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DESIGN AND ANALYSIS OF
PRESSURE VESSEL
BY JIMIT VYAS AND MAHAVIR SOLANKI
GUIDED BY : MR BHAVESH PATEL
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ACKNOWLEDGEMENT
Certainly, help and encouragement from others are always appreciated, but in
different times, such magnanimity is valued even more. This said, thisDissertation would never have been completed without the generous help and
support that I received from numerous people along the way.
I wish to express my deepest thanks and gratitude to my elite guide Mr Bhavesh
P Patel, Mechanical Engineering Dept., U.V. Patel College of Engg., Mehsana, for
his invaluable guidance and advice, without that the Dissertation would not
have appear in present shape. He also motivated me at every moment during
entire dissertation.
I also hearty thankful and express deep sense of gratitude to Mr. Bhavesh
Prajapati, senior manager at GMM Pflauder, for giving opportunity to undertake
a dissertation in the industry and furnishing the details and help.
Special thanks to Mr. Ankit Prajapati, Design Engineer, at GMM Pflauder, for
his keen interest and guidance in carrying out the work.
I wish to thank the principal Dr. J. L. Juneja and all the staff members of
Mechatronics & Mechanical Dept., U. V. Patel College of Engg., especially to ,
Prof. J. M. Prajapati,Prof. J. P. Patel, Prof. V. B. Patel, for their co-operation,
guidance and support during the work.
Jimit Vyas & Mahavir Solanki
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ASTRACT
The significance of the title of the project comes to front with designing structure of the
pressure vessel for static loading and its assessment by Ansys , is basically a project
concerned with design of different pressure vessel elements such as shell, Dish end
,operating manhole ,support leg based on standards and codes ; and evolution of shell and
dish end analysed by means of ansys .The key feature included in the project is to check
the behaviour of pressure vessel in case of fluctuating load .The [procedural step includes
various aspects such as selecting the material based on ASME codes ,and then designing
on the standards procedures with referring standard manuals based on ASME .Further we
have included the different manufacturing methods practice by the industries and
different aspects of it . And step by step approaches to the NTD method practice by the
industries followed with standards and also included within the report work. This will be
making a clear picture f this method among the reader .
conclusively, this modus operandi of design based on technical standard and
codes ., can be employed on practical design of pressure vessel as per required by the
industry or the problem statement given associated to the field of pressure vessel.
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INTRODUTION:
The pressure vessels (i.e. cylinder or tanks) are used to store fluids under pressure. The
fluid being stored may undergo a change of state inside the pressure vessel as in case of
steam boilers or it may combine with other reagents as in a chemical plant. The pressure
vessels are designed with great care because rupture of pressure vessels means an explosion
which may cause loss of life and property. The material of pressure vessels may be brittle
such that cast iron or ductile such as mild steel.
Cylindrical or spherical pressure vessels (e.g., hydraulic cylinders, gun barrels, pipes,
boilers and tanks) are commonly used in industry to carry both liquids and gases under
pressure. When the pressure vessel is exposed to this pressure, the material comprising the
vessel is subjected to pressure loading, and hence stresses, from all directions. The normalstresses resulting from this pressure are functions of the radius of the element under
consideration, the shape of the pressure vessel (i.e., open ended cylinder, closed end cylinder,
or sphere) as well as the applied pressure.
Two types of analysis are commonly applied to pressure vessels. The most
common method is based on a simple mechanics approach and is applicable to thin wall
pressure vessels which by definition have a ratio of inner radius, r, to wall thickness, t, of
r/t10. The second method is based on elasticity solution and is always applicable regardless
of the r/t ratio and can be referred to as the solution for thick wall pressure vessels. Both
types of analysis are discussed here, although for most engineering applications, the thin wall
pressure vessel can be used.
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Classification of Pressure Vessels
Unfired Cylindrical Pressure Vessels
(Classification Based on IS 2825-1969)
a) Class 1 :
Vessels that are to contain lethal or toxic substances.
Vessels designed for the operation below -20 C and
Vessels intended for any other operation not stipulated in the code.
b) Class 2:
vessels which do not fall in the scope of clas1 and class 3 are to be termed as
class2 vessels. The maximum thickness of shell is limited to 38 mm.
c) class 3:
there are vessels for relatively light duties having plate thickness not in excess of
16 mm,
and they are built for working pressures at temperatures not exceeding 250 c and
unfired .
class3 vessels are not recommended for services at temperatutre below 0c.
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Categories Of Welded Joints
The term categories specifies the location of the joint in a vessels, but not the
type of joint. These categories are intended for specifying the special requirements
regarding the joint type and degree of inspection. IS-2825 specifies 4 categories of welds.
(Refer fig.)
a) category A: longitudinal welded joints within the main sheet, communicating
chambers ,nozzles and any welded joints within a formed or flat head.
b) Category B: circumferential welded joints with in the main shell, communicating
chambers, nozzles and transitions in diameter including joints between the
transtations and a cylinder at either the large of small end, circumferential welded
joints connecting from heads to main shells to nozzles and to communicating
chambers.
c) Category c: welded joints connecting flanges, tubes sheets and flat heads to main
shells , to formed heads , to nozzles or to communicating chambers and any
welded joints connecting one side plate to another side plate of a flat sided vessel.
d) Category d: welded joints connecting communicating chambers or nozzles to
main sheels ,to heads and to flat sided vessels and those joints connecting nozzles
to communicating chambers.
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STRESS
Types of Stresses
Tensile
Compressive Shear
Bending Bearing
Axial Discontinuity
Membrane Tensile
Principal Thermal
Tangential Load induced
Strain induced Circumferential
Longitudinal Radial
Normal
Classes of stress
z Primary Stress
{ General:
z Primary general membrane stress Pm
z Primary general bending stress Pb
{ Primary local stress, PL
z Secondary stress:
{ Secondary membrane stress. Qm
{ Secondary bending stress Qb
z Peak stress. F
Definition and Examples
z PRIMARY GENERAL STRESS:
z These stress act over a full cross section of the vessel. Primary stress are
generally due to internal or external pressure or produced by sustained external
forces and moments. Primary general stress are divided into membrane and
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bending stresses. Calculated value of a primary bending stress may be allowed to
go higher than that of a primary membrane stress.
z Primary general membrane stress, Pm
z Circumferential and longitudinal stress due to pressure.
z Compressive and tensile axial stresses due to wind.
z Longitudinal stress due to the bending of the horizontal vessel over the saddles.
z Membrane stress in the centre of the flat head.
z Membrane stress in the nozzle wall within the area of reinforcement due to
pressure or external loads.
z Axial compression due to weight.
z Primary general bending stress, Pb
z Bending stress in the centre of a flat head or crown of a dished head.
z Bending stress in a shallow conical head.
z Bending stress in the ligaments of closely spaced openings.
LOCAL PRIMARY MEMBRANE STESS, PL
z Pm+ membrane stress at local discontinuities:
{ Head-shell juncture
{ Cone-cylinder juncture
{ Nozzle-shell juncture
{ Shell-flange juncture
{ Head-skirt juncture
{ Shell-stiffening ring juncture
z Pm+ membrane stresses from local sustained loads:
{ Support legs
{ Nozzle loads
{ Beam supports
{ Major attachments
SECONDARY STRESS
z Secondary membrane stress Qm
z Axial stress at the juncture of a flange and the hub of the flange
z Thermal stresses.
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z Membrane stress in the knuckle area of the head.
z Membrane stress due to local relenting loads.
z Secondary bending stress, Qb
z Bending stress at the gross structural discontinuity: nozzle, lugs, etc., (relenting
loadings only).
z The nonuniform portion of the stress distribution in a thick-walled vessels due to
internal pressure.
z The stress variation of the radial stress due to internal pressure in thick-walled
vessels.
z Discontinuity stresses at stiffening or support ring.
z Peak Stress F
z Stress at the corner of discontinuity.
z Thermal stress in a wall caused by a sudden change in the surface temperature.
z Thermal stresses in cladding or weld overlay.
z Stress due to notch effect. (stress concentration).
LOADINGS
z Loadings or forces are the causes of stress in pressure vessels. Loadings may be
applied over a large portion (general area) of the vessel or over a local area of the
vessel. General and local loads can produce membrane and bending stresses.
These stresses are additive and define the overall state of stress in the vessel or
component.
z The stresses applied more or less continuously and uniformly across an entire
section of the vessel are primary stresses.
z The stresses due to pressure and wind are primary membrane stresses.
z O the other hand, the stresses from the inward radial load could be either a
primary local stress or secondary stress. It is primary local stress if it is produced
from an unrelenting load or a secondary stress if produced by a relenting load.
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z If it is a primary stress, the stress will be redistributed; if it is a secondary stress,
the load will relax once slight deformation occurs.
z Basically each combination of stresses ( stress categories will have different
allowables, i.e.,
z Primary stress: Pm < SE
z Primary membrane local (PL):
z PL=Pm+ PL
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Types of Loadings
z 1) Steady loadsLong-term duration, continuous.
z a. Internal/external
pressure.
z b. Dead weight.
z c. Vessel contents.
z d. Loading due to attached
piping and equipment.
z e. Loadings to and from vessel
supports.
z f. Thermal loads.
z g. Wind Loads
Types of Loadings
z 1) Non-steady loads- Short-term duration, Variable.
{ Shop and field hydro-test
{ Earthquake
{ Erection
{ Transportation
{ Upset, emergency
{ Thermal Loads
{ Startup, shut down
FAILURE IN PRESSURE VESSELS
zCategories of Failures:
z Material--Improper Selection of materials; defects in material.
z DesignIncorrect design data; inaccurate or incorrect design methods;
inadequate shop testing.
z Fabrication Poor quality control; improper or insufficient fabrication procedures
including welding; heat treatment or forming methods.
