cl308

CL 308

Process Equipment Design andEconomics [3 0 0 6]

Course Content

Mechanical design of process equipment: pressure vessels, tall columns, etc., process

piping design; Materials and Fabrication Selection;

Design Strategy and Optimum Equipment Design: Economic Design criteria; Cost

and Asset Accounting; Cost Estimation; Interest and Investment Costs; Taxes and

Insurance; Depreciation; Profitability, Alternative Investments and Replacement;

Illustrative Case Study in Process Equipment Design and Costing of Equipment in

each of the following categories: Material Transfer, Handling and Treatment Equip-

ment

• Heat Transfer Equipment: Shell and tube heat exchangers (Kern and Bell-

Delaware design methods), Plate heat exchangers, Evaporators

• Mass Transfer Equipment: Absorption/ Stripping columns (packed/tray), Mul-

ticomponent distillation column (Fenske – Underwood-Gilliland correlations)

• Reactors: Choices of reactors, non-isothermal reactors, reactor configuration,

interstage heating/cooling, multi-tubular reactors, catalyst deactivation.

Texts/References

• M.S. Peters, K.D. Timmerhaus, Ronald E. West, Plant Design and Economics

for Chemical Engineers (5th edn.), McGraw Hill, 2004.

• M.V. Joshi and V. V. Mahajani, Process Equipment Design (3rd Edn.), McMil-

lan India, New Delhi, 1996.

1

• Relevant Design Codes BS, IS and ASME.

• D.F. Rudd and C.C. Watson, Strategy of Process Engineering, John Wiley,

1969.

• F.C. Jelen and J.H. Black, Cost and Optimization Engineering, McGraw Hill,

3rd ed., 1992.

• S. Walas, Chemical Process Equipment Selection and Design, Butterworth, 1988

• R.K. Sinnot, An Introduction to Chemical Engineering Design, Pergamon Press,

Oxford, 1989.

• R. Smith, Chemical Process Design, McGraw Hill, 1995

Weightage

• Assignment 40%

• Quiz 20%

• Mid semester 15%

• End semester 25%

2

1 Materials properties and applications

Important criteria is properties of materials. Final choice depends on the ease of

fabrication and cost of the materials. Mainly two types of materials - Metal and

Non-metal are used as material of construction. Again in the metal there are Ferrous

metal and non-ferrous metal. Important characteristics to be considered for selecting

the materials of construction are

• Mechanical properties

– Strength (maximum stress a materials can withstand) – tensile strength.

– Stiffness (resistance to bending or buckling) – elastic modulus (Young’s

modulus)

– Toughness – fracture resistance

– Hardness (resistance by the materials to indentation and scratching) – wear

resistance

– fatigue resistance (failure of materials upon cyclic load)

– Creep resistance (progressive deformation of materials under constant stress)

• The effect of temperature (high and low) on mechanical properties.

• Corrosion resistance

• Any special properties require like thermal conductivity, electrical resistance,

magnetic properties.

• Properties related to fabrication are machinibility, weldability, malleability (ma-

terials ability to deform in the form of sheet under compressive stress), casta-

bility.

• Availability in standard size – plate section, tubes.

• Cost of the materials.

Following is the composition of material, properties and application from M. V. Joshi

and V. V. Mahajani, Process Equipment Design (3rd Edn.)

3

Composition Properties Applications

1. Ferrous Metals Known for strength, availability and ease of machining.

Classified based on % of C - Wrought iron, Cast iron and

Steel

A. Wrought Iron: al-

most pure Fe with low

C and Mn

Not considered for corrosion resistance materials, but ex-

cellent for atmospheric corrosion. Alkalis, alkaline solu-

tion, concentrated and cold HNO3, H2SO4 and organic

acid can very little attack on metal. Easily formed into

desired shape, forged, machined and welded

Extensive use in elevated temperatures;

mainly in steam lines, condensate return

lines, heating coils, exhaust lines, smoke

stacks.

