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Abstract

Fire is one of the main hazards associated with storage tanks containing flammable liquids.

These tanks are usually closely spaced and in large groups, so where a petroleum fire

occurs, adjacent tanks are susceptible to damage leading to further development of the

fire. The structural behavior such as thermal stability and failure modes of the tanks under

such fire scenario are very important to the safety design and assessment of oil depots.

However, no much previous studies are available at the moment. This report presents a

systematic exploration of the potential thermal and structural behaviors of an oil tank when

one of its neighbor tanks is on fire. Under such scenario, the oil tanks are found to easily

buckle under rather moderate temperature rises. The causes of such buckling failures are

the reduced modulus of steel at elevated temperatures, coupled with thermally-induced

stresses due to the restraint of thermal expansion. Since the temperatures reached in such

structures can be several hundred Centigrade degrees, any restraint to thermal expansioncan lead to the development of compressive stresses.

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Acknowledgements

The project group is deeply grateful to its internal supervisors Dr.Younis Jamal (Mechanical

Department, UET Lahore) and external advisor Rana Ijaz Sahib (Descon) for their

tremendous guidance and encouragement during this project. Many thanks to the

Chairman Mechanical department Dr. Hameed ullah Mughal for providing us with such

learning opportunity for our better grooming of technical skills.

Finally our project group would like to thank Mechanical Department and University of

Engineering and Technology for their continued support and corporation.

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Abstract.I

AcknowledgementII

1.Introduction ...................................................................................................... 1

1.1 Properties Of Fluids Stored In The Steel Tank ............................................ 1

1.2 Types Of Tank .............................................................................................. 2

1.3 The Cylinder ................................................................................................. 7

1.4 Tank Bottom ................................................................................................ 8

1.5 Foundation Of Tanks .................................................................................. 10

1.6 Materials .................................................................................................... 11

1.7 Codes And Design Consideration ............................................................... 12

2. Failures Of The Storage Tanks ......................................................................... 14

2.1 Motivation .................................................................................................. 14

2.2 Major Causes Of Tank Failure In Large Depot Fires.................................... 16

2.3 Methodologies ............................................................................................ 18

2.4 Analytical Solution ...................................................................................... 18

2.5 Heat Transfer Analysis ................................................................................ 19

2.6 Proposition Of Empirical Model ................................................................. 19

2.7 Thermal Shell Buckling ............................................................................... 20

3. Calculations...........21

3.2 Problem Statement.......................................................................................31

4. References..........32

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1. INTRODUCTION

The principal scope of this report is the study of steel tanks that failed due to natural

hazards and ways to mitigate damage in future events. This chapter contains a number of

considerations that are important to isolate theme structures that are representative of

what would be found in practice.

1.1 Properties Of Fluids Stored In Steel Tanks:

a) Density:

The density of the liquid is its mass per unit volume. Water has a density of 1 gm. /cm3

at4C. The density of a liquid plays an important role in the design of a tank, because larger

densities require thicker shells.

b) Specific Gravity:

Specific gravity is another important physical property of the liquid stored. It is a measure of

the relative weight of one liquid compared to water. Specifically it is the ratio of the density

of the liquid divided by the density of the water at 15.5C. For example, petroleum oil,

kerosene and gasoline have a specific gravity of 0.82, 0.80 and 0.70 respectively. Care must

be exercised if there is a significant increase in the specific gravity of the new liquid because

the effective hydrostatic pressure acting on the tank walls will be greater if the design level

is not reduced, and could cause damage on the cylindrical shell.

c) Vapor Pressure:

The vapor pressure of a pure liquid is the pressure of the vapor space above the liquid in a

closed container, and increases with increasing temperature. It is an important

consideration in order to select the type of tank and its roof and is crucial for the purpose of

characterizing fire hazardousness.

d) Boiling Point:

The boiling point is also important. It is necessary to know the temperatures at which some

liquids should be stored, always below its boiling point. For example, some flammable and

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combustible liquids are prohibited by the fire codes to be stored at temperatures above

their boiling point.

e) Pressure:

Pressure is defined as force per unit area. In the United States, the engineers working in

this field commonly use inches of water column or ounces per square inches to express the

value of pressure or vacuum in the vapor space of a tank, because the pressures are usually

very low relative to atmospheric pressure. According to this pressure the designer should

determine the strength and thus thickness of the tank. For both cylindrical and spherical

shells, the most complex part of the tank to design is the junction between the roof and the

cylinder because several conditions may occur:

I. When the pressures dominate on the cylinder, the roof deflects to accompany the

lower shellII. When there is an internal pressure that exceeds the weight of the plates and framing

of the roof, this junction tends to separate from the shell.