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z ServiceChange of service condition by the user; inexperienced operations or
maintenance personnel; upset conditions. Some types of services which requires
special attention both for selection of materials, design details, and fabrication
methods are as follows:
{ Lethal
{ Fatigue (cyclic)
{ Brittle (low temperature)
{ High Temperature
{ High shock or vibration
{ Vessel contents
z Hydrogen
z Ammonia
z Compressed air
z Caustic
z Chlorides
z TYPES OF FAILURES
z Elastic deformationElastic instability or elastic buckling, vessel geometry, and
stiffness as well as properties of materials are protecting against buckling.
z Brittle fractureCan occur at low or intermediate temperature. Brittle fractures
have occurred in vessels made of low carbon steel in the 40-50 F range during
hydrotest where minor flaws exist.
z Excessive plastic deformationThe primary and secondary stress limits as
outlined in ASME Section VIII, Division 2, are intended to prevent excessive
plastic deformation and incremental collapse.
z Stress ruptureCreep deformation as a result of fatigue or cyclic loading, i.e.,
progressive fracture. Creep is a time-dependent phenomenon, whereas fatigue is a
cyclic-dependent phenomenon
o TYPES OF FAILURES
o Plastic instabilityIncremental collapse; incremental collapse is cyclic strain
accumulation or cumulative cyclic deformation. Cumulative damage leads to
instability of vessel by plastic deformation.
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o High StrainLow cyclic fatigue is strain-governed and occurs mainly in lower-
strength/high-ductile materials.
o Stress corrosionIt is well know that chlorides cause stress corrosion cracking in
stainless steels; likewise caustic service can cause stress corrosion cracking in
carbon steel. Materials selection is critical in these services.
o Corrosion fatigueOccurs when corrosive and fatigue effects occur
simultaneously. Corrosion can reduce fatigue life by pitting the surface and
propagating cracks. Material selection and fatigue properties are the major
considerations.
SPECIAL PROBLEMS
z Thick Walled Pressure Vessels
z Mono-bloc- Solid vessel wall.
z MultilayerBegins with a core about in. thick and successive layers are
applied. Each layer is vented (except the core) and welded individually with no
overlapping welds.
z Multi-wallBegins with a core about in. to 2 in. thick. Outer layers about the
same thickness are successive shrunk fit over the core. This creates
compressive stress in the core, which is relaxed during pressurization. The process
of compressing layers is called auto-frettage from the French word meaning self-
hooping.
z Multilayer auto-frettageBegins with a core about in. thick. Bands or forged
rings are slipped outside and then the core is expanded hydraulically. The core is
stressed into plastic range but below ultimate strength. The outer rings are
maintained at a margin below yield strength. The elastic deformation residual in
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the outer bands induces compressive stress in the core, which is relaxed during
pressurization.
z Wire wrapped vessels: Begin with inner core of thickness less than required for
pressure. Core is wrapped with steel cables in tension until the desired auto-
frettage is achieved.
z Coil wrapped vessels: Begin with a core that is subsequently wrapped or coiled
with a thin steel sheet until the desired thickness is obtained. Only two
longitudinal welds are used, one attaching the sheet to the core and the final
closures weld. Vessels 5 to 6 ft in diameter for pressure up to 5000psi have been
made in this manner.
z THERMAL STRESS
z Whenever the expansion or contraction that would occur normally as a result of
heating or cooling an object is prevented, thermal stresses are developed. The
stress is always caused by some form of mechanical restrain.
z Thermal stresses are secondary stresses because they are self-limiting. Thermal
stresses will not cause failure by rupture. They can however, cause failure due to
excessive deformations.
DISCONTINUITY STRESSES
Vessel sections of different thickness, material, diameter and change in directions
would all have different displacements if allowed to expand freely. However, since they
are connected in a continuous structure, they must deflect and rotate together. The
stresses in the respective parts at or near the juncture are called discontinuity stresses.
Discontinuity stresses are secondary stresses and are self-limiting.
Discontinuity stresses do become an important factor in fatigue design where
cyclic loading is a consideration.
zFATIGUE ANALYSIS
z When a vessel is subject to repeated loading that could cause failure by the
development of a progressive fracture, the vessel is in cyclic service.
z Fatigue analysis can also be a result of thermal vibrations as well as other
loadings.
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z In fatigue service the localized stresses at abrupt changes in section, such as at a
head junction or nozzle opening, misalignment, defects in construction, and
thermal gradients are the significant stresses.
NOZZLE REINFORCEMENT
Fig : nozzle reinforcement
Limits.
a. No reinforcement other than that inherent in the construction is required for
nozzles.
3-in. pipe size and smaller in vessel walls 3/8 in. and less.
2-in. pipe size and smaller in vessel walls greater than 3/8 in.
b. Normal reinforcement methods apply to
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Vessels 60-in. diameter and less-1/2 the vessel diameter but not to exceed 20 in.
Vessels greater than 60-in. diameter-1/3 the vessel
diameter but not to exceed 40.in
a. 1b, reinforcement shall be in accordance with para. 1-7 of ASME Code.
2. Strength
It is advisable but not mandatory for reinforcing pad material to be the same as the
vessel material.
a. If a higher strength material is used, either in the pad or in the nozzle neck, no
additional credit may be taken for the higher strength.
3. Thickness
It is recommended that pad be not less then 75% nor more than 150% of the part to
which they are attached.
4. Width
While no minimum is stated, it is recommended that re-pads be atleast 2in wide.
5. Forming:
Reinforcing pads should be formed as closely to the contour of the vessel aspossible. While normally put on the outside of the vessel, re-pads can also be put
inside providing they do not interfere with the vessels operation.
8. Openings in flat heads:
Reinforcements for the openings in the flats heads and blind flanges shall be as
follows
a. Openings < head diameter- area to be replaced equals 0.5(tr), or thickness of
head or flange may be increased by:
Doubling C value
Using C=0.75
Increasing head thickness by 1.414
b. Openings>1/2 head diameter shall be designed as a bolted flange connection.
9. Openings in torispherical heads.
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When a nozzle openings and all its reinforcement fall within the dished portion,
the required thickness of head for reinforcement purpose shall be computed using
M=1
10. Openings in elliptical heads
When a nozzle openings and all its reinforcement fall within 0.8 D of an elliptical
head, the required thickness of the head for reinforcement purpose shall be equal to the
thickness required for a seamless sphere of radius K(D).
11. General
Reinforcement should be calculated in the corroded condition assuming maximum
tolerance (minimum t)
12. Openings through seams.
a. Openings that have been reinforcement may located in a welded joint. ASME
code, division 1, does not allow a welded joint to have two different weld joint
efficiencies
13. Re-pads over seams
If at all possible, pads should not cover weld seams. When unavoidable, the seam
should be ground flush before attaching the pad.
14. Openings near seamsSmall nozzles ( for which the code does not require, the reinforcement to be checked)
shall not be located closer than in. to the edge of a main seam.
15. External pressures.
Reinforcement required for openings subject to external pressure only or when
longitudinal compression governs shall only be 50 % of that required for internal pressure
and tr, is thickness required for external pressure
16. Ligaments
When there is a series of closely spaced openings in a vessel shell and it is
impractical to reinforce each opening, the construction is acceptable, provided the
efficiency of the ligaments between the holes is acceptable.
17. Multiple openings:
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a. For two openings closer than 2 times the average diameters and where limits of
reinforcement overlap, the area between the openings shall meet the following
1. Must have a combined area equal to the sum of the two areas
2. No portion of the cross-section shall apply to more than one openings.
3. Any overlap area shall be proportional between the two openings by the ratio of
the diameters.
b. When more than two openings are to be provided with combined reinforcement:
17 b. When more than two openings are to be provided with combined reinforcement:
1. The minimum distance between the two centers is 1 1/3 the average diameters.
2. The area of reinforcement between the two nozzle shall be atleast 50% of the area
required for the two openings.
c. Multiple openings may be reinforced s an opening equal in diameter to that of a
circle circumscribing the multiple openings.
18. Plane of reinforcement.
A correction factor f may be used for integrally reinforced nozzle to compensate
for differences in stress from longitudinal to circumferential axis of the vessel. Value of f
vary from 1.0 for the longitudinal axis to 0.5 for circumferential.
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CHAPTER 2
ENGINEERING GUIDELINES FOR
DESIGN OF PRESSURE VESSELS
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Engineering Design Guidelines For Pressure Vessels
1.0 SCOPE
This specification covers the design basis for following equipment:
- Vessels
- Columns
- Reactors
- Spheres
- Storage Tanks
- Steel silos, Bins. Hoppers
- Steel Flare Stacks
2.0 CODES AND STANDARDS
The following codes and standards shall be followed unless otherwise specified:
ASME SEC. VIII DIV.1 / For Pressure vesselsIS: 2825
ASME SEC. VIII DIV.2 For Pressure vessels (Selectively for high
pressure / high thickness / critical service)
ASME SEC. VIII DIV.2 For Storage Spheres
ASME SEC. VIII DIV.3 For Pressure vessels (Selectively for high pressure)
API 650 / IS: 803 For Storage Tanks.
API 620 For Low Pressure Storage Tanks,
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API 620 / BS 7777 Cryogenic Storage Tanks (Double Wall)
ASME SEC. VIIIDIV.1 For workmanship of Vessels not categorized under
any other code.
ISO R831/ IBR For Steam producing, steam storage catch water
vessels, condensate flash drums and similar vessels
IS: 9178 / DIN 1055 For Silos Hoppers and Bins
BS: 4994 / ASME SEC X FRP vessels / tanks.`
ASME: B 96.1 Welded Aluminium Alloy Storage Tanks.