B. Cast Iron: mainly

Fe with 2.5 to 4.5% C

Cheap, easy to cast even in complicated shape for fluidity

in molten state. Depending on the cooling rate of molten

state it can be - Grey cast iron or White cast iron

Mainly used to produce complicated

shape which introduces fabrication diffi-

culties and where resistance to abrasion

and corrosion resistance is desired.

a. Grey cast iron C is in graphite form, distributed as free crystals through-

out the Fe, compressive strength 3 times of tensile

strength, Hardness number between 180 and 240. No out-

standing corrosion resistance but not corroded by alkali

solution < 20% conc. at any T

Applications are in pump, valves, spe-

cial piping, acid coolers, acid reaction and

concentration vessels.

b. White cast iron C is in chemical composition with Fe, Highly brittle in

nature.

Use in parts of furnace bars, teeth, jaws

of crushing and grinding machines.

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c. Cast iron with

small quantity of cal-

cium silicide

After heat treatment - better tensile and shear strength

resulting high duty cast iron

Use for fabricating pressure vessel, high

pressure and temperature pipes and fit-

tings.

d. Alloy cast iron improvement of basic properties of cast iron - extend the

range of applications.

i. High silicon cast

iron

Poor mechanical properties. They are hard but brittle -

difficult in machining, vulnerable to mechanical shock and

excessive strain. But superior degree of chemical resis-

tance.

Unaffected by H2SO4 (any concentration

and any Temperature), hot strong HNO3,

atmospheric conditions etc.

ii. High silicon cast

iron with 3% Mo

Improve chemical resistance further. Imparts high degree of resistance to HCl

and Chlorine containing chemicals.

iii. High silicon

cast iron with small

amount of Cu and Ni

(Hastelloy D)

Superior mechanical properties and good chemical resis-

tance

Resistance to most of the organic com-

pounds, solvents, alkalies and H3PO4.

Also resistance to atmospheric oxidation,

flue gases, hydrocarbon as well as wet and

dry NH3.

iv. Cast iron with

high Ni with Cu and

Cr (Ni-resists)

Unique engineering properties of corrosion resistance, wear

resistance, strength, heat resistance, toughness, good

castability and mechinability.

Alkali and neutral salts can be handled

by this materials.

5


C. Steel (Fe alloyed

with 0.05 to 2% C). In

addition small amount

of P, S, Si, Mn

Normally known as plain carbon steels. Some

cases, alloying elements are added these steels

are known as alloy steels

I. Plain carbon steels Depending upon the % of C - known as low,

medium and high carbon steels

i. Low carbon / Mild

steels (Fe alloyed with

0.05 to 0.3% C)

Most versatile material, Good mechanical

strength and ductility, easily rolled, forged and

drawn, Fabrication by welding and machining

is easily carried out. Corrosion resistance is

comparatively low.

If rate of corrosion is slow, certainly economical to

use. Use in pressure vessels, pipes, fittings, machine

components, and structural sections. To avoid corro-

sion, steel may be protected by paint, metal spraying,

or other protective linings.

ii. Medium carbon

steels (Fe alloyed with

0.3 to 0.5% C)

Improved hardness, strength and fatigue resis-

tance.

Mainly used for fabrication of shaft, springs, gears,

bolts and certain structural sections.

iii. High carbon steels

(Fe alloyed with 0.5 to

2% C)

Much harder and stronger than mild steels and

medium carbon steel but much less ductile.

Normally used in dies, cutting tools.

6


II. Alloy steels:

mainly low carbon

steel or mild steel

with variety of alloy-

ing elements like Ni,

Cr, Si, Mn, Mo, W,

Be, V, Co, Ti.

• Mn gives abrasion resistance and toughness,

• Ni and Cr use for corrosion and high temperature resistance,

• Cr, W, V, Mo, Co for cutting action,

• Ni, Cr, Ti for creep resistance,

• Si and Mn for elasticity

i. Low alloy steels

(<10% of Ni, Cr, Mo,

Mn etc.). Usually ∼

0.15% C, ∼ 1% Mn, ∼

0.3% Si.