1.2 Types Of Tanks:

a)Above-Ground Tanks:

The aboveground tanks have almost all their structure exposed. The bottom part of these

tanks is placed directly over soil or on a concrete foundation. The majority of the steel

tanks are built on concrete foundations. In some cases they are placed on a grillage,

formed by structural members or heavy screens, so that the bottom of the tank can be

inspected from the underside. Advantages of this type of tank includes that they are easier

to construct, can be built in far larger capacities than underground storage tank, and costs

less than those built underground.

b) Elevated Tanks:

A less common class of aboveground tanks supported by columns or frames is called

elevated tanks. They are almost exclusively employed by municipal water supplycompanies.

c) Underground Tanks:

Underground tanks have less capacity than aboveground tanks and are usually limited to

between 20,000 and 75,000 liters (5,000 and 20,000 gal) with most being less than 45,000

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liters (12,000 gal). They require special considerations for the earth loads to which they are

subjected, because of their contents. Underground tanks store fuels as well as a variety of

chemicals. Another aspect to consider is buoyancy, because they are anchored into the

ground, they should not be able to pop out during periods when ground water surrounds

the tank. In addition, because they are underground, they may be subjected to severecorrosion. For the purpose of this work, attention is restricted to aboveground tanks, for

which buckling is an important design consideration for wind loads.

Classification Based On The Internal Pressure:

This classification is commonly employed by codes, standards and regulations all over the

world.

a) Atmospheric Tanks:

These tanks are the most common. Although they are called atmospheric, they are usually

operated at internal pressure slightly above atmospheric pressure. The fire codes define an

atmospheric tank as operating from atmospheric up to 3.5 kN/m2 above atmospheric

pressure.

b) Low-Pressure Tanks:

Within the context of tanks, low pressure means that tanks are designed for a pressure

higher than atmospheric tanks. This also means that these tanks are relatively high-pressure

tanks. Tanks of this type are designed to operate from atmospheric pressure up to about

100 kN/m2.

c) Pressure Vessels (High-Pressure Tanks):

Since high-pressure tanks are really pressure vessels, the term high-pressure tank is not

frequently used; instead they are called only vessels. However, they are treated separately

from other tanks by all codes, standards, and regulations.

d) The Roof Of A Tank

The shape of the roof is useful indicator of the type of a tank because it is self-explanatory

to tank designer, fabricator and erector.

e) Fixed-Roof Tank:

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A shallow cone roof deck on a tank approximates a flat surface and is typically built of 4.76

mm thick steel. Most aboveground tanks have cylindrical shapes on the part that contains

fluids. The cylinder is an economical, easily fabricated shape for pressure containment. An

important feature of such cylindrical tanks is that the top end must be closed. As discussed

before, the relatively flat roof and bottom or closures of tanks do not lend themselves tomuch internal pressures. As internal pressure increases, the tank designers use domes or

spherical caps.

f) Conical Roof:

Cone-roof tanks have also cylindrical shells in the lower part. These are the most widely

used tanks for storage of relatively large quantities of fluid. The tanks that we will study in

the following chapters are of this type. They have a vertical axis of symmetry, the bottom is

usually flat, and the top is made in the form of shallow cone as illustrated in Figure 1.1.

They are economical to build and the economy supports a number of contractors capable of

building them. Cone-roof tanks typically have roof rafters and support columns except in

very small-diameters tanks, see Figure 1.2. Details of the central part of the roof are also

shown in Figure 1.2.

Fig.1.1 Conical Roof Tank

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Fig.1.2 Cone Roof Tank with Column Support

g) Umbrella-Roof Tanks:

They are very similar to cone-roof tanks, but the roof looks like an umbrella. They are

usually constructed with diameters not much larger than 20 m. Another difference is that

the umbrella-roof does not have to be supported by columns to the bottom of the tank, so

that they can be a self-supporting structure.

h) Dome-Roof Tanks:

This type has almost the same shape of theumbrella type except that the dome

approximates a spherical surface more closely

than the segmented sections of an umbrella-

roof, see Figure 1.3. There are several ways to

fabricate such tanks. One of them is known as

the tank airlift method, in which the roofand

the upper course of shell are fabricated first,

then lifted by air that is blown into the tanks as

the remaining lower courses of steel shell arewelded into place.

