Tank Design Literature

8/2/2019 Tank Design Literature

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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.


36/114

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


50/114

DESIGN APPROCH 2 BY ASME

CODES


51/114

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


57/114

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


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


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



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


Results

Minimum 7.9674 6.9674


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Information

Time 1. s

Load Step 1

Substep 1

Iteration Number 1

TABLE 14


Object Name Max Shear Stress

State Solved

Definition

Theory Max Shear Stress

Factor 0.5


TABLE 15

Model > Static Structural > Solution > Max Shear Stress > Results

Object Name Safety Factor Safety MarginState Solved

Scope

Geometry All Bodies

Definition



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


76/114

Contents

x Model

o Geometry

FATIGUEANALYSIS

o Mesh

o Static Structural

Analysis Settings

Loads

Solution


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




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 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


Object Name Max Equivalent Stress

State Solved

Definition

Theory Max Equivalent Stress


TABLE

Model > Static Structural > Solution > Max Equivalent Stress > Results


State Solved

Scope


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Geometry All Bodies

Definition



Results

Minimum 3.8627 2.8627

Information

Time 1. s

Load Step 1

Substep 1

Iteration Number 1

TABLE


Object Name Max Shear Stress

State Solved

Definition

Theory Max Shear Stress

Factor 0.5


TABLE

Model > Static Structural > Solution > Max Shear Stress > Results


State Solved

Scope

Geometry All Bodies

Definition



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


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


86/114

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


87/114

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

Tank Design Literature

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