ASME SEC.II For material specification
ASTM / IS For material specification (Tanks)
IS: 875 / SITE DATA For wind load consideration
IS: 1893 / SITE DATA For seismic design consideration
ASME SEC. IX For welding.
WRC BULLETIN#
107, 297 / PD 5500 For Local load / stress analysis
3.0 DESIGN CRITERIA
Equipment shall be designed in compliance with the latest design code requirements, and
applicable standards/ Specifications.
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4.0 MINIMUM SHELL/HEAD THICKNESS
Minimum thickness shall be as given below
a) For carbon and low alloy steel vessels- 6mm (Including corrosion allowance not
exceeding 3.0mm), but not less than that calculated as per following:
FOR DIAMETERS LESS THAN 2400mm
Wall thickness = Dia/1000 +1.5 + Corrosion Allowance
FOR DIAMETERS 2400mm AND ABOVE
Wall thickness = Dia/1000 +2.5 + Corrosion Allowance
All dimension are in mm.
b) For stainless steel vessel and high alloy vessels -3 mm, but not less than that
calculated as per following for diameter more than 1500mm.
Wall thickness (mm) = Dia/1000 + 2.5
Corrosion Allowance, if any shall be added to minimum thickness.
c) Tangent to Tangent height (H) to Diameter (D) ratio (H/D) greater than 5 shall be
considered as column and designed accordingly.
d) For carbon and low alloy steel columns / towers -8mm (including corrosion allowance
not exceeding 3.0mm.
e) For stainless steel and high alloy columns / towers -5mm.
Corrosion allowance, if any, shall be added to minimum thickness.
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5.0 GENERAL CONSIDERATIONS
5.1 Vessel sizing
All Columns Based on inside diameterAll Clad/Lined Vessels Based on inside diameter
Vessels (Thickness>50mm) Based on inside diameter
All Other Vessels Based on outside diameter
Tanks & Spheres Based on inside diameter
5.2 Vessel End Closures :
- Unless otherwise specified Deep Torispherical Dished End or 2:1 Ellipsoidal Dished
End as per IS - 4049 shall be used for pressure vessels. Seamless dished end shall be used
for specific services whenever specified by process licensor.
- Hemispherical Ends shall be considered when the thickness of shell exceeds 70mm.
- Flat Covers may be used for atmospheric vessels
- Pipe Caps may be used for vessels diameter < 600mm having no internals.
- Flanged Covers shall be used for Vessels /Columns of Diameter < 900mm having
internals.
- All columns below 900mm shall be provided with intermediate body flanges. Numbers
of Intermediate flanges shall be decided based on column height and type of internals
5.3 Pressure
Pressure for each vessel shall be specified in the following manner:
5.3.1 Operating Pressure
Maximum pressure likely to occur any time during the lifetime of the vessel
5.3.2 Design Pressure
a) When operating pressure is up to 70 Kg./cm2 g , Design pressure shall be equal to
operating pressure plus 10% ( minimum 1Kg./cm2 g ).
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b) When operating pressure is over 70 Kg./cm2 g , Design pressure shall be equal to
operating pressure plus 5% ( minimum 7 Kg./cm2g).
c) Design pressure calculated above shall be at the top of vertical vessel or at the highest
point of horizontal vessel.
d) The design pressure at any lower point is to be determined by adding the maximum
operating liquid head and any pressure gradient within the vessel.
e) Vessels operating under vacuum / partial vacuum shall be designed for an external
pressure of 1.055 Kg./cm2 g.
f) Vessels shall be designed for steam out conditions if specified on process data sheet.
5.3.3 Test Pressure
a) Pressure Vessels shall be hydrostatically tested in the fabricators shop to 1.5 /1.3/ 1.25
(depending on design code) times the design pressure corrected for temperature.
b) In addition, all vertical vessels / columns shall be designed so as to permit site testing
of the vessel at a pressure of 1.5/ 1.3 / 1.25 (depending on design code) times the design
pressure measured at the top with the vessel in the vertical position and completely filled
with water. The design shall be based on fully corroded condition.
c) Vessels open to atmosphere shall be tested by filling with water to the top.
d) 1. Pressure Chambers of combination units that have been designed to operate
independently shall be hydrostatically tested to code test pressure as separate vessels i.e.
each chamber shall be tested without pressure in the adjacent chamber.
2. When pressure chambers of combination units have their common elements
designed for maximum differential pressure the common elements shall be subjected to
1.5/ 1.3 times the differential pressure.
3. Coils shall be tested separately to code test pressure.
e) Unless otherwise specified in applicable design code allowable stress during hydro test
in tension shall not exceed 90% of yield point.
f) Storage tanks shall be tested as per applicable code and specifications.
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5.4 Temperature
Temperature for each vessel shall be specified in the following manner:
5.4.1 Operating TemperatureMaximum / minimum temperature likely to occur any during the lifetime of vessel.
5.4.2 Design temperature
a) For vessels operating at0C and over:
Design temperature shall be equal to maximum operating temperature plus 150C.
b) For Vessels operating below0C:
Design temperature shall be equal to lowest operating temperature.
c) Minimum Design Metal Temperature (MDMT) shall be lower of minimum
atmospheric temperature and minimum operating temperature.
5.5 Corrosion allowance :
Unless otherwise specified by Process Licensor, minimum corrosion allowance shall be
considered as follows :
- Carbon Steel, low alloy steel column, Vessels, Spheres : 1.5 mm
- Clad / Lined vessel: Nil
- Storage Tank, shell and bottom : 1.5 mm
- Storage tank, Fixed roof / Floating Roof : Nil
For alloy lined or clad vessels, no corrosion allowance is required on the base metal. The
cladding or lining material (in no case less than 1.5 mm thickness) shall be considered for
corrosion allowance.
Cladding or lining thickness shall not be included in strength calculations.
Corrosion allowance for flange faces of Girth / Body flanges shall be considered equal to
that specified for vessel.
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5.6 Wind Consideration
Wind load shall be calculated on the basis of IS : 875 / site data.
a) Drag coefficient for cylindrical vessels shall be 0.7 minimum.
b) Drag coefficient for spherical vessel shall be 0.6 minimum.
5.7 Earthquake Consideration :
Earthquake load shall be calculated in accordance with IS : 1893 / site data if specially
developed and available
5.8 Capacity
5.8.1 Tank
Capacity shall be specified as Nominal capacity and stored capacity
Nominal capacity for fixed roof tanks be volume of cylindrical shell.
Nominal capacity for floating roof tanks shall be volume of cylindrical shell minus free
board volume.
Stored capacity shall be 90% of Nominal capacity.
5.8.2 Sphere
Stored capacity shall be 85% of nominal capacity.
5.9 Manholes :
a) Vessels and columns with diameter between 900 and 1000 mm shall be
provided with 450 NB manhole. Vessels and columns with diameter greater than
1000mm shall be provided with 500 NB manhole. However, if required vessels and
columns with diameter 1200mm and above may be provided with 600NB manhole.
b) For storage tanks minimum number of manholes (Size 500mm) shall be as
follows:
Tank Diameter Shell Roof
Dia. < 8m 1 1
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> 8m dia. < 36 dia 2 2
Dia. > 36m 4 2
Floating roofs (pontoon or double deck type) shall be provided with manholes to inspect
the entire interior of the roofs. Size of manhole shall be 500 mm minimum.
5.10 Floating Roof :
5.10.1 Unless otherwise specified floating roof shall be of following construction.
Tank Diameter Type of Roof
12 M < Double Deck Type
>12 M < 60M Pontoon Type
> 60M Double Deck Type
5.10.2 Floating roof design shall be in fabricators scope having proven track record.
Foam seal of proven make shall be provided unless otherwise specified.
5.11 Nozzle size : Unless otherwise specified
- Minimum nozzle Size : 40 NB
- Minimum Nozzle Size, Column : 50 NB
- Safety Valve Nozzle : Based on I.D.
- Self Reinforced Nozzle Neck : Based on I.D.
5.11.1 a) All nozzles and man-ways including self-reinforced type shall be 'set in' type
and attached to vessel with full penetration welds.
b) Self reinforced nozzles up to 80mm NB may be 'set on' type.
5.12 Flanges
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5.12.1 Unless otherwise specified nozzle flanges up to 600NB shall be as per ASME
/ANSI B16.5 and above 600 NB shall be as per ASME /ANSI B 16.47 (SERIES
'B')
5.12.2 For nozzles 100 NB and below, only weld neck flange shall be used. Slip on
flanges may be used for nozzles above 100NB in Class 150 rating only. All
flanges above Class 150 rating shall be weld neck type
5.12.3 Slip on flanges shall not be used in Lethal, Hydrogen, caustic, severe cyclic
service and corrosive service (where corrosion allowance is in excess of 3mm).
5.13 Internals :
Removable internals shall be bolted type and bolting shall be stainless steel Type 304,
unless specified otherwise.
5.14 Spares :
Gaskets : Two sets for each installed gasket.
Fasteners: 10 % (Minimum two in each size) of installed fasteners.
Sight/Light Glass: 4 sets for each installed glass.
5.15 Vent/Drain Connections:
Vessel shall be provided with one number each, vent/drain connection as per following :
VESSEL VOLUME, m3 VENT SIZE, NB (mm) DRAIN SIZE, NB
(mm)
6.0 and smaller 40 406.0 to 17.0 40 50
17.0 to 71.0 50 80
71.0 and larger 80 100
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5.16 Pipe Davit :
Vertical Vessel / Column having safety valve size > 80 NB and or having internals, shall
be provided with pipe davit per relevant standard.
6.0 INSULATION THICKNESS :
As indicated on process data sheet by process licensor
7.0 PAINTING
As per Standard Specification, unless otherwise stated.