Fig.1.3 Doom Roof Tank

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i) Aluminum Geodesic Dome-Roof Tanks:

Although most tanks are made of steel, some fixed-roof tanks have aluminum geodesic

dome-roof. Some advantages include that they have a superior corrosion resistance for a

wide range of conditions compared with steel tanks. Also they are often an economical

choice and are clear-span structures that do not require internal supports. They can also be

built to virtually any required diameter.

j) Floating-Roof Tanks:

These tanks have a cover that

floats on the surface of the liquid.

The floating cover or roof is a diskstructure that has sufficient

buoyancy to ensure that the roof

will float under all expected

conditions, even if leaks develop

in the roof. They are frequently

used in large diameter tanks to

prevent the evaporation of

volatile fluids. The disk is built

with approximately 200 mm gapbetween the roof and the shell,

avoiding contact between both

elements as the roof moves up Fig.1.4 External Floating Roof in a Tank

and down with the liquid level. A rim seal seals the gap between the floating roof and the

shell, as shown in Figure 1.5.The two categories of floating-roof tanks are external floating

roof (EFR) and internal floating roof (IFR). If the tank is open on top, it is called an EFR tank.

If a fixed roof on top of the tank covers the floating roof, it is called an IFR tank. The

function of the cover is to reduce air pollution and evaporation losses by reducing thesurface area of liquid that is exposed to the atmosphere. A fixed-roof tank can easily be

converted to an internal floating-roof tank by simply installing a floating roof inside the

fixed-roof tank. Similarly an external floating-roof tank can be converted into internal

floating-roof tank by covering the tank with a fixed roof or a geodesic dome.

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EFR tanks have no vapor space pressure associated with them and operate strictly at

atmospheric pressure. IFR tanks, like fixed-roof tanks, can operate at or above atmospheric

pressure in the space between the floating roof and the fixed roof. A flexible seal is

provided in floating roof tanks to seal the gap between the cylinder and the roof. A detail of

such designs is shown in Figure 1.5, as presented by Kamyab and Palmer (1994)

(Fig.1.5)

A seal can take a radial deflection of the cylindrical shell not larger than about 150mm, and

this is enough to account for construction imperfections, thermal deflections and

deflections due to pressure of the liquid stored. However, vertical settlements of the

foundation may induce large radial displacements and this would make that the seal

becomes ineffective and the roof does not operate well.

1.3 The Cylinder:

Most tanks have a cylindrical body, which is used as storage volume. Some are formed by a

cylinder, such as in Figures 1.1 and 1.2. The walls may have a constant thickness or a

tapered wall with different values of the thickness at different elevations. The outer surfaceof the tank is smooth and it is the inner surface where the thickness changes are observed.

The maximum thickness is governed by the internal pressures and may be as high as 40mm;

however, in most tanks it is of the order of 10 mm. The cylinder itself is formed by curved

plates that are welded. The quality of the welds is very important for the integrity of the

shell, and several failures have been reported that initiated at welds in the lower part of the

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shell. Some tanks without a roof have a wind girder ring welded on the outside; a girder

may have a thickness of the order of 7 mm with a width that may range between 100 and

200 mm. Other tanks have a stiffening ring to prevent local buckling of the shell under wind

pressures,as shown in Figure 1.6.

Fig.1.6 Cylinder with ring stiffeners

1.4 Tank Bottom:

Another important component of tanks are the bottoms made of welded steel plates. In

the analysis, tanks are usually modeled as fixed to the ground, so that it is not a problem to

know exactly the shape of the bottom. But for the designer this aspect is very important

because of the varying conditions to which a tank bottom may be subjected. A tank bottom

may be broadly classified as flat bottom or conical.

