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A REPORT

ON

PRESSURE VESSEL DESIGN AND ANALYSIS

BY

Alok Saxena (2010A4PS319G)

(B.E (Hons.)Mechanical)

Bhavik Kakka (2010A4PS237G)

(B.E (Hons.)Mechanical)

Under the guidance of:

Dr. D.M. Kulkarni

(Dept. of Mechanical Engineering, BITS Pilani K.K. Birla Goa Campus)

Prepared in partial fulfilment of the Computer Oriented Project;

Course No: BITS C331

AT

BITS Pilani K.K Birla Goa Campus

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ACKNOWLEDGEMENT

A Project of any kind is a boon for budding engineers. It

develops work ethic and orients students towards a career in

applied research. I am lucky to have an opportunity to carry

out a computer oriented project. Compiling this report has

been a great learning curve and a satisfying one. This report

was made possible due to the great help of certain people i

would like to acknowledge.

Dr. D.M. Kulkarni for giving me such an interesting project

and for his valuable inputs.

My friend Ravi Teja for helping with the technical difficulties

faced during modelling.

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ABSTRACT

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. This project is to

develop an interactive system to design pressure vessels

besides the understanding of the algorithm in designing

pressure vessel. Results generated by the system were to

compare with manual calculations using ASME VIII-1

design code. Besides that, a finite element model was

created using the results generated by the system and the

maximum stress value in finite element analysis was

compared with theoretical calculation. This project

includes comparison studies to compare self-defined

material with material library and self-defined load. As a

conclusion, designing pressure vessel using computer

aided tool is easier and interactive.

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Table of Contents

Pg no.

Stress

Loadings

Failures in pressure vessel

Strength theories

Nozzle openings and

reinforcements

Design of shell and its

components

Design calculations

Model

Ansys analysis

Problems encountered

Design Summary

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8

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10

13

14

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19

21

29

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INTRODUCTION

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 normal stresses 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/t≥10. 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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STRESS Types of Stresses

Tensile, Compressive Shear, Bending, Axial Discontinuity Membrane Tensile Tangential Load induced Strain induced Circumferential Longitudinal Radial Normal

Classes of stress Primary Stress General:

Primary general membrane stress Primary general bending stress

Local: Primary local stress,

Secondary stress:

Secondary membrane stress. Secondary bending stress Peak stress

PRIMARY GENERAL STRESS: 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 bending stresses. Calculated value of a primary bending stress may be allowed to go higher than that of a primary membrane stress. Primary general membrane stress

Circumferential and longitudinal stress due to pressure.

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Longitudinal stress due to the bending of the horizontal vessel over the saddles.

Membrane stress in the centre of the head. Membrane stress in the nozzle wall Axial compression due to weight.

LOCAL PRIMARY MEMBRANE STESS Membrane stress at local discontinuities:

Head-shell juncture Nozzle-shell juncture Shell-flange juncture

Membrane stresses from local sustained loads: Support legs Nozzle loads Beam supports Major attachments

SECONDARY STRESS Secondary membrane stress

Axial stress at the juncture of a flange and the hub of the flange

Membrane stress in the knuckle area of the head. Secondary bending stress

Bending stress at the gross structural discontinuity: for eg: nozzle

The non-uniform portion of the stress distribution in a thick-walled vessel due to internal pressure.

The stress variation of the radial stress due to internal pressure in thick-walled vessels.

Peak Stress

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Stress at the corner of discontinuity. Stress due to notch effect. (stress concentration).

LOADINGS 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. The stresses applied more or less continuously and uniformly across an intersection of the vessel are primary stresses. The stresses due to pressure and wind are primary membrane stresses. On 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. 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. Loading can be outlined as follows:

Categories of loadings General loads—Applied more or less continuously across a

vessel section. Pressure loads—Internal or external pressure (design,

operating, hydro test, and hydrostatic head of liquid). Moment loads—Due to wind, seismic, erection,

transportation. Compressive/tensile loads—Due to dead weight, installed

equipment, ladders, platforms, piping and vessel contents. Local loads—Due to reactions from supports, internal,

attached Piping, attached equipment, i.e., platforms, mixers, etc.