8.0 MATERIAL SELECTION :Material of various parts of equipment shall be selected per process data sheet guidelines
and proper care shall be taken for the points as given in Annexure- I or as specified.
9.0 SPECIAL CONSIDERATION FOR TALL COLUMN DESIGN
Mechanical design of self supporting Tall Column / Tower shall be carried out for
various load combinations as per Annexure-II
10.0 STATUTORY PROVISIONS :
National laws and statutory provisions together with any local byelaws for the state shall
be complied with.
Annexure : I
1. PRESSURE VESSEL STEEL PLATES ARE PURCHASED TO THE
REQUIREMENT OF THE STANDARD ASME SA-20, WHICH REQUIRES
TESTING OF INDIVIDUAL PLATES FOR LOW TEMPERATURE SERVICE.
CARBON STEEL MATERIAL IS ORDERED TO MEET THE IMPACT
REQUIREMENTS OF SUPPLEMENT OF STANDARD ASME SA 20. TYPICAL
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MATERIAL SPECIFICATION IS AS FOLLOWS SA 516 GR.60. NORMALISED TO
MEET IMPACT REQUIREMENTS PER SUPPLEMENT SS OF SA 20 AT-50F
2. ALL PERMANENT ATTACHMENTS WELDED DIRECTLY TO 9 %
NICKEL STEEL SHOULD BE OF THE SAME MATERIAL OR OF AN AUSTENTIC
STAINLESS STEEL TYPE WHICH CANNOT BE HARDENED BY HEAT
TREATMENT.
3. CHECK FOR IMPACT TESTING REQUIREMENT AS PER UCS-66 FOR
COINCIDENT TEMPERATURE AND PART THICKNESS.
4. SELECTION OF STAINLESS STEEL MATERIAL SHALL BE BASED ON
PROCESS RECOMMENDATION/PROCESS LICENSOR.
5. ATMOSPHERIC/LOW PRESSURE STORAGE TANKS. MATERIAL SHALL
BE SELECTED AS PER API 650 /API 620 AS APPLICABLE.
6. MATERIALS FOR CAUSTIC SERVICE SOUR SERVICE OR SOUR + HIC
SHALL BE SELECTED BASED ON SPECIFIC RECOMMENDATION OF PROCESSLICENSOR.
7. MATERIAL FOR PRESSURE VESSELS DESIGNED ACCORDING TO
ASME SECTION VIII DIVISION 2 SHALL BE GIVEN SPECIAL CONSIDERATION
AS PER CODE.
8. ALL PIPES SHALL BE OF SEAMLESS CONSTRUCTION.
9. NONFERROUS MATERIAL AND SUPER ALLOYS SHALL BE SELECTED
BASED ON SPECIFIC RECOMMENDATION.
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10. MATERIAL FOR VESSEL /COLUMN SKIRT SHALL BE THE SAME
MATERIAL AS OF VESSEL/ COLUMN SHELL FOR THE UPPER PART WITH A
MINIMUM OF 500MM.
Annexure -II
DESIGN PHILOSOPHY OF TALL COLUMNS
Mechanical design of self-supporting tall column and its anchorage block shall be carried
out considering combination of various loads.
1.0 Loadings
The loadings to be considered in designing a self-supporting tall column/tower shall
include:
1.1 Internal and or external design pressure specified on process data sheets.
1.2 Self weight of column inclusive of piping, platforms, ladders, manholes, nozzles,
trays, welded and removable attachments, insulation and operating liquid etc. The
weight of attachments to be considered shall be as per Table -1 enclosed
Other loading as specified in UG-22 of ASME Code Sec, VIII Div.1. wherever
applicable.
1.3 Seismic forces and moments shall be computed in accordance with IS 1893 (latest
edition). Unless otherwise specified importance factor and damping coefficient
shall be considered as 2 and 2% respectively.
1.4 Basic wind pressure and wind velocity (including that due to winds of short
duration as in squalls) for the computation of forces / moments and dynamic
analysis respectively shall be in accordance with IS 875 (latest edition).Additional wind loading on column due to external attachments like platforms,
ladders piping and attached equipment should be given due consideration.
1.5 Loadings resulting in localised and gross stresses due to attachment or mounting
of reflux / reboiler / condenser etc.
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2.0 Loading Condition
Analysis shall be carries out for following conditions :
2.1 Erection Condition: Column (un-corroded) erected on foundation without
insulation, platforms, trays etc. but with welded attachments plus full wind on
column.
2.2 Operation Condition: Column (in corroded condition) under design pressure,
including welded items, trays removable internals, piping, platforms, ladder,
reboiler mounted on column, insulating and operating liquid etc. plus full wind on
insulated column with all other projections open to wind, or earthquake force.
2.3 Test Condition: Column (in corroded condition) under test pressure filled with
water plus 33% of specified wind load on uninsulated column considered.
2.4 EARTHQUAKE AND WIND SHALL BE CONSIDERED NOT ACTING
CONCURRENTLY
3.0 Deflection of Column
Maximum allowable deflection at top of column shall be equal to height of the column
divided by 200.
3.1 If the deflection of column exceeds the above allowable limit the thickness of
skirt shall be increased as first trial up to a maximum value equal to the columnthickness and this exercise shall be stopped if the deflection falls within allowable
limit.
3.2 If the above step is inadequate, skirt shall be gradually flared to reduce the
deflection. Flaring of skirt shall be stopped if the deflection falls within limits or
half angle of cone reaches maximum limit of 9 deg.
3.3 If the above two steps prove inadequate in limiting the deflection within
allowable limits, the thickness of shell courses shall be increased one starting
from bottom course above skirt and proceeding upwards till the deflection falls
within allowable limits.
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4.0 Stress Limits
The stresses due to pressure weight wind / seismic loads shall be combined using
maximum principle stress theory for ASME Section VIII Div. I. Thicknesses are
accordingly chosen to keep the within limits as per Table-2.
5.0 Skirt Support Base
Base supporting including base plate, anchor chairs compression ring, foundation bolting
etc. shall be designed based on overturning moment (greater of seismic or wind). A
minimum number of 8 foundation bolts shall be provided. Numbers of foundation bolts
shall be in multiple of four.
6.0 Minimum Hydrotest Pressure
Minimum Hydrotest Pressure (in Horizontal position) shall be equal to 1.3 x design
pressure x temperature correction factor as specified in ASME Code Section VIII Div. I
(Clause UG-99) at top of column.
7.0 Dynamic Analysis
Dynamic analysis of each column shall be carried out for stability under transverse wind
induced vibrations as per standard design practice. The recommended magnificationamplitude shall be limited to tower diameter divided by five.
TABLE-1
DETAILS AND WEIGHT OF COLUMN ATTACHMENT
1. Shape factor for shell (for wind force calculation) : 0.7
2. Weight of trays (with liquid) to be considered. : 120 Kg./m2
3. Weight of plain Ladder: 15 Kg./m
4. Weight of caged ladder: 37 Kg./m
5 Equivalent projection to be considered for wind load on caged ladder : 300 mm
6. Distance of platform below each manhole : Approx. 1000 mm
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7. Maximum distance between consecutive platform : 5000 mm
8. Projection of Platform : 900mm up to 1meter dia. column; 1200 mm for column
dia.> 1 meter, from column insulation surface.
9. Equivalent height of platform (for wind load computation) : 1000 mm
10. Weight of platforms : 170 Kg./m2.
11. Platform shall be considered all around
TABLE -2
ALLOWABLE STRESSES FOR COMBINED LOADING
VESSEL CONDITION / TEMP./ CONDITIONS
TYPE OF STRESSES ERECTION
OPERATING TEST
NEW OR CORRODED NEW CORRODED
CORRODED
TEMPERATURE AMBIENT DESIGNAMBIENT
LONGITUDINAL KxSxE KxSxE
0.90xY.PxE
LONGITUDINAL COMPRESSIVE
STRESS KxB KxB B
Where
S = Basic allowable Tensile Stress as per Clause UG 23 (a) of ASME Code Sec. VIII
Div.1.
B = 'B' value calculated as per Clause UG-23 (b).
E = Weld joint efficiency of circumferential weld, depending on extent of radiography.
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K = Factor for increasing basic allowable value when wind or seismic load is present, 1.2
as per ASME Sec VIII Div 1.
Note : Allowable stresses in skirt to shell joint shall be as per following :
a) 0.49S, if joint is shear type.
b) 0.70S, if joint is compression type.
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CHAPTER 3
DESIGN PROCEDURE AND
CALUCULATION
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DESIGN THEORY
Circumferential or Hoop Stress
A tensile stress acting in a direction tangential to the circumference is called
Circumferential or Hoop Stress. In other words, it is on longitudinal section(or on thecylinder walls).
Let,
p = Intensity of internal pressure,
d = Internal diameter of the cylinder shell,
l = length of cylinder,
t = Thickness of the shell, and
t1
V = hoop stress for the material of the cylinder.
Now,
We know that total force on a longitudinal section of the shell
= Intensity of pressure projected Area = p d l ..i
and the total resisting force acting on the cylinder walls
= t1V 2t l .( of two section)
ii
From equation (i) and (ii) , we have
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t1V 2t l = p d l or t1V =p d
2t
uor t =
t1
p d
2
u
V
..ii
Longitudinal Stress
A tensile stress acting in a direction of the axis is called longitudinal stress. In
other words, it is a tensile stress acting on the transverse or circumferential section.
Fig of Longitudinal stress
Let t 2V = Longitudinal stress.
In this case, the total force acting on the transverse section
= Intensity of pressure Cross- sectional Area
= p 4
S(d) i
and total resisting force = t2V d.t ii
From equation (i) and (ii), we have
t 2V d.t = p 4
S(d)
t 2V =p d
4t
uor t =
t 2
p d
4
u
V
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Design of Shell Due to Internal Pressure
As discussed in article on thin vessel are cylindrical pressure vessel is subjected to
tangential ( tV ) and longitudinal ( LV ) stresses.