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a) Flat Bottom

They are the most common end closures of tanks. These tanks appear flat but usually have

a small designed slope and shape. For tanks less than about 6-9 m in diameter, the flat-

bottom tank is used. The inclusion of a small slope as describe above does not provide any

substantial benefit, so they are fabricated as close to flat as possible.

b) Cone Up:

These bottoms are built with a high point in the center of the tank. Crowning the

foundation and constructing the tank on the crown accomplish this. The slope is limited to

about 25 to 50 mm per 3 m run.

c) Cone Down:

The cone-down design slopes toward the center of the tank. Usually, there is a collection

sump at the center. It is very effective for water removal from tanks. This design is

inherently more complex because it requires a sump, underground piping, and an external

sump outside the tank.

d) Single Slope:

This design uses a planar bottom but it is tilted slightly to one side. This allows for drainage

to be directed to the low point on the perimeter, where it may be effectively collected.

Since there is a constant rise across the diameter of the tank, the difference in elevationfrom one side to the other can be quite large. Therefore, this design is usually limited to

about 30 m.

e) Conical Bottom:

The second type is the conical bottom. The designers often use it to provide a complete

drainage or even removal of solids. Since these types of tanks are more costly, they are

limited to the smaller sizes and are often found in the chemical industry or in processing

plants.

1.5 Foundations Of Tanks:

This section applies to the tanks considered in this study, i.e. cylindrical tanks with

uniformly supported flat bottoms. A geotechnical study of the site is required in the design

of the foundation; however, in many cases (especially for tanks located in coastal areas) the

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soils are susceptible to have uniform or differential settlements. While it is difficult to

classify all possible foundation types for storage tanks, some general types have proved to

be most common for specific applications. Foundation types may be broken into several

classifications in generally increasing order of costs.

a) Compact Soil Foundations:

These foundations can be used where the soil quality and bearing capacity are good.

Generally, the top 7 to 15 cm of soil is removed and replaced with a sand or granular

backfill. These are often called sand pad foundations, laid directly on earth. The advantage

of this type of foundation is the relatively low cost. Crushed-stone ring-wall foundations:

This design happens to incorporate a leak detection system. While it costs less than the

concrete ring-wall, it has many of the advantage of the concrete ring-wall. It provides

uniform support of the tank bottom by dissipating concentrated loads in a granular pattern.

Catastrophic failure of the bottom is possible if a leak starts and washes out the underlying

support.

b) Concrete Ring-wall Foundations:

The concrete ring-wall foundation is so called because of its appearance. It is used in

foundations for tanks of a diameter of at least 10 m or more. In the large-diameter tanks

this is usually the most cost-effective reinforced concrete foundation, with many

advantages such as reducing the probabilities of settlements failures.

c) Slab Foundations:

The concrete slab foundation has the

advantages of the concrete ring-wall but is

usually limited to tanks with diameters less

than 10 m. Often the edge of the slab will be

sufficiently thick to provide for anchorage. A

slab foundation is very versatile, but its high

cost limits it to use in small tanks. The slab

provides a level and plane-working surface

that facilitates rapid field erection. Pile-

supported foundations: The pile-supported Fig.1.7 Tank with Slab Foundation

foundation is usually found where the soil bearing pressures are very low. Examples might

be river deltas and land adjacent to bays. They are also used where high foundation uplift

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forces are encountered resulting from internal pressure or seismic loading. The tank shown

in Figure 1.7 has a concrete slab and 432 piles supporting it.

1.6 Materials:

Tanks are constructed from a number of different materials based upon the availability and

cost of the material, ease of fabrication, resistance to corrosion, compatibility with the fluid

stored. Sometimes specialized composites and techniques are used in tank construction,

but these are the exception.

a) Carbon Steel:

Carbon steel or mild steel is by far the most common material for tank construction. This

material is readily available, and because of the ease with which it is fabricated, machined,

formed, and welded, it results in low overall costs. The material properties most commonlyassumed for modeling are a modulus of elasticity of 2.068 x 10

11N/m2, Poissons ratio of

0.3, mass density of 7849.7 kg/m3, and yield strength of 2.156 x 10

8N/m

2.

b) Stainless Steel:

Stainless steel, usually the austenitic group of stainless steels, is an important material used

for storage of corrosive liquids. Although the material cost is significantly more than that of

steel, it has the same ease of availability as carbon steel.

c) Fiberglass Reinforced Polymers (FRP) Tanks:

Fiberglass reinforced polymers (FRP) tanks are noted for their resistance to chemicals

where stainless steel or aluminum tanks are not acceptable. However, the fabrication and

construction techniques are somewhat more specialized than those for metals fabrication.

d) Aluminum Tanks:

Aluminum tanks are suitable for a limited number of materials. It is the less common metal

used to build tanks. These tanks remain ductile at temperatures much lower than those of

carbon steel. However, nickel steels and stainless steels have largely supplanted the market

for aluminum tanks. Code requirements that govern tank designs often have very specific

material selection requirements and limitations. Most modern codes include provisions in

the material selection criteria that ensure materials with sufficient toughness under the

service conditions to prevent brittle fracture.

