below.
Fig. 3.1.1 Model of Pressure Vessel

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Detailed drawing of pressure vessel is shown in fig. 3.1.2. All the dimensions of pressure vessels
are provided in the drawing of fig. 3.1.2.
Fig. 3.1.2 Detailed Drawing of Pressure Vessel

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4. Upgradation in Model
After modeling, number of static analysis performed, in order to have an idea that, where
modification is needed. Some of those analysis with respective changes are shown in Table.4.1.1.
After observing results of those analysis with different changes in model, few modifications had
been made in the model. All those changes made without disobeying any standards and it didn’t
have any effect on design considerations. Following are the modifications which had been made:
 Length of manhole: 196 to 146 mm
 Thickness of manhole: 25 to 34 mm
 Geometry of outlet nozzle (refer fig. 4.1.1)
 Position of outlet nozzle (refer fig. 4.1.1)
 Welding material added R10 & R15 fillets
 Fillet at manhole junction R10
 External reinforcement on manhole: 15 mm
 Thickness of outlet nozzle: 10 to 15 mm
Final model of pressure vessel is shown in fig. 4.1.1.

17
Fig. 4.1.1 Modified Model of Pressure Vessel

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5. Hydrostatic Test Analysis
As this model of pressure vessel designed for working as an adsorber in chemical plant, it will be
subjected to hydrostatic loading. Hence, it must be analyzed for hydrostatic loading.
5.1 ASME Guideline for Hydrostatic Test Analysis
From ASME general requirements section, following loadings should be considered in hydrostatic
test analysis:
 Static Pressure, Ps (Internal pressure = 9.316 MPa)
 Hydrostatic Pressure, PHS (For Respective Height & Given Fluid)
 Dead Weight, W (Earth Gravitational Effect = 9.8066 m/s2
)
 Total loading on pressure vessel, PT: Ps + PHS + W
As per ASME BPVC Section VIII / Division 2, Part AD-151.1,
a) A calculated primary membrane stress intensity Pm of 90% of the tabulated yield strength Sy
at test temperature as given in Section II, Part D.
means, membrane stress, Pm ≤ 0.9Sy (Where, Sy = 262 MPa)
Pm ≤ 235.8 MPa
b) A calculated primary membrane plus primary bending stress intensity Pm + Pb not to exceed
the applicable limit given below:
1. If Pm ≤ 0.67Sy, then Pm + Pb ≤ 1.35Sy
If Pm ≤ 175.54 MPa, then Pm + Pb ≤ 353.7 MPa
2. If 0.67Sy < Pm < 0.9Sy, then Pm + Pb ≤ 2.35Sy – 1.50Pm
If 175.54 MPa < Pm < 235.8 MPa, then Pm + Pb ≤ (615.7 – 1.50Pm) MPa
5.2 Hydrostatic Test Analysis in ANSYS
 Analysis Input Data:
1. Mesh Type: Hex Dominant
2. Mesh Size: 30 mm
3. Fixed Support: At Bottom Face
4. Static Pressure: 9.316 MPa normal to surface
5. Hydrostatic Pressure: For fluid density 832 kg/m3
and for total height of 5350 mm
6. Earth gravity (Dead Weight): 9.8066 m/s2
 Results of Analysis:
1. Equivalent (von-mises) Stress = 361.56 MPa [Refer Fig. 5.2.1]
2. Total Deformation = 2.0905 mm [Refer Fig. 5.2.2]

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3. Maximum Stress Location: At Manhole Junction [Refer Fig. 5.2.3]
Hence, it is required to perform stress linearization at that section.
4. Membrane Stress, Pm [Refer Table. 5.2.1]
Pm = 190.63 MPa (≤ 235.8 MPa. Hence, it is Safe)
Pm + Pb = 192.06 MPa (≤ 329.8 MPa. Hence, it is Safe.)
Hence, from result of Hydrostatic Test Analysis, it can be seen that the pressure vessel is
safe under static loading.
Fig. 5.2.1 Equivalent (von-mises) stress