2
i it
P D
tV
u and
4
i iL
P D
tV
u where D= mean diameter
= iD + t
Rule
The design pressure is taken as 5% to 10% more than internal pressure, where as
the test pressure is taken as 30% more than internal pressure.
Considering the joint efficiency,
The thickness of shell can be found by following procedure,
( )2
i iP D tt
K V u u
2 ( )i it P D t K Vu u u
2( )
i i
i
P Dt
PK V
u
u
Design of Elliptical Head:
Elliptical heads are suitable for cylinders subjected to pressures over 1.5 MPa. The
shallow forming reduces manufacturing cost. Its thickness can be calculated by the
following equation:
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t =2
i ip d W
JV
where,
id= Major axis of ellipse
W= Stress intensification factor
21 (2 )6
W k
Where , k =Major Axis Diameter
Major Axis Diameter= i
0.5d
c
Rule Generally, k = 2 ( how ever k should not be greater than 2.6)
21 (2 2 )6
W
= 1
2
Pi di Wt
JV
Design of Manhole
Let,
id = internal dia. Of nozzle
d = id + 2 CA
where, CA = corrosion Allowance in mm
t = Actual thickness of shell in mm
tr = require thickness as per calculation in mm.
tn = Actual thickness of nozzle
trn = Required thickness as per calculation in mm
2rnPi Di
Pit
V K
u
u u
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1actualh = Height of the nozzle above the shell in mm
2actualh = Height of the nozzle below the shell in mm
1h = Height till where the effect of the nozzle persists above the shell in mm
2h = Height till where the effect of the nozzle persists below the shell in mm
To calculate 1h and 2h consider a term h
h = 2.5 ( t CA) or h = 2.5 ( tn CA) (whichever is smaller)
1h = h or 1actualh (whichever is smaller)
2h = h or 2actualh (whichever is smaller)
X = Distance where the effect of the nozzle persists in mm on each side of the
centre line
X = d.
or X = id
2
+ t + tn -3CA (whichever is maximum)
opd = outer dia. Of Reinforcing Pad in mm
ipd = inner dia. Of Reinforcing Pad in mm
pt = Thickness of Reinforcing Pad in mm
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Area Calculation
Area pertaining to material removed, A = d u tr
Excess area in the Shell, A1 = (2X d ) ( t tr CA)
Excess area in the Nozzle, A2 = 2h1(tn trn CA)
Excess area in the nozzle inside the shell A3 = 2 h2 (tn 2CA)
Area Required, rA = ( opd - ipd ) pt
Area required, Ar = A ( A1 + A2 + A3)
When Ar = 0 or negative, no reinforcement is necessary as the vessel thickness self
compensates.
Design of Leg:
A) Legs support
In certain cases, legs can be made detachable to the vessel. These legs can
be bolted to plates. The design for leg supports is similar to that for bracket support. If
the legs are welded to the shell, then the shear stresses in the weld will be given by:
2
2 1 220.707
W o
W W
Ww P KPH D mm
t L nW
u u u
0.707W
W W
W
t L nW
u u u
Where, Wt = Weld Height
WL = Weld Length.
These types of supports are suitable only for small vessels as there is a concentrated
local stress at the joint.
B) Wind Load
Wind load can be estimated as :
w1P = K P1H oD
This equation is valid for heights upto 20m. Beyond 20m, the wind pressure is
higher and hence for heights above 20m.
2 2 2w oP KP H D
Generally, 1P lies between 400 N/2
mm and 2P may be upto 2000 N/2
m .
Therefore, the bending moment due to wind at the base will be
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(IF H 20 m) wM =w1 1P h
2
(IF H> 20m) wM =w1 1P h
2+ w 2P ( 1h +
2h
2)
Therefore, bending stress will be,
bwV =wM
zWhere Z= section Modulus
The wind load would create tensile stress on the wind side and compressive on the other
side.
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Design Calculation
1) Thickness of cylinder
Given data
Internal pressure (P) = 0.588 MPa
Internal Diameter (Di) = 496mm
Corrosion Allowance (CA) = Nil.
Joint Efficiency for shell = 1.
As per Equation,
2
Pi Dit
PiV K
u
u u
+ CA
(0.588) (496)
2 137 1 0.588t
u
u u ( CA is NIL)
= 1.066
? t = 1.066mm
2) Elliptical Head
21 (2 )6
W k
where ,
k =Major Axis Diameter
Major Axis Diameter= i
0.5d
c
k = 2
Rule Generally, k = 2 ( how ever k should not be greater than 2.6)
21 (2 2 )6
W
= 1
2
Pi di Wt
JV
where,
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di = Major axis of ellipse = 496mm
W = Stress intensification factor = 1
2
Pi di W
t JV
0.588 496 1
2 137 1t
u u
u u
= 1.06 mm
?t = 1.06 mm
3) Design Of Manhole
INLET NOZZLE (N1)
GIVEN DATA
Internal pressure (Pi) = 0.588 N/ 2mm
Internal diameter (Di) = 496 mm
Thickness (t) = 6 mm.
CA = NIL
Joint Efficiency (K) = 1
Internal diameter of nozzle (di) = 254.51 mm
d = di + CA = 254.51 mm.
tr = require thickness = 1.066 mm.
tn = Actual thickness of nozzle = 9.27 mm.
trn = Required thickness as per calculation in mm.
1
0.588 254.51
2 137 1 0.588A
u
u u 2rnPi Di
Pit
V K
u
u u
0.588 254.51
2 137 1 0.588rnt
u
u u
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= 0.547 mm.
rnt = 0.547 mm.
Area Calculation
Area Pertaining to material removed, A = d u tr
= 254.51u 1.066
= 271.3 2mm
Excess area in the shell, A1 = (2X d ) ( t tr CA)
Generally,
X = d = 254.51 mm.
X = di + t + tn -3CA
2
= 254.51 + 6 +9.27 0
2
= 142.52 mm.
( Take X whichever maximum)
Therefore,
A = (2u254.51-254.51)(6-1.066-0)
= 1255.75 2mm
Excess area in the nozzle, A2 = 2h1(tn trn CA)
h = 2.5 ( t CA) or h = 2.5 ( tn CA)
= 2.5 u6 = 2.5 (9.27)
= 15mm = 23.175 mm
( Take X whichever smaller)
h1 = h2 = h = 15 mm.
Therefore,
A2 = 2u15 ( 9.27 0.547 0)
= 261.69 2mm
Excess area in the nozzle inside the shell A3 = 2 h2 (tn 2CA)
= 2u 15 ( 9.27-0)
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= 278.1 2mm
Area required Ar = A ( A1 + A2 + A3)
= -1524.24
As Ar is ve or zero reinforcement is not necessary.
4) Design of leg
Wind load
Here ,
K = Coefficient depending on shape factor = 0.7
P1
= Wind pressure = 730 N/ 2mm
H = Height of the vessel above foundation =2413 mm
oD = Outer Diameter Of Vessels
Wind load can be estimated as :
w1P = K P1H oD
= 0.77302.4130.508
= 626.38 N
(IF H 20 m) wM =w1 1P h
2
(IF H> 20m) wM =w1 1P h
2+ w 2P ( 1h +
2h
2)
Here we use ,
wM =w1 1P h
2
= 626.38 1206.47
= 755.41 N.m
Here we use I- Section,
Therefore, Z = section Modulus
Z =3 3
1 1bh b h
6h
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=3 34t(5t) 3t(3t)
6(5t)
= 13.96 3t
Therefore, Bending Stress will be ,
bwV =wM
z(as bwV = 350 N/mm)
350 610 =3
755.41
13.96t
t = 5.36 310 m
? L =123
3+
123
3+ 1834
= 1916 mm
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SUMMARY
INTERNALDIAMETER(Di) 496mm
SHELL LENGTH(L) 1734mm
THICKNESS(t) 6mm
HEAD THICKNESS(t) 6mm
HEIGHT(h) 173mm
MANHOLE DIAMETEROFOPENING(di) 254.51
THICKNESSOFNOZZLE(tn) 9.27
REINFORCEMENT
ASAREACALCULATEDISve
RFPADISNOTREQUIRED
PAD
LEG THICKNESSOFLEGS 5.36mm
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DESIGN APPROCH 2 BY ASME
CODES
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DESIGN THEORY
PPRREESSSSUURREE VVEESSSSEELL HHEEAADD DDEESSIIGGNN UUNNDDEERRIINNTTEERRNNAALL PPRREESSSSUURREE
THICKNESS OF HEADS/ CLOSURES:
ELLIPSOIDAL HEAD:
t = P.Di / (2SE- 0.2P) + CA
OTHERS;
t = P.K.Di/ (2SE-0.2P) + CA
K =CONSTANT BASED ON THE RATIO OF
MAJOR & MINOR AXIS (D/2H)
VVAALLUUEESS OOFF FFAACCTTOORRKK
D/2H 3.0 2.8 2.6 2.5 2.4 2.2 2.1 2.0
K 1.83 1.64 1.46 1.37 1.29 1.14 1.07 1.00
D/2H 1.8 1.6 1.5 1.4 1.2 1.0
K 0.87 0.76 0.71 0.66 0.57 0.50
TORISPHERICAL HEAD:
t = 0.885 PL/ (SE-0.1P) + CA
FOR KNUCKLE RADIUS, r = 6% OF CROWN RADIUS (L)
t =PLM/ (2S.E- 0.2P) + CA
where L=CROWN RADIUS
M=CONSTANT BASED ON RATIO OF CROWN AND KNUCLE
RADIUS(L/r)
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VVAALLUUEESS OOFF FFAACCTTOORRMM
L/r 1.0 1.50 2.00 2.50 3.00 3.50 4.0
M 1.00 1.06 1.10 1.15 1.18 1.22 1.25
L/r 5.0 6.0 7.0 8.0 9.0 10.0 11.0
M 1.31 1.36 1.41 1.46 1.50 1.54 1.58
L/r 12.0 13.0 14.0 15.0 16.0 16.67
M 1.62 1.65 1.69 1.72 1.75 1.77
z (USE NEAREST VALUE OF L/r; INTERPOLATION UNNECESSARY)
z NOTE:
MAXIMUM RATIO ALLOWED BY UG-32 (j) WHEN L EQUALS THE
OUTSIDE DIAMETER OF THE SKIRT OF THE HEAD. KNUCKLE
RADIUS, r SHALL NOT BE LESS THAN 3t.