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I. The susceptibility of the material to brittle fracture is also one of the most important

material selection considerations. Brittle fracture is the tensile failure of a material

showing little deformation or yielding. Brittle fractures typically start at a flaw and

can propagate at high speeds, resulting in catastrophic failures.

II.

Corrosive effects in tanks may be divided into internal and external ones. The mostcommon is the external corrosion that is usually minimized by the used of coatings

for carbon steel tanks.

III. The selection of a design metal temperature is important in ensuring that materials

are selected which are tough enough to prevent brittle fractures under the service

conditions.

IV. Ensuring a material with adequate toughness. One way to ensure that selected steel

has adequate toughness for the design metal temperature of the tank is to proof-

test each plate by impact toughness testing samples at or below the design metal

temperature (DMT).

1.7 Codes And Design Considerations:

Industry standards and codes have been developed primarily on a voluntary basis by

national standards-setting bodies by industries affected by them. Because the standards-

setting bodies in most cases represent the interests of all parties, they must be consensus

standards. The purpose of this standards and codes has been to provide acceptable,

practical, and useful standards that ensure quality, safety, and reliability in equipment,

practices, operations, or designs. Most of the organizations produce different levels ofstandards, which can be generalized into the following basic categories:

Standards: These are considered to be mandatory practices that must be complied

with, so that the equipment manufactured may be considered in compliance or may be

marked as complying with the standard. Standards are also often called codes.

Recommended Practices: These are advisory documents that provide technological

background and practices, which may be useful for the specific application at hand. They

are not mandatory.

Publications or bulletins:These are primarily for the purpose of informing the user of

general aspects of the industry technology or practices.

Specifications:They are considered interchangeable with standards. Specifications may

also be a component of standards or codes.

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Many organizations have contributed in some way to storage tank technology. The most

important ones are:

The American Petroleum Institute (API).

American Society of Mechanical Engineers (ASME).

The fire protection organizations and codes (application and jurisdiction of U.S.

fire codes): Uniform Fire Code (UFC) and National Fire Protection Association

(NFPA).

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2. FAILURES OF THE STORAGE TANKS

2.1 Motivation:

The Buncefield oil storage depot incident Storage tanks in refineries and chemical plantscontain large volumes of flammable and hazardous chemicals. A small accident may lead to

serious property damage, business interruption, and loss of money and life. According to an

investigation of 242 accidents (Chang and Lin 2006) related to storage tanks, fire and

explosion account for 85% of the accidents. The event of a massive conflagration at the

Buncefield Oil Storage Depot north of London on December 11, 2005, drew international

attention to the serious risks associated with fires in petroleum storage tanks. This fire is

the ever largest peacetime fire in Europe, in which 23 large oil storage tanks were

destroyed (Board 2010).

Figure 2-1a

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Figure 2-1b

Figure 2-1c

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A global view of the site during the burning stage of damage to tanks during and after the

fire is shown in Figures 2-1a, 2-1b and 2-1c. This striking recent fire incident offers the direct

motivation of this study.

2.2 Major Causes Of Oil Tank Failures In A Large Oil Depot Fire:

The main hazards associated with storage tanks containing flammable liquids are fire and

explosion (Chang and Lin 2006). Fires or explosions are likely to occur when vapors or

liquids are released into areas where there may be an ignition source, or when an ignition

source is introduced into an area where there may be flammable atmospheres. The extent

of the fire or explosion hazard, depends largely on the temperature of the liquid, how much

of the surface area is exposed, how long it is exposed for, and the air movement over the

surface. From the structural safety point of view, explosion is without doubt the most

dangerous hazard for the adjacent tanks, as the shockwave from explosions is easy to cause

structural damage (Baker et al. 1982, Ruiz et al. 1989, Islam et al. 1992).