Used for machine components

and to a limits extent for pres-

sure vessel

Quenched and tempered low alloy steels has extensive use due to high

strength, high toughness, weldability, high corrosion resistance, heat

resistance and good workability. Yield stress values of these steel are

∼ 3 times of ordinary mild steel of structural and boiler quality.

Mainly pressure vessels, also

use for high and low temper-

ature service conditions.

7


Steels with 0.5, 1, 2.25, 3% Cr have better corrosion resis-

tance than ordinary mild steel

Normally used for high temperature ser-

vice under mild corrosive conditions.

Medium carbon steel with 1% Cr-Mo with or without V Most suitable for bolting.

ii. High alloy steels:

Cr-steel having 13 to

17% Cr and Cr-Ni

steels i.e., stainless

steels with 18 to 25%

Cr and 8 to 20% Ni.

C varies from 0.04 to

0.25%.

Stainless steels are high Cr and high Cr-Ni alloy with small

amounts of other essential elements. Excellent corrosion

resistance and heat resistance properties. Common variety

stainless steel ∼ 18% Cr and 8% Ni. Addition of Mo in-

creases corrosion resistance and high temperate strength.

Surface oxidation or passivation of stainless steels makes it

more corrosion resistive. Many types of stainless steels are

available depend on alloy content/microstructure/major

characteristics.

Major applications in Vessel such as stor-

age tank, reactors, absorption and dis-

tillation columns, heat exchangers, Ma-

chinery such as pumps, fans, compres-

sors, centrifuges, dryers, coolers and fil-

ters. Material handling equipments such

as pipes, conveyors and tankers. Used for

cladding for plain carbon steel or low al-

loy steel (8-20% of the total thickness).

Chromium steels

Chromium steel with 0.08% C Use for plates.

Chromium steel with 0.1% C Use for forging.

Chromium steel with 0.2% C Use for coatings.

Chromium steel with 0.15% C Use for bolting

Chromium steel > 0.1% C, hardenable by heat treatment

8


III. Types of stainless steels based on

micro structure

i. Austenitic stainless steels (Fe and Ni

6 to 22%, Cr 16 to 26%)

American Iron and Steel Institute (AISI) 300

series predominant type for their high strength

to weight ratio, ductility and ease of fabrica-

tion, resistance to heat, clod mechanical dam-

age, fatigue and corrosion

In chemical industry they are used

around 70%. Much better corro-

sion resistance than the other type.

But susceptibility to stress corro-

sion cracking.

ii. Martensitic stainless steels: Gener-

ally lowest alloy content. Cr > 11%, Ni

1.25 to 2.5% or higher C content (0.1

to 0.6%)

Higher C content steels having poor corrosion

resistivity

iii. Ferrite stainless steels: 13 to 30%

Cr with low C

AISI 400 series. Good oxidation resistance,

good for mild corrosive service.

Use in high temperature

iv. Ferrite-austenitic stainless steels: ∼

26% Cr, 5% Ni.

Have higher mechanical strength and improved

resistance against stress corrosion compared to

austenitic stainless steels.

v. Nitrogen added stainless steels: 0.15

to 0.20% N2 added to stainless steels.

Substantial increase of yield strength - called

as“high proof stainless steels”. 304, 316 and

316 L are important variations.

Use in moderately high temperature

applications.

9


2. Non-Ferrous Metals Mainly metals other than Fe and its alloy

i. Al and Al-alloy Light metal and easy to fabricate. But pure Al relatively week. Sur-

face film of inert Al2O3 protect the metallic Al. Provides Al-alloy

having better mechanical properties. Common alloying elements are

Cu, Si, Zn, Mn, Ni, Mn. Al-Zn-Mg alloy is the strongest among all

Al alloys.

Al-alloy good for the low tem-

perature service up to -1500C.