z CONICAL HEAD:
t = PDi/ 2 COS (SE-0.6P) + CA
= half apex angle
z HEMISPHERICAL HEAD:
t = P.Ri/ (2SE- 0.2P) + CA
z FLAT HEADS & COVERS (UG- 34)
CIRCULAR COVER/ HEADS
t = Di * SQRT(CP/SE) + CA
Where C = Factor, dependent on joint geometry of head cover to shell (range 0.1
0.33)
z OBROUND/ NON-CIRCULAR HEADS
(INCLUDING SQUARE/ RECTANGULAR)
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t = Di * SQRT(Z*CP/SE) + CA
where Z = 3.4 - (2.4 d / D)
PPRREESSSSUURREE VVEESSSSEELL SSHHEELLLL CCOOMMPPOONNEENNTT DDEESSIIGGNN UUNNDDEERR
IINNTTEERRNNAALL PPRREESSSSUURREE
z Pressure Vessel Definition:
Containers of Pressure
z Internal
z External
Pressure Source
z External
z Application of Heat
z Code Coverage:
Subsections
z Rule, Guidelines, Specifications
Mandatory Appendices
z Specific Important Subjects to Supplement Subsections
Non-Mandatory Appendices
z Additional Information, Suggested Good Practices
z Inclusions:
Unfired Steam Boilers/ Generators
z Evaporators
z Heat Exchangers
Direct Fired Vessels
z Gas Fired Jacketed Steam Kettles(Jacket Pressure less than 50
PSI)
z Additional Interpretation:
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The code rules may not cover all designs & constructions procedures.
z Such additional design & construction procedure may be
adopted which are safe and acceptable.
Field fabrication are acceptable.
Other standards for components are acceptable
z Guidelines for Designed Thickness (To be adopted):
(1/16) excluding corrosion allowance for shell & head (Min.)
The above will not apply to heat transfer surface
(1/4) min. for unfired steam boiler shell
(3/32) min. excluding corrosion allowance for compressed air/ steam/
water service(for CS/AS)
Corrosion allowance shall be based on experience/ field data(No
value/ code recommended).
THICKNESS CALCULATIONS
UNDER INTERNAL PRESSURE,CYLINDRICAL SHELL:
Circumferential stress:
t = P.Ri / (SE- 0.6P) + CA
Longitudinal stress:
t = P.Ri / (2SE+0.4P) + CA
SPHERICAL SHELL:
t = P.Ri / (2SE- 0.2P) + CA
CONICAL SECTION: (INTERNAL PRESSURE)
t =P.Di/ 2COS(SE- 0.6P) + CA
z Stress Calculation
UNDER INTERNAL PRESSURE,
CYLINDRICAL SHELL:
Circumferential stress:
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Sc = P (Ri + 0.6t)/ Et
Longitudinal stress:
Sl = P (Ri - 0.4t)/ 2Et
SPHERICAL SHELL:
Sc = P (Ri + 0.2t)/ 2Et
CONICAL SHELL SECTION:
Sc =P (Di + 1.2 tCOS)/2Et COS
Sl =P (Di 0.8tCOS)/4Et COS
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ANALYSIS OF PRESSURE VESSEL
ProjectAuthor
jimit and mahavir
Subject
shell analysis
Prepared For
project report
Project Created
Sunday, May 25, 2008 at 10:04:27 PM
Project Last Modified
Sunday, May 25, 2008 at 10:04:27 PM
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1 Introduction
The ANSYS CAE (Computer-Aided Engineering) software program was used inconjunction with 3D CAD (Computer-Aided Design) solid geometry to simulate the
behavior of mechanical bodies under thermal/structural loading conditions. ANSYS
automated FEA (Finite Element Analysis) technologies from ANSYS, Inc. to generatethe results listed in this report.
Each scenario presented below represents one complete engineering simulation. Thedefinition of a simulation includes known factors about a design such as material
properties per body, contact behavior between bodies (in an assembly), and types and
magnitudes of loading conditions. The results of a simulation provide insight into howthe bodies may perform and how the design might be improved. Multiple scenarios allow
comparison of results given different loading conditions, materials or geometric
configurations.
Convergence and alert criteria may be defined for any of the results and can serve asguides for evaluating the quality of calculated results and the acceptability of values in
the context of known design requirements.
Solution history provides a means of assessing the quality of results by examining how values change during successive
iterations of solution refinement. Convergence criteria sets a specific limit on the allowable change in a result between
iterations. A result meeting this criteria is said to be "converged".
Alert criteria define "allowable" ranges for result values. Alert ranges typically represent known aspects of the design
specification.
All values are presented in the "SI Metric (m, kg, N, C, s, V, A)"unit system.
Notice
Do not accept or reject a design based solely on the data presented in this report. Evaluatedesigns by considering this information in conjunction with experimental test data and
the practical experience of design engineers and analysts. A quality approach toengineering design usually mandates physical testing as the final means of validating
structural integrity to a measured precision.
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2. Scenario 1
2.1. "Model"
"Model" obtains geometry from the Pro/ENGINEER part "H:\shaell andcylinder\SHEEL.PRT.2".
The bounding box for the model measures 1.73 by 0.52 by 0.52 m along the global x, y and z axes, respectively.
The model has a total mass of 109.69 kg.
The model has a total volume of 1.410-2 m.
Table 2.1.1. Bodies
Name Material Nonlinear Material Effects Bounding Box(m) Mass (kg) Volume (m) Nodes Elements
"SHEEL" "Structural Steel" Yes 1.73, 0.52, 0.52 109.69 1.410-2 4968 684
2.1.1. Mesh
"Mesh", associated with "Model"has an overall relevance of 0.
"Mesh"contains 4968 nodes and 684 elements.
No mesh controls specified.
2.2. "Environment"
Simulation Type is set to Static
Analysis Type is set to Static Structural
"Environment"contains all loading conditions defined for"Model"in this scenario.
2.2.1. Structural Loading
Table 3.2.1.1. Structural Loads
Name Type Magnitude VectorReaction
Force
Reaction Force
Vector
Reaction
Moment
Reaction Moment
Vector
"Pressure" Pressure 600,000.0 Pa N/A N/A N/A N/A N/A
2.2.2. Structural Supports
Table 3.2.2.1. Structural Supports
Name TypeReaction
ForceReaction Force Vector
Reaction
MomentReaction Moment Vector
"Fixed
Support"
Fixed
Surface1.7110-3 N
[-1.7110-3 N x, 1.1610-7 N y,
3.6710-9 N z]1.8110-5 Nm
[1.8110-5 Nm x, 3.1610-9 Nm y,
1.0610-7 Nm z]
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2.3. "Solution"
Solver Type is set to Program Controlled
Weak Springs is set to Program Controlled
Large Deflection is set to Off
"Solution"contains the calculated response for"Model"given loading conditions definedin "Environment".
Thermal expansion calculations use a constant reference temperature of 22.0 C for"SHEEL". Theoretically, at a uniform
temperature of 22.0 C no strain results from thermal expansion or contraction.
2.3.1. Structural Results
Table 3.3.1.1. Values
Name Figure Scope Minimum MaximumMinimum Occurs
On
Maximum Occurs
On
Alert
Criteria
"Equivalent Stress" A1.1 "Model" 8.6106 Pa 3.5107 Pa SHEEL SHEEL None
"Maximum Shear
Stress"None "Model" 4.96106 Pa 1.87107 Pa SHEEL SHEEL None
"Total Deformation" A1.2 "Model" 0.0 m 4.2710-5 m SHEEL SHEEL None
Convergence tracking not enabled.
2.3.2. Equivalent Stress Safety
Table 3.3.2.1. Definition
Name Stress Limit
"Stress Tool" Yield strength per material.
Table 3.3.2.2. Results
Name Scope Type Minimum Alert Criteria
"Stress Tool" "Model" Safety Factor 7.13 None
"Stress Tool" "Model" Safety Margin 6.13 None
Convergence tracking not enabled.
2.3.3. Shear Stress Safety
Table 3.3.3.1. Definition
Name Shear Limit Shear Factor
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"Stress Tool 2" Yield strength per material. 0.5
Table 3.3.3.2. Results
Name Scope Type Minimum Alert Criteria
"Stress Tool 2" "Model" Safety Factor 6.69 None
"Stress Tool 2" "Model" Safety Margin 5.69 None
Convergence tracking not enabled.
stress
Figure A1.1. "Equivalent Stress" Contours
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Scenario 1 Figuresdeformation
Figure A1.2. "Total Deformation" Contours
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AppendicesA1.