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a. Radial load—Inward or Outward. b. Shear load—Longitudinal or circumferential. c. Torsional load. d. Tangential load. e. Moment load—Longitudinal or circumferential.

FAILURE IN PRESSURE VESSELS Categories of Failures:

Material--Improper Selection of materials; defects in material.

Design—Incorrect design data; inaccurate or incorrect design methods; inadequate shop testing.

Fabrication – Poor quality control; improper or insufficient fabrication procedure including welding; heat treatment or forming methods.

Service—Change of service condition by the user; inexperienced operations or maintenance personnel; upset conditions.

TYPES OF FAILURES Elastic deformation—Elastic instability or elastic buckling, vessel geometry, and stiffness as well as properties of materials are protecting against buckling. Brittle fracture—Can occur at low or intermediate temperature. Brittle fractures have occurred in vessels made of low carbon steel in the 40-50 F range during hydro test where minor flaws exist. Excessive plastic deformation—The primary and secondary stress limits as outlined in ASME Section VIII, Division 2, are intended to prevent excessive plastic deformation and incremental collapse. Stress rupture—Creep 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.

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Strength Theories

The majority of material strength data is based on uniaxial tensile

test results. Usually, we have to work with is the yield strength Sy

and/or the ultimate tensile strength Su.

This is fine if we only have the one normal stress component

present : this is true for simple tension or compression members

and for parts loaded only in bending.

In this case, failure (defined as the onset of plastic deformation)

occurs when

σx = σ1 =Sy/FOS

‘FOS’ is the factor of safety.

In many loading cases, we have more than just one normal stress

component.

E.g. in torsion, we have a single shear stress component:

Or, combined bending and torsion in a shaft:

These cases can all be reduced to a simple biaxial case by finding

the principal stresses,

σ1 and σ2

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For ductile materials there are two commonly used

Strength theories - the Maximum Shear Stress (MSS) or Tresca

theory and the von Mises Stress criterion

Strength Theories

1. Maximum Shear Stress:

This states that failure occurs when the maximum shear

stress in the component being designed equals the

maximum shear stress in a uniaxial tensile test at the yield

stress:

This gives τmax = Sy/2FOS or

| σ1 – σ2 | = Sy/FOS or | σ2 – σ3 | = Sy/FOS or | σ3 – σ1 | =

Sy/FOS

Which ever of the last three leads to the safest result. The latter

usually involves σ3 being zero, i.e. plane stress, and both σ1 and

σ2 having the same sign.

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2. Von Mises Theory:

This states that failure occurs when the von Mises stress σe in the

component being designed equals the von Mises stress σe in a

uniaxial tensile test at the yield stress:

This gives: σe = √2/2 [(σ1 – σ2)2 + (σ2 – σ3)2+ (σ3 – σ1)2]0.5 =

Sy/FOS

In the plane stress case we have σ3 = 0 and hence:

σe = [σ12 – σ1σ2 + σ22]0.5 = Sy/FOS

This is the most commonly used of the strength equations.

A third theory, the Maximum Normal Stress theory is similarly

defined. It must NEVER be used for design with ductile materials.

A modified version of this theory is sometimes used with brittle

materials

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NOZZLES, OPENINGS AND REINFORCEMENTS

Nozzles and openings are necessary components of pressure

vessels for the process industries. Openings in a cylindrical shell,

conical section or closure may produce stress concentrations,

adjacent to the opening and weaken that portion of the vessel. In

order to minimize such stress concentrations, it is preferable that

the opening be circular in shape. As a second choice the openings

may be made elliptical, as a third choice they may be made

around. An around opening has two parallel sides and two semi-

circular ends. Openings of other shapes are permissible if the

vessel is tested hydrostatically. If the opening in a closure of

cylindrical vessel exceed one-half the inside diameter of shell, the

opening and closure should be fabricated. Others require

reinforcement. Small sizes of openings welded or brazed to a

vessel do not require reinforcement.