Mainly use for storage vessel,

reaction vessel, heat exchang-

ers and absorption column.

ii. Cu and Cu-alloy Pure Cu good ductile, malleablity, high electric and thermal con-

ductivity. Fair mechanical strength, different shapes can be easily

fabricated. Easily joined by welding and soldering. Good corrosion

resistance to alkali and organic solvents. Also protective to atmo-

spheric and oxygen atmosphere because of inert oxide layer.

Used in sheets and tubes.

Can be alloyed with Zn, Sn, Ni, Cr, Al, Pb, Be and Mn. Cu-alloy

provide greater strength and ease of machining and coating capability.

Cu-Zn alloy (Brass): 55%

Cu and 45% Zn

Suitable for tube, wires, sheet

for clod work

Cu-Sn alloy (Bronze): 5% Sn for wrought work and 10% Sn for casting work. Use in pump valve pipe fit-

tings etc.

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Cu-Al alloy (Aluminum

bronze): 14% Al

high resistance to oxidation and scaling. They are best Cu-alloy

for moderately elevated temperature.

Use in pump casting, condenser,

tube, valves, seats etc.

Cu-Ni alloy: contain 10 to

30% Ni

Good strength, ductility and corrosion resistance Extensively used for condenser

fabrication.

iii. Ni and Ni -alloy High corrosion resistance to most of the alkalies. Strength and

hardness of Ni is similar to carbon steel and metal can be fab-

ricated.

Economical use of steel claded

Ni extensively in production of

NaOH and alkalies.

Ni-Cu alloy (Monel): 67%

Ni and 30% Cu

Less resistive to molten salts and alkali metals than Ni. But

presence of Cu impart superior resistance to non-oxidizing chlo-

rine solution and hot dilute solution of non-oxidizing acids.

Mainly use in food industries. In

chemical industries, it is used in

evaporator, heat exchanger etc.

Ni-Cr-Fe (Inconel): 76% Ni,

15% Cr and rest is Fe

Presence of Cr increases the resistance to oxidizing condition.

Good heat resistance.

Use in digester, exchanger etc.

Ni-Mo alloy (Hastelloy C): High resistance to corrosion over wider range of materials at

higher temperature and concentrations.

Hastilloys C: 56% Ni, 17%

Mo, 16% Cr, 5% Fe, 4% W

Excellent corrosion resistance at elevated temperatures. Use in valve, pipping, heat ex-

changers and vessels.

To meet severely corrosive condition, Ni-Mo alloys are often the

only alternatives to precious metals like Pt, Ag etc.

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Cr and Cr-alloys Cr used for either plating of Fe or steel or as alloying elements

in low and high alloying steels. Provide corrosion, creep and

wear resistance along with the cutting action of steel.

Lead Resistance to corrosion, low creep and fatigue resistance. It is

soft and malleable. Provide protective surface film to resists sul-

phate, carbonate or phosphate, good corrosion resistance prop-

erties.

Use for lining and cladding of

metal equipment, Lead sheets

and pipes used for equipment fab-

rication.

3. Non-Metals Different types of materials - carbon and graphite, glass, rubber,

plastic etc.12


i. Carbon and

Graphite

Available in different form depending upon the basic structure,

orientation, crystal size, pore spacing etc. Generally inert to all

chemicals except the strongly oxidizing application.

Mainly use for corrosion re-

sistance.

C is good insulator and graphite has good conductivity. C brick use in high temper-

ature vessel for insulation.

Graphite is use in heat ex-

changers.

ii. Glass Low tensile strength but high compressive strength, excellent

resistance to corrosion except HF and alkaline solution.

Steel coated glass have cor-

rosion resistive power like

glass and strength like steel.

iii. Rubber

(natural and

synthetic)

Mainly use for lining of

chemical equipment, also

use as gasket.