A2. Definition of "Structural Steel"
Table A2.1. "Structural Steel" Constant Properties
Name Value
Compressive Ultimate Strength 0.0 Pa
Compressive Yield Strength 2.5108 Pa
Density 7,850.0 kg/m
Poisson's Ratio 0.3
Tensile Yield Strength 2.5108 Pa
Tensile Ultimate Strength 4.6108 Pa
Young's Modulus 2.01011 Pa
Thermal Expansion 1.210-5 1/C
Specific Heat 434.0 J/kgC
Thermal Conductivity 60.5 W/mC
Relative Permeability 10,000.0
Resistivity 1.710-7 Ohmm
Table A2.2. Alternating Stress
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Mean Value 0.0
Table A2.3. "Alternating Stress"
Cycles Alternating Stress
10.0 4.0109 Pa
20.0 2.83109 Pa
50.0 1.9109 Pa
100.0 1.41109 Pa
200.0 1.07109 Pa
2,000.0 4.41108 Pa
10,000.0 2.62108 Pa
20,000.0 2.14108 Pa
100,000.0 1.38108 Pa
200,000.0 1.14108 Pa
1,000,000.0 8.62107 Pa
Table A2.4. Strain-Life Parameters
Table A2.5. "Strain-Life Parameters"
Strength Coefficient 9.2108 Pa
Strength Exponent -0.11
Ductility Coefficient 0.21
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Ductility Exponent -0.47
Cyclic Strength Coefficient 1.0109 Pa
Cyclic Strain Hardening Exponent 0.2
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Project
Author Jimit vyas and mahavir solanki
Subject Ellipsoidal dish end
Prepared for project analysis
First Saved Sunday, May 25, 2008
Last Saved Sunday, May 25, 2008
Product Version 11.0 Release
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Contents
x Modelo Geometry
ELIPTICALHEADo
Mesh CFX-Mesh Methodo Static Structural
Analysis Settings Loads Solution
Solution Information Results Max Equivalent Stress
Results Max Shear Stress
Resultsx Material Data
o Structural Steel
Units
TABLE 1
Unit System Metric (m, kg, N, C, s, V, A)
Angle Degrees
Rotational Velocity rad/s
Model
Geometry
TABLE 3
Model > Geometry > Parts
Object Name ELIPTICALHEAD
State Meshed
Graphics Properties
Visible Yes
Transparency 1
Definition
Suppressed NoMaterial Structural Steel
Stiffness Behavior Flexible
Nonlinear Material Effects Yes
Bounding Box
Length X 0.508 m
Length Y 0.508 m
Length Z 0.173 m
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Properties
Volume 1.9271e-003 m
Mass 15.128 kg
Centroid X -8.1168e-017 m
Centroid Y 1.0962e-017 m
Centroid Z -3.7996e-002 m
Moment of Inertia Ip1 0.34417 kgm
Moment of Inertia Ip2 0.343 kgm
Moment of Inertia Ip3 0.6178 kgm
Statistics
Nodes 2289
Elements 6232
Mesh
TABLE 4
Model > Mesh
Object Name MeshState Solved
Defaults
Physics Preference CFD
Relevance 0
Advanced
Relevance Center Fine
Element Size Default
Shape Checking CFD
Solid Element Midside Nodes Dropped
Straight Sided Elements
Initial Size Seed Active Assembly
Smoothing Medium
Transition Slow
Statistics
Nodes 2289
Elements 6232
TABLE 5
Model > Mesh > Mesh Controls
Object Name CFX-Mesh Method
State Fully Defined
Scope
Scoping Method Geometry SelectionGeometry 1 Body
Definition
Suppressed No
Method CFX-Mesh
Element Midside Nodes Dropped
Static Structural
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TABLE 6
Model > Analysis
Object Name Static Structural
State Fully Defined
Definition
Physics Type Structural
Analysis Type Static Structural
Options
Reference Temp 22. C
TABLE 8
Model > Static Structural > Loads
Object Name Pressure Fixed Support 2
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 4 Faces 1 Face
DefinitionDefine By Normal To
Type Pressure Fixed Support
Magnitude 6.e+005 Pa (ramped)
Suppressed No
FIGURE 1
Model > Static Structural > Pressure
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Solution
TABLE 9
Model > Static Structural > Solution
Object Name Solution
State Solved
Adaptive Mesh Refinement
Max Refinement Loops 1.
Refinement Depth 2.
TABLE 10
Model > Static Structural > Solution > Solution Information
Object Name Solution Information
State Solved
Solution Information
Solution Output Solver Output
Newton-Raphson Residuals 0
Update Interval 2.5 sDisplay Points All
TABLE 11
Model > Static Structural > Solution > Results
Object Name Equivalent Stress Maximum Shear Stress Total Deformation
State Solved
Scope
Geometry All Bodies
Definition
Type Equivalent (von-Mises) Stress Maximum Shear Stress Total Deformation
Display Time End Time
ResultsMinimum 3.101e+006 Pa 1.6131e+006 Pa 0. m
Maximum 3.1378e+007 Pa 1.6963e+007 Pa 4.1032e-005 m
Information
Time 1. s
Load Step 1
Substep 1
Iteration Number 1
FIGURE 2
Model > Static Structural > Solution > Equivalent Stress > Figure
equivalent stress
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FIGURE 3
Model > Static Structural > Solution > Maximum Shear Stress > Figure
maximum shear stress
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TABLE 12
Model > Static Structural > Solution > Stress Safety Tools
Object Name Max Equivalent Stress
State Solved
Definition
Theory Max Equivalent Stress
Stress Limit Type Tensile Yield Per Material
TABLE 13
Model > Static Structural > Solution > Max Equivalent Stress > Results
Object Name Safety Factor Safety Margin
State SolvedScope
Geometry All Bodies
Definition
Type Safety Factor Safety Margin
Display Time End Time
Results
Minimum 7.9674 6.9674
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Information
Time 1. s
Load Step 1
Substep 1
Iteration Number 1
TABLE 14
Model > Static Structural > Solution > Stress Safety Tools
Object Name Max Shear Stress
State Solved
Definition
Theory Max Shear Stress
Factor 0.5
Stress Limit Type Tensile Yield Per Material
TABLE 15
Model > Static Structural > Solution > Max Shear Stress > Results
Object Name Safety Factor Safety MarginState Solved
Scope
Geometry All Bodies
Definition
Type Safety Factor Safety Margin
Display Time End Time
Results
Minimum 7.369 6.369
Information
Time 1. s
Load Step 1
Substep 1
Iteration Number 1
Material Data
Structural Steel
TABLE 16
Structural Steel > Constants
Structural
Young's Modulus 2.e+011 Pa
Poisson's Ratio 0.3
Density 7850. kg/m
Thermal Expansion 1.2e-005 1/C
Tensile Yield Strength 2.5e+008 Pa
Compressive Yield Strength 2.5e+008 Pa
Tensile Ultimate Strength 4.6e+008 Pa
Compressive Ultimate Strength 0. Pa
Thermal
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Thermal Conductivity 60.5 W/mC
Specific Heat 434. J/kgC
Electromagnetics
Relative Permeability 10000
Resistivity 1.7e-007 Ohmm
FIGURE 4
Structural Steel > Alternating Stress
TABLE 17
Structural Steel > Alternating Stress > Property Attributes
Interpolation Log-Log
Mean Curve Type Mean Stress
TABLE 18
Structural Steel > Alternating Stress > Alternating Stress Curve Data
Mean Value Pa
0.
TABLE 19
Structural Steel > Alternating Stress > Alternating Stress vs. Cycles
Cycles Alternating Stress Pa
10. 3.999e+009
20. 2.827e+009
50. 1.896e+009
100. 1.413e+009
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200. 1.069e+009
2000. 4.41e+008
10000 2.62e+008
20000 2.14e+008
1.e+005 1.38e+008
2.e+005 1.14e+008
1.e+006 8.62e+007
FIGURE 5
Structural Steel > Strain-Life Parameters
TABLE 20
Structural Steel > Strain-Life Parameters > Property Attributes
Display Curve Type Strain-Life
TABLE 21
Structural Steel > Strain-Life Parameters > Strain-Life Parameters
Strength Coefficient Pa 9.2e+008
Strength Exponent -0.106Ductility Coefficient 0.213
Ductility Exponent -0.47
Cyclic Strength Coefficient Pa 1.e+009
Cyclic Strain Hardening Exponent 0.2
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FATIGUE ANALYSIS
Project
Author JIMIT AND MAHAVIR
Subject FATIGUE ANALYSIS
Prepared for DESIGN AND ANALYSIS OF PRESSURE VESSEL
First Saved Monday, March 17, 2008
Last Saved Tuesday, March 18, 2008
Product Version 11.0 Release
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Contents
x Model
o Geometry
FATIGUEANALYSIS
o Mesh
o Static Structural
Analysis Settings
Loads
Solution
Solution Information
Results
Max Equivalent Stress
Results
Max Shear Stress
Results
Fatigue Tool
Results
Result Charts
goodman stress life rl
Results
xMaterial Data
o Structural Steel 2
Units
TABLE 1
Unit System Metric (m, kg, N, C, s, V, A)
Angle Degrees
Rotational Velocity rad/s
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Model
Geometry
TABLE
Model > Geometry
Object Name Geometry
State Fully Defined
Definition
Source D:\pressurevesselanalysis\fatigueanalysis\FATIGUEANALYSIS.PRT.3
Type ProEngineer
Length Unit Millimeters
Element Control Program Controlled
Display Style Part Color
Bounding Box
Length X 0.762 m
Length Y 0.782 m
Length Z 2.08 m
Properties
Volume 0.30847 m
Mass 2421.5 kg
Statistics
Bodies 1
Active Bodies 1
Nodes 12181
Elements 6191
TABLE
Model > Geometry > Parts
Object Name FATIGUEANALYSIS
State Meshed
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Graphics Properties
Visible Yes
Transparency 1
Definition
Suppressed No
Material Structural Steel 2
Stiffness Behavior Flexible
Nonlinear Material Effects Yes
Bounding Box
Length X 0.762 m
Length Y 0.782 m
Length Z 2.08 m
Properties
Volume 0.30847 m
Mass 2421.5 kg
Centroid X -2.3696e-003 m
Centroid Y 2.1709e-003 m
Centroid Z -8.3295e-004 m
Moment of Inertia Ip1 522.75 kgm
Moment of Inertia Ip2 522.8 kgm
Moment of Inertia Ip3 80.459 kgm
Statistics
Nodes 12181
Elements 6191
Common Decisions to Both Types of Fatigue Analysis
Once the decision on which type of fatigue analysis to perform, Stress Life or Strain Life,
there are 4 other topics upon which your fatigue results are dependent upon. Input decisions
that are common to both types of fatigue analyses are listed below:
Loading Type
Mean Stress Effects
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Multiaxial Stress Correction
Fatigue Modification Factor
Within Mean Stress Effects, the available options are quite different. In the following
ections, we will explore all of these additional decisions. These input decision trees for
both Stress Life and Strain Life are outlined in Figures 1 and 2. fatigue analysis in both
predicted life and types of post processing available. We will look at each of these choices
in detail below.