■ In the case of shell, opening requiring reinforcement in vessel under internal pressure the metal removed must be replaced by the metal of reinforcement. In addition to providing the area of reinforcement, adequate welds must be provided to attach the metal of reinforcement and the induced stresses must be evaluated. Materials used for reinforcement shall have an allowable stress

value equal to or greater than of the material in this vessel wall

except that, when such material is not available, lower strength

material may be used; provided, the reinforcement is increased in

inversed proportion to the ratio of the allowable stress values of

the two materials to the ratio of the two materials to compensate

for the lower allowable stress value of any reinforcement having a

higher allowable stress value than that of the vessel wall.

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DESIGN OF SHELL AND ITS COMPONENTS

The pressure vessel considered here is a single unit when

fabricated. However, for the Convenience of design, it is divided

into the following part: (1) Shell; (2)head or cover; (3) nozzles;

(4) support; Most of the components are fabricated from plates or

sheets. Seamless or welded pipes can also be used. Parts of

vessels formed are connected by welded or riveted joints. In

designing these parts and connections between them, it is

essential to take r into account, the efficiency of joints. For welded

joints, the efficiency may be taken as 100% if the joint is fully

checked by a radiograph and taken as 85%, even if it is checked at

only a few points. If the radiographic test is not carried out 50 to

80%, I efficiency is taken. Efficiencies vary between 70 to 85% in

the case of riveted joints. All these are made for pressure vessels

operating at pressures less than 200kg/kmA2. Design procedure

is primarily based on fabrication by welding.

Design Calculation

Given data

Internal pressure (P) = 10 Mpa

Internal Diameter (Di) = 500mm

Corrosion Allowance (CA) = 3mm

Joint Efficiency for shell = 1

a=500mm ( Major axis of elliptical head )

b=250mm (Minor axis of elliptical head)

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Thickness Calculation (ASME CODE)

Head Thickness (t): t=Pi Di K

2𝜎𝑡 ɳ−.2𝑃𝑖+ 𝐶𝐴

Cylinder shell thickness (T): T=Pi Di K

2𝜎𝑡 ɳ−𝑃𝑖+ 𝐶𝐴

K=1

6[2 + (

𝑎2

𝑏2)]

a=semi-major axis of ellipsoidal head

b=semi-minor axis of ellipsoidal head

CA=corrosion allowance; K=stress intensity factor

Pi=pressure in MPa; Di=internal diameter of cylinder

ɳ=joint efficiency; σt=allowable stress.

a=500mm, b=250mm

K=1

6[2 + (

𝑎2

𝑏2)]

=1

6[2 + (

5002

2502)] =1

Pi =10 MPa, Di=1000mm, K=1, Syt=350 MPa, FoS=2 ɳ=1(double welded butt joint with full penetration, fully radiographed) CA=3mm

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Using Max. Shear stress criteria:

σt=0.5Syt

2 (where Factor of safety=2)=87.5 MPa

t=Pi Di K

2𝜎𝑡 ɳ−.2𝑃𝑖+ 𝐶𝐴 (ASME design code)

=(10) (1000) (1)

2(87.5) (1)−.2(10)+ 3

≈61mm

T=(Pi Di K

2𝜎𝑡 ɳ−𝑃𝑖+ 𝐶𝐴 )=

(10)(1000) (1)

2(87.5) (1)−10+ 3 ≈64mm

Nozzle reinforcement calculations:

trs= required shell thickness, ts=shell thickness,

trn=required nozzle thickness, tn=nozzle thickness (a

reference thickness), d=internal diameter of nozzle,

d0=external diameter, Rs= Internal radius of the

cylindrical shell

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tn=27.75mm, ts=64mm, d=154mm, P=10 Mpa, Rs=500mm Design by ASME code:

trs=𝑃Rs

σt−.6P=

(10)(500)

87.5−(.6)(10)=61.35mm

trn=𝑃Rn

σt−.6P=

(10)(77)

87.5−(.6)(10)=9.44mm

Now, (a) ts+tn+.5d=168.5mm (b) d=154mm

Also, (a)2.5 ts=160mm (b)2.5 tn=69.375mm The reinforcement area required is : Ar=dXtrs=9447.9mm2 The reinforcement area available in the shell:

A1=(2a-d)( ts-trs)