Natural rubber resistance to dilute acid, alkalis, salts but affect

by oxidizing media, oils, benzene etc. Some of the synthetic

rubbers are ploychloroprene or neoprene, nitrile, butyle, silicon,

viton, urethane etc. They are resistance to oil and solvents.

Silicon and viton are excellent high temperature resistance, ure-

thane has good abrasion resistance, hardness and resilience.

Due to resistance to acid

and alkali, rubber lining

is use in stirrers, fans,

centrifuge baskets, pumps,

valves, storage vessels etc.

13


iv. Plastics Low weight, good thermal and electrical insulation, ease of fabrication,

pleasing appearance. Excellent resistance to weak mineral acids and salt

solutions and resistance to atmospheric conditions. However, can be used

only moderate pressure and temperatures. It has low strength and only fair

resistance to solvents. two types of plastics - thermoplastic (soften under

application of heat) and thermosetting plastics (cured under temperate and

pressure to make it hard which does not deform under heat again).

a. Thermoplas-

tic

Available in the form of sheets, films, rods, pipes. Can be moulded and

extruded to various shapes and sizes. Common thermoplatics are nylon,

methacrylate, polystyrene, polyethylene, polyvinyl chloride etc.

Mainly use as reaction ves-

sel, storage tanks, gas wash-

ing towers, ducting, venti-

lating system,m fan pipe,

fittings, gasket etc.

b. Thermoset-

ting plastic

Comparatively hard and brittle. Therefore added with fillers (wood flour,

cotton flock, asbestos etc.). Polyester and epoxy resins with glass fiber rein-

forcements are useful. Common thermosetting plastics are formaldehyde,

urea formaldehyde, melamine formaldehyde, ployester, epoxy and silicon

resins etc.

Use as lining material and

to make pipes, fittings,

ducts, vessels, tank etc.

Can also use for laminating

materials.

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2 Materials selection practice

Table 1: Materials selection practice (Joshi and Mahajani).

Environment Materials

Non-staining atmospheric exposure Al

Oxidizing environment Cr- alloy

Reducing and non-oxidizing environment Cu and Cu- alloy

Hot HCl Hastealloys

Diluted H2SO4 Pb

Concentrated H2SO4 Steel

HF Monel

Caustic, reducing and nn-oxidizing environments Ni and Ni alloy

Distilled water Sn

Hot strong oxidizing solution Ti

3 Effect of temperature on mechanical properties

• Effect on tensile strength and elastic modulus: With increase in temper-

ature, tensile strength and elastic modulus of metal decreases. For example,

mild steel (MS) following is the data,

Tensile strength: 450 N/mm2 (250C) → 210 N/mm2 (5000C).

Young’s modulus: 200,000 N/mm2 (250C) → 150, 000 N/mm2 (5000C)

• Effect on creep stress: Creep resistance is important for materials at high

stress at high temperature e.g., furnace tube are mainly made of special alloy -

Inconel.

• Effect on ductile material: Normally ductile materials become very brittle

in the low temperature zone < 100C. For low temperature application, cryogenic

15

plant and liquefied gas storage , astenitic SS and aluminum alloy are generally

employed.

4 Type of corrosion

Many metals form a natural protective film under certain condition. Like Al, Ni, Cr

form an comparatively inactive oxide layer on top of the metal. Similarly, stainless

steel (SS) in oxidizing environment form a protective film on its surface. These

materials are comparatively resistive to corrosion. But in the cases, where this type

of passive layer does’t form or the cases, where the protective layer gets damaged due

to high stress or fatigue, there is a high chance of corrosion. Following are different

types of corrosion

• Uniform corrosion: Corrosion due to chemical/electrochemical reaction through-

out the exposed surface area of the equipment.

• Galvanic corrosion: Two dissimilar metals in presence of conducting process

fluid form a electrochemical cell where one metal work as anode and other one

act as cathode. Due to this electrochemical action, anode gets corroded. Thus

general recommendation for choosing the metal combination which are far apart

in the electrochemical series.