20
Fig. 5.2.2 Total Deformation
Fig. 5.2.3 Stress Linearization

21
6. Fatigue Analysis
6.1 ASME Guideline for Fatigue Analysis
From ASME BPVC Section VIII / Division 2 (2015) [8], Part 5, 5.5 (Protection against failure
from cyclic loading),
 A fatigue evaluation shall be performed if the component is subjected to cyclic operation. The
evaluation for the fatigue is made on the basis of the number of applied cycles of a stress or
strain range at a point in a component. The allowable number of cycles should be adequate
for the specified number of cycles as given in the user’s design specification.
 Screening criteria are provided in 5.5.2 that can be used to determine, “is fatigue analysis
required as part of a design or not?”. If the component does not satisfy the screening criteria,
a fatigue evaluation shall be performed using the techniques in 5.5.3, 5.5.4 or 5.5.5.
As per 5.5.2. (Screening criteria for fatigue analysis),
a) Gives three screening option if any one of the screening options is satisfied, then a fatigue
analysis is not required.
1. Based on experience
If manufacturer having pressure vessel of same characteristics as already designed one.
2. Method A (limited applicability)
Applicable only if minimum tensile strength of selected material is less than or equal to 552
MPa.
3. Method B (unlimited applicability)
b) Only some of the components (non-integral parts such as nozzles) are required fatigue
screening.
c) If the specified number of cycles is greater the 106
, then the screening criteria is not applicable
and a fatigue analysis is required.
Since, minimum tensile strength of selected material is 482.63 MPa (≤ 552 MPa), so Method
A is applicable for fatigue screening.
As per Method-A,
Step-1: Determine load history based on the information in the user’s design specifications. The
load history should include all cyclic operating loads and events that are applied to components.
*Note: Since these data are not provided to us so this screening process accomplished with some
assumed data.
 Design Pressure Cycles: 10,000 cycles
 Maximum Pressure Limit: 60 bar (65 ℃)
 Minimum Pressure Limit: 50 bar (65 ℃)

22
Step-2: Based on the load history in step 1, determine the expected (design) number of full-range
pressure cycles including startup and shutdown, and designate this value as N∆𝐹𝑃 = 10000.
Step-3: Determine expected number of cycles in which pressure variations exceeds 20 % of the
design pressure for non-integral construction, and designate this value as N∆PO (≥ 0).
Step-4 & 5: Based on temperature difference, hence not applicable because temperature remains
constant.
Step-6: If the expected number of operating cycles from step 2, 3, 4, 5 satisfy the criterion in Table
6.1.1. then a fatigue analysis is not required as part of the vessel design. If it does not satisfy that
then fatigue analysis is required.
From Table. 6.1.1,
For Nonintegral Construction,
NΔFP+NΔPO+NΔTE+NΔTα ≤ 60 (For junctions, nozzle attachments knuckle reinforced h-heads)
NΔFP+NΔPO+NΔTE+NΔTα ≤ 400 (For other components)
As per given load history data, model does not satisfy any of the consideration. Hence, fatigue
analysis is required as a part of the vessel design.
6.2 Fatigue Analysis in ANSYS
Analysis input data is same as that of static analysis. In result Fatigue Life is obtained for reversed
loading of combined loads, using Gerber Theory criteria which is best suited for ductile material.
For result refer fig. 6.2.1.
 Fatigue Life: 3695.1 cycles.
Fig. 6.2.1 Fatigue Life

23
7. Conclusion
After getting this problem, pressure vessel designed as per ASME Codes. During the designing,
different sections of codes are used for each and every step. After obtaining all the designed data,
3D model of pressure vessel prepared as per obtained data.
During the modeling of pressure vessel, some dimensions are undefined, so assumption of those
dimensions is made in order to complete the model. These assumed dimensions do not affect any
design consideration. Selection of these dimensions based on trial and error method.
Pressure Vessel model then analyzed for hydrostatic test and it comes safe under static loading.
For fatigue loading, pressure vessel analyzed under reversed loading. In result, pressure vessel can
be run for at least 3695.1 cycles.

24
Appendix:
Table. 2.1.1 Selection of Material from ASME Section II/Part D [cont’d]

25
Table. 2.1.1 Selection of Material from ASME Section II/Part D [cont’d]

26
Table. 2.1.1 Selection of Material from ASME Section II/Part D

27
Table. 2.1.2 Allowable stress values for selected material
Table 2.7.1 Design of Skirt Base

28
Model
No.
Changes in Model Loading
Mesh
Size
Result
Equivalent
Stress
Total
Deformation
1
Manhole: Blind Flange
Handhole: Blind Flange
Static
Pressure
50
mm
618.54 MPa 33.34 mm
2
Outlet Nozzle: Positioned to
manhole
Manhole: 1000 mm OD & 15
mm reinforcement
Static
Pressure
25
mm
733.43 MPa 11.058 mm
3
Outlet Nozzle: Reduced Area &
Chamfer of 12 mm
Manhole: 20 mm thickness
reinforcement
Static
Pressure
20
mm
552.2 MPa 7.392 mm
4
Outlet Nozzle: Remove sweep
part, 10 mm fillet at junction &
thickness from 10 to 12 mm
Manhole: Thickness 25 mm to
28 mm
Static
Pressure
20
mm
377.94 MPa 2.323 mm
5
Outlet Nozzle: Fillet 10 to 15
mm & Thickness: 12 to 15 mm
Manhole: Fillet 50 mm
Static
Pressure
50
mm
367.91 MPa 1.92 mm
6
Manhole: Fillet increased
Handhole: Reinforcement from
20 to 25 mm
Weld R30 at Handhole & Weld
R20 at Reinforcement
Static
Pressure &
Hydrostatic
Pressure
50
mm
376.35 MPa 1.77 mm
Table. 4.1.1 Different analysis results with different modification in model