=466.5mm2

The reinforcement area available in nozzle wall is available in two parts : A2=2(2.5 ts)( ts- trn)=17459.2mm2

A3=2(2.5 ts) ts=20480mm2 The total area available for reinforcement :

The limit parallel to the surface of the shell is the larger of two quantities = 168.5mm

The limit normal to the

surface of the shell is the

smaller of

quantities=69.375mm

Where a=

Greater of d+2CA=160mm &

(d/2 +ts +tn -3CA)=157.75mm

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At=A1+A2+A3=38405.7mm2

At > Ar Result: The available reinforcement At therefore exceeds the reinforcement required Ar and the method is acceptable. Hence padding is not necessary. Height of nozzle outside the vessel: H1=2.5(ts-CA)=152.5mm OR H1=2.5(tn-CA)=62mm The extension of nozzle inside the vessel: H2 18mm Determined experimentally as discussed in the problems encountered section

Smaller of the two values is

chosen as H1.

So H1=62mm

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MODEL

Material Used Properties AISI 1020 Steel, Cold rolled

Main Components 1) Ellipsoidal head (a:b=2), a=500mm, b=250mm. Thickness=61mm a=major axis b=minor axis

2) Cylindrical shell Internal radius=500mm Thickness=64mm

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3) Nozzle and flange Internal diameter =154mm Thickness = 27.75mm H1=62mm H2=18mm

CUT SECTION FOR ANALYSIS

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Analysis layout:

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Fixed support and loads

MESHING

Fine Mesh 49322 nodes 27628 elements Element type and size program controlled.

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Max Shear stress criteria

Max allowable stress

87.5Mpa ((.5Syt)/2) where Syt=350 Mpa, FoS=2

Max stress from analysis

85.48 Mpa

Min stress from analysis 64797 pa Result : Design Passed Since max stress < max

allowable stress

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Von-Mises stress Criteria:

Max allowable stress 175 Mpa ,((Syt)/2), Fos=2 Syt=350 Mpa

Max stress from analysis 162.3 Mpa Min stress from analysis 123300 pa Result: Design Passed Since Max stress at any

point < Max allowable stress

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Problems Encountered

The main problem faced during the analysis was near the

openings of the pressure vessel i.e. near the welding at the

extension of nozzle inside the vessel. Here, for both

strength criteria 1) Maximum shear stress criterion 2) Von

mises criterion, the stress exceeded the allowable stress.

Therefore H2 i.e. length of extension of nozzle inside the

pressure vessel was varied starting from minimum 15mm

to 20mm for which H2=18mm gave accepted stress value

that was less than the maximum allowable stress.

Maximum allowable shear stress =

87.5N/mm2

H2 (mm)

Max Shear stress(N/mm2)

Pass/Fail

15 97 Fail 16 105 Fail 17 146 Fail 18 85.48 Pass 19 93 Fail 20 158 Fail

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Summary

Pressure vessel requirement Design a pressure vessel of capacity 10 MPa to carry compressed air at room temperature with allowance for corrosion.

Material used and its properties (AISI 1020 steel, cold rolled)

Elastic Modulus in X 205000 N/mm^2

Poisson's Ration in XY 0.29 N/A

Shear Modulus in XY 80000 N/mm^2

Mass Density 7870 kg/m^3

Tensile Strength in X 420 N/mm^2

Yield Strength 350 N/mm^2

Thermal Expansion 1.17e-005/K

Thermal Conductivity 51.9 W/(m·K)

in X Specific Heat

486 J/(kg·K) Type and components Pressure vessel with semi

ellipsoidal head(major axis to minor axis ratio of the ellipse = 2:1,thickness=61mm) with cylindrical body(thickness=64mm)

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Components: semi-ellipsoidal head caps, cylindrical body, supports and nozzle(thickness 27.75mm,extension outside=62mm,extension inside=18mm)

Criteria used to test for failure

Von misces stress: Max stress: 162.3N/mm^2 Min stress: .12330 N/mm^2 Max shear stress : Max stress: 85.48N/mm^2 Min stress: .064797N/mm^2

Results The maximum stresses obtained from analysis are below the maximum allowed stresses given by the above mentioned theories. Hence design is safe.