Mesh
TABLE
Model > Mesh
Object Name Mesh
State Solved
Defaults
Physics Preference Mechanical
Relevance 0
Advanced
Relevance Center Coarse
Element Size DefaultShape Checking Standard Mechanical
Solid Element Midside Nodes Program Controlled
Straight Sided Elements No
Initial Size Seed Active Assembly
Smoothing Low
Transition Fast
Statistics
Nodes 12181Elements 6191
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Static Structural
TABLE
Model > Analysis
Object Name Static Structural
State Fully Defined
Definition
Physics Type Structural
Analysis Type Static Structural
Options
Reference Temp 22. C
TABLE
Model > Static Structural > Analysis Settings
Object Name Analysis Settings
State Fully Defined
Step Controls
Number Of Steps 1.
Current Step Number 1.
Step End Time 1. s
Program Controlled
TABLE
Model > Static Structural > Loads
Object Name Pressure Fixed Support
State Fully Defined
Scope
Scoping Method Geometry Selection
Geometry 10 Faces 2 Faces
Definition
Define By Normal To
Type Pressure Fixed Support
Magnitude -6.e+005 Pa (ramped)
Suppressed No
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FIGURE
Model > Static Structural > Pressure
Solution
TABLE
Model > Static Structural > Solution
Object Name Solution
State Obsolete
Adaptive Mesh Refinement
Max Refinement Loops 1.
Refinement Depth 2.
TABLE
Model > Static Structural > Solution > Solution Information
Object Name Solution Information
State Not Solved
Solution Information
Solution Output Solver Output
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Newton-Raphson Residuals 0
Update Interval 2.5 s
Display Points All
TABLE
Model > Static Structural > Solution > Results
Object Name Equivalent Stress Maximum Shear Stress Total Deformation
State Solved
Scope
Geometry All Bodies
Definition
Type Equivalent (von-Mises) Stress Maximum Shear Stress Total Deformation
Display Time End TimeResults
Minimum 4.7782 Pa 2.757 Pa 0. m
Maximum 6.4722e+007 Pa 3.5341e+007 Pa 4.4133e-004 m
Information
Time 1. s
Load Step 1
Substep 1
Iteration Number 1
TABLE
Model > Static Structural > Solution > Stress Safety Tools
Object Name Max Equivalent Stress
State Solved
Definition
Theory Max Equivalent Stress
Stress Limit Type Tensile Yield Per Material
TABLE
Model > Static Structural > Solution > Max Equivalent Stress > Results
Object Name Safety Factor Safety Margin
State Solved
Scope
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Geometry All Bodies
Definition
Type Safety Factor Safety Margin
Display Time End Time
Results
Minimum 3.8627 2.8627
Information
Time 1. s
Load Step 1
Substep 1
Iteration Number 1
TABLE
Model > Static Structural > Solution > Stress Safety Tools
Object Name Max Shear Stress
State Solved
Definition
Theory Max Shear Stress
Factor 0.5
Stress Limit Type Tensile Yield Per Material
TABLE
Model > Static Structural > Solution > Max Shear Stress > Results
Object Name Safety Factor Safety Margin
State Solved
Scope
Geometry All Bodies
Definition
Type Safety Factor Safety Margin
Display Time End Time
Results
Minimum 3.537 2.537
Information
Time 1. s
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Load Step 1
Substep 1
Iteration Number 1
TABLE
Model > Static Structural > Solution > Fatigue Tools
Object Name Fatigue Tool
State Solved
Materials
Fatigue Strength
Factor (Kf)1.
Loading
Type History Data
History Data
Location
C:\Program Files\Ansys Inc\v110\AISOL\CommonFiles\Language\en-
us\EngineeringData\Load Histories\sampleHistory2.dat
Scale Factor 5.e-003
Definition
Display Time End Time
Options
Analysis Type Stress Life
Mean Stress Theory Goodman
Stress Component Equivalent (Von Mises)
Bin Size 32
Use Quick Rainflow
CountingYes
Infinite Life 1.e+009 cycles
Maximum Data
Points To Plot5000.
Life Units
Units Name cycles
1 block is equal to 1.e+006 cycles
Non-constant amplitude, Proportional Loading
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Non-constant amplitude, proportional loading also needs only one set of FE results. But
instead of using a single load ratio to calculate alternating and mean values, the load ratio
varies over time. Think of this as coupling an FE analysis with strain-gauge results
collected over a given time interval. Since loading is proportional, the critical fatigue
location can be found by looking at a single set of FE results. However, the fatigue
loading which causes the maximum damage cannot easily be seen. Thus, cumulative
damage calculations (including cycle counting such as Rainflow and damage summation
such as Miners rule) need to be done to determine the total amount of fatigue damage and
which cycle combinations cause thatdamage. Cycle counting is a means to reduce a
complex load history into a number of events, which can be compared to the available
constant amplitude test data. Non-constantAmplitude, proportional loading within the
ANSYS Fatigue Module uses a quick counting technique to substantially reduce runtime
and memory. In quick counting, alternating andmean stresses are sorted into bins before
partial damage is calculated. Without quick counting, data is not sorted into bins until after
partial damages are found. The accuracy of quick
counting is usually very good if a proper number of bins are used when counting. The bin
size defines how many divisions the cycle counting history should be organized into for the
history data loading type. Strictly speaking, bin size specifies the number of divisions of the
rainflow matrix. A larger bin size has greater precision but will take longer to solve and usemore memory. Bin size defaults to 32, meaning that the Rainflow Matrix is 32 x 32 in
dimension.
For Stress Life, another available option when conducting a variable amplitude fatigue
analysis is the ability to set the value used for infinite life. In constant amplitude loading,
if the alternating stress is lower than the lowest alternating stress on the fatigue curve, the
fatigue tool will use the life at the last point. This provides for an added level of safety
because many materials do not exhibit an endurance limit. However, in non-constant
amplitude loading, cycles with very small alternating stresses may be present and may
incorrectly predict too much damage if the number of the small stress cycles is high
enough. To help control this, the user can set the infinite life value that will be used if the
alternating stress is beyond the limit of the SN curve. Setting a higher value will make
small stress cycles less damaging if they occur many times. The Rainflow and damage
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matrix results can be helpful in determining the effects of small stress cycles in your
loading history.
FIGURE
Model > Static Structural > Solution > Fatigue Tool
FIGURE
Model > Static Structural > Solution > Fatigue Tool
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TABLE
Model > Static Structural > Solution > Fatigue Tool > Results
Object Name Life Safety Factor Damage
State Solved
Scope
Geometry All Bodies
Definition
Type Life Safety Factor Damage
Design Life 1.e+009 cycles
Results
Minimum 2.e+007 cycles 0.
Maximum 50.
TABLE
Model > Static Structural > Solution > Fatigue Tool > Result Charts
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Object Name Rainflow Matrix Damage Matrix
State Solved
Scope
Geometry All Bodies
Options
Chart Viewing Style Three Dimensional
Results
Minimum Range 0. Pa
Maximum Range 1.9246e+008 Pa
Minimum Mean -3.2328e+008 Pa
Maximum Mean 6.1628e+007 Pa
Definition
Design Life 1.e+009 cycles
FIGURE
Model > Static Structural > Solution > Fatigue Tool > Rainflow Matrix
Rainflow Matrix Chart Rainflow Matrix Chart is a plot of the rainflow matrix at the
critical location. This result is onlyapplicable for non-constant amplitude loading where
rainflow counting is needed. This result may be scoped. In this 3-D histogram,
alternating and mean stress is divided into bins and plotted. The Z-axis corresponds
to the number of counts for a given alternating and mean stress bin. This result gives
the user a measure of the composition of a loading history. (Such as if most of the
alternating stress cycles occur at a negative mean stress.) From the rainflow matrix
figure, the user can see that most of the alternating stresses have a positive mean
stress and that in this case the majority of alternating stresses are quite low.
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FIGURE
Model > Static Structural > Solution > Fatigue Tool > Damage Matrix
Damage Matrix Chart
Damage Matrix Chart is a plot of the damage matrix at the critical location on the
model. This result is only applicable for non-constant amplitude loading where
rainflow counting is needed. This result may be scoped. This result is similar to the
rainflow matrix except that the percent damage that each of the Rainflow bin cause is
plotted as the Z-axis. As can be seen from the \corresponding damage matrix for the
above rainflow matrix, in this particular case although most of the counts occur at the
lower stress amplitudes, most of the damage occurs at the higher stress amplitudes.
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TABLE
Model > Static Structural > Solution > Fatigue Tools
Object Name goodman stress life rl
State Solved
Materials
Fatigue S
Recommended