• Crevice corrosion: Localized corrosion due to stagnant process fluid in the

gaps/contact area between parts (under bolts/rivet head), under the gaskets

and seals, mild cracks etc.

• Pitting: Localized corrosion that form pits in the metal surface. Can be caused

by presence of rough spots, impurities, inclusion of slag during welding, impinge-

ment of bubbles, effect of cavitation in pumps etc.

• Intergranular corrosion: Preferential corrosion of materials at grain (crys-

tal) boundary. This is mainly due to impurities at the grain boundaries or

accumulation or depletion of one of the alloying elements at grain boundary.

16

• Selective leaching: One of the element of metals or alloy become reactive

with the liquid in contact and it leached out from the structure, e.g., in case of

CS, under certain condition iron corrodes and leaves from the structure leaving

a porous graphite residue.

• Stress corrosion: Corrosion results from internal/external stress and forma-

tion of crack, which grow rapidly and can cause premature brittle failure of the

metal. Necessary condition is the simultaneous stress and presence of corrosive

substance, particularly Cl−, OH−, NO−

3 or NH4+ ions etc.

• Fatigue corrosion: Stress due to cyclic load causes rupture of the protective

passive layer or crack formation and material gets contact of corrosive environ-

ment.

• Errosion corrosion: Due to impinging motion of corrosive fluid or abrasion

due to suspended solid particles in the liquid, equipment gets wear and exposed

to corrosion environment.

• High temperature oxidation: In dry condition, CS and low alloy steel nor-

mally oxidize rapidly in high temperature both in air and steam. Thus their use

is limited in < 5000C. For higher temperature (> 5000C), normally chromium

alloy is recommend for oxidizing environment.

• Hydrogen embrittlement: Loss of ductility due to reaction or H2 absorption

in the metal. Mainly important for material selection for reforming section.

At high temperature, alloy steel serves better purpose than plain carbon steel

(CS). At temperature < 500 0C, CS can be used.

5 Quantifying corrosion and its limits

Usually expressed as a penetration rate in inch per year (ipy). Also expressed as mills

per year (mpy) (1 mill = 10−3 inches) and sometimes as milligram of weight loss per

17

square decimeter per day (mdd).

ipy =12w

tAρ(1)

Where w is lb of mass loss in time t, A is the surface area in ft2, ρ is the density

of material in lb/ft3 and t is in year. 1 ipy = 25 mm per year. Acceptable rate of

attack depends on cost of material, duty, safety and the economic life of the plant.

For most of the metals, penetration rate is 0.12 mm/y is satisfactory. Corrosion rate

between 0.12 to 1.2 mm/y may be economic, depending on th cost of materials, alter-

native materials etc. Corrosion also depends on the temperature and concentration

of corrosive fluid. Most of the cases, increase in temperature corrosion increases.

18

6 Shell thickness and combined stress analysis

Tensile stress taken as +ve and compressive stress as -ve

6.1 Thickness of shell

Shell thickness,

t =PDi

2fdsJ − P(2)

where t is the shell thickness in mm, P is the design pressure (10% more than the

operating pressure (usual practice), fds is the design stress, Di is the inside diameter

of the vessel and J is the joint efficiency. For full radiography of welded joint, J = 1.

6.2 Stress due to internal pressure

1. Circumferential stress (tensile),

fc =PDi

2t(3)

2. Axial stress (compressive),

fa =PDi

4t=

fc

2(4)

6.3 Stress due to weight (compressive)

fw =W

π(Di + t)t(5)

where W is the total weight of the vertical vessel.

• Approximate expression for total weight of the shell (of uniform wall thickness)

excluding internal fittings in N

Wshell = CvπρmDmg(Hv + 0.8Dm)t× 10−3 (6)

where

– Hv = height/length of the cylindrical shell, m

– ρm = density of vessel materials, kg/m3

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– t = wall thickness, mm

– g = gravitational acceleration, 9.81 m/s2

– Dm = mean diameter of the vessel (Di + t × 10−3), m

– Cv is the factor to account for the weight of nozzle, manhole, internal

support etc. for vessel with only few internal it is taken as 1.08. for

distillation column or similar vessel with several manhole or plate normally

taken as 1.15.