29
Table. 5.2.1 Result of Stress Linearization
Node Length [mm] Membrane [MPa] Bending [MPa] Membrane+Bending [MPa] Peak [MPa] Total [MPa]
1 0 190.63 14.212 190.25 8.5367 187.19
2 0.51683 190.63 13.62 190.24 7.6762 187.46
3 1.0337 190.63 13.028 190.24 6.8175 187.74
4 1.5505 190.63 12.436 190.24 5.961 188.01
5 2.0673 190.63 11.843 190.24 5.1072 188.29
6 2.5842 190.63 11.251 190.24 4.2569 188.56
7 3.101 190.63 10.659 190.24 3.4109 188.84
8 3.6178 190.63 10.067 190.25 2.5708 189.13
9 4.1347 190.63 9.4747 190.26 1.7408 189.41
10 4.6515 190.63 8.8825 190.26 0.93823 189.7
11 5.1683 190.63 8.2903 190.28 0.37148 189.98
12 5.6852 190.63 7.6982 190.29 0.88365 190.27
13 6.202 190.63 7.106 190.3 1.6685 190.56
14 6.7188 190.63 6.5138 190.32 2.4738 190.85
15 7.2356 190.63 5.9217 190.34 3.28 191.14
16 7.7525 190.63 5.3295 190.36 4.0828 191.43
17 8.2693 190.63 4.7373 190.38 4.2548 191.71
18 8.7861 190.63 4.1452 190.41 4.4708 191.96
19 9.303 190.63 3.553 190.43 4.6566 192.19
20 9.8198 190.63 2.9608 190.46 4.8078 192.4
21 10.337 190.63 2.3687 190.49 4.9208 192.58
22 10.853 190.63 1.7765 190.52 4.9923 192.74
23 11.37 190.63 1.1843 190.55 5.0192 192.87
24 11.887 190.63 0.59217 190.59 4.9987 192.97
25 12.404 190.63 9.73E-14 190.63 4.9277 193.05
26 12.921 190.63 0.59217 190.67 4.8033 193.09
27 13.438 190.63 1.1843 190.71 4.6224 193.1
28 13.954 190.63 1.7765 190.75 4.3816 193.07
29 14.471 190.63 2.3687 190.79 4.0778 193.01
30 14.988 190.63 2.9608 190.84 3.7073 192.91
31 15.505 190.63 3.553 190.89 3.267 192.76
32 16.022 190.63 4.1452 190.94 2.7543 192.58
33 16.539 190.63 4.7373 190.99 2.1691 192.35
34 17.055 190.63 5.3295 191.04 1.5224 192.07
35 17.572 190.63 5.9217 191.1 0.88852 191.74
36 18.089 190.63 6.5138 191.15 0.76214 191.35
37 18.606 190.63 7.106 191.21 1.5069 190.9
38 19.123 190.63 7.6982 191.27 2.5662 190.39
39 19.64 190.63 8.2903 191.34 3.7992 189.81
40 20.156 190.63 8.8825 191.4 5.1924 189.15
41 20.673 190.63 9.4747 191.47 6.7533 188.41
42 21.19 190.63 10.067 191.54 8.4972 187.58
43 21.707 190.63 10.659 191.6 7.2661 188.15
44 22.224 190.63 11.251 191.68 5.4173 189.05
45 22.741 190.63 11.843 191.75 3.8187 189.94
46 23.257 190.63 12.436 191.82 2.7895 190.82
47 23.774 190.63 13.028 191.9 2.8803 191.68
48 24.291 190.63 13.62 191.98 3.9426 192.52
49 24.808 190.63 14.212 192.06 5.3852 193.36

30
Table. 6.1.1 Fatigue Screening Criteria for Method A

31
Bibliography:
Books:
[2] “Rules for Construction of Pressure Vessel (BPVC VIII/Division 1)”, The American
Society of Mechanical Engineers, 1998, pp. 13-59.
[4] “ASME BPVC II Materials Part D”, The American Society of Mechanical Engineers,
2015, pp. 18-21, 922-923.
[5] “ASME BPVC II Materials Part C”, The American Society of Mechanical Engineers, 2015.
[6] “Pipe Flanges and Flanged Fittings (ASME B16.5)”, The American Society of Mechanical
Engineers, 2003, pp. 23, 90-94.
[7] “EIL Standards”, Engineers India Limited, 2014, pp. 216.
[8] “ASME BPVC Section VIII/Division 2”, The American Society of Mechanical Engineers,
2015, pp. 557-560, 582.
Research Paper:
[3] Sumit Dubal and Hemantkumar kadam, “Pressure Vessel Accidents: Safety Approach”,
International Research Journal of Engineering and Technology (IRJET), 2017, pp.3-4.
Websites:
[1] https://en.wikipedia.org/wiki/Pressure_vessel

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