For stainless steel, it is (in N)

Wsteel shell = 240CvDm(Hv + 0.8Dm)t (7)

• Weight due to fittings (rough guide)

– plain ladders made of steel ∼ 150 N/m length

– caged ladders made of steel ∼ 360 N/m length

– platform made of steel for vertical columns ∼ 1.7 kN/m2

– contacting plates made of steel, including the typical liquid loading 1.2

kN/m2 plate area

– for insulating materials, double the density to allow for attachment fittings,

sealing and moisture absorption etc.

Winsulation = π(Di + t)Htin(2ρin)g (8)

where tin insulation thickness, ρin is the density of insulation.

• For a column total weight W = Wshell + Winsulation + Wplate + Wplatform

+ Wladders + ...

6.4 Bending stress due to wind (tensile or compressive)

fb = ±M

πD2i t

(9)

M is the total bending moment.

20

• Bending moment for tall column at any height h from the top of the column

without any support

M =Fwh

2

2(10)

where Fw is the loading per unit length of the column and for total height of

the column, h = H

• loading per unit length of the column, Fw (N/m)

Fw = PwDeff (11)

where Deff is the effective column diameter calculated from outside diameter

and insulation including any attachment as pipe or ladder. Pw is the dynamic

wind pressure (load/area) due to wind.

• Dynamic wind pressure, Pw (load/area)

Pw =1

2Cdρau

2w (12)

where

– uw is the air velocity

– Cd is drag coefficient

– ρa is air density

For smooth cylindrical column or stack, approximate load due to wind (in N/m2)

Pw = 0.05u2w (13)

where uw is the km/h

6.5 Torsional shear stress caused by load offset piping and

wind

fs =2T

πDi(Di + t)t(14)

where T is the torque

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6.6 Combined stress analysis based on the shear strain en-

ergy theory

• Combined stress analysis require following stresses

– total circumferential stress, fc

– total longitudinal stress, fL = fa + fw ± fb

∗ f(+)L = fa + fw + fb

∗ f(−)L = fa + fw - fb

– total shear stress, fs

• Axial compressive stress, fL,compressive = fw + fb

• Axial tensile stress, fL,tensile = fa+fb

• Critical buckling stress,

fc,bucking =2E

√

3(1− µ2)

(

t

D0

)

×1

FS(15)

where E is the young’s modulus of the material of construction, D0 is the outside

diameter of the vessel, Poisson’s ratio and factor of safety (FS) is 12 (usual

practice).

• Resultant stress from shear strain energy theory, fR

fR =[

(f 2c − fcfL + f 2

L + 3f 2s

]2(16)

• For satisfactory design,

– fR < fds

– fL,tensile < fds

– fL,compressive < fc,bucking

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6.7 Combined stress : based on maximum shear stress theory

• Different stresses

– Principal stresses (fx and fy)

(fx, fy) =1

2

[

(fc + fL)±√

(fc − fL)2 + 4f 2s

]

(17)

– Principal stress in radial direction, fr = 0.5 P (in general)

• For satisfactory design

– Numerical greatest value of (fx - fy), (fx - fr) and (fy and fr) < fds

– fL,compressive < fc,bucking

6.8 For satisfactory design

If design is within the satisfactory limit, shell thickness can be further reduced and

re-calculate everything. Check whether stress criteria satisfied or not.

To ensure that vessel is sufficient rigid and it can withstand attached loads, it

should have minimal wall thickness. General practice is given in the table. For dif-

ferent shell diameter, thickness is provided including corrosion allowance of 2 mm.

Vessel diameter (m) Minimum thickness (mm)

1 5

1 to 2 7

2 to 2.5 9

2.5 to 3.0 10

3.0 to 3.5 12

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