Explosions are believed to be the major reason of the failure of tanks in Buncefield as in the

Report (Board 2010). Another possibility of causing the tank failure could be heating from

the fire, however this factor was somehow less mentioned in the Buncefield Report.

In the presence of a fire impinging on the tank shell, the metal undergoes a degradation of

mechanical properties therefore causes structural weakening and eventual collapse. In

other situations, where the fire is not spreading on the tank, the adjacent tank may still be

in danger of failure. The hazards arising from such a situation are due to fire radiation.Radiation heats up the neighboring tanks and results in a non-uniform temperature rise in

the tank where the part facing the fire is hotter than the part opposite to it. This can lead

to the buckling failure of tanks, because the modulus of the steel (or other metals) used for

constructing the tank is reduced at elevated temperatures, coupled with thermally-induced

stresses due to the restraint of thermal expansion. Since the temperatures reached in such

structures can be several hundred degrees in Centigrade, any restraint to thermal

expansion can lead to the development of large compressive stresses. The high

susceptibility of thin shell structures to elastic buckling under very low stresses means that

this type of failure is easily provoked. However, no previous studies on this problem are

known to the best knowledge of the author.

Back to the Buncefield incident, although the pressure wave generated by explosions are

believed to be the major cause of the tremendous damage to the outlying area and the

huge fires involving 23 large oil fuel tanks (Johnson 2010, Board 2010), it is possible that

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thermal buckling was an important triggering event for the leakage or spill of the stored oil

that occurred before the explosion. In fact, thermal buckling of the tank may actually induce

or accelerate the following explosion thus contributed to the catastrophic failure. Indeed, it

is difficult and even impossible to judge whether some of the failures in Fig. 2-1a were due

to explosion or thermal buckling. The buckling of the green tank in Fig. 2-1c was more likelycaused by thermal buckling rather than explosion, as will be seen in this thesis. Therefore, a

safety evaluation of the possibility of thermal buckling and its role in the possible tank

failures is urgently needed.

Currently, thermal buckling of oil tanks under fire scenario is a poorly studied problem,

relevant research is very rare. The current oil tank design codes (e.g. API 650 2007, NFPA 30

1996, EN1993 4-2 2007) have not provided any guidance for tanks under such fire scenarios

either. The role of thermal loading in structural failure has been almost ignored in the past

research or industrial tank design practices. This study stands as a complementary work tothe past investigations of oil tank failures.

A basic approach to minimize the risk of storages under fire condition is to do a proper

layout for the whole tank farm with safe separation distances. Various regulatory and

professional bodies like American Petroleum Institute (API) and National Fire Protection

Association (NFPA) have suggested standards on such issue. The tanks are arranged in

groups by dike wall or bunds and separated from each other within one group. However,

for economic reasons, the minimum spacing specified in the codes does not guarantee the

safety of tanks from a fire. The researches on safe separation distance between two storage

tanks in a tank farm from fire therefore emerge (Sengupta et al. 2010, Atallah and Allan

1971).

The safe separation distance is defined as that at which the thermal radiation flux is equal

to a prescribed level. This level depends on what is required to conserve or protect (Atallah

and Allan 1971). The critical heat flux of 4.732kW/m2 is considered to be the safe inter-

tank distances on the basis of that no material is expected to ignite (Crowl and Louvar

2002, Lees 1996, DiNenno 1995). This heat flux is equal to the energy radiated from a black

body with a temperature of 260. In another research a critical temperature of 540 is

deemed to be a threshold for the safety of steel tanks (Beyler 2004b) in determining safe

separations. However, would the steel tank really be safe under these critical

temperature? Although this defined temperature seems not very high to soften the steel

tank, the most important issue here is not the reduction of strength of steel under the given

temperature, but the stresses arisen from non- uniform temperature distribution in the

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steel tank which may easily lead to catastrophic failure even if the maximum temperature is

much lower.

The aim of this study is to reveal and understand the behavior of a steel oil tank when it is

exposed to an adjacent fire, from a thermal buckling prospective view. The objectives

include revealing the thermal distribution patterns developed in an oil tank under the

heating from an adjacent tank fire, exploring the underlying mechanism responsible for the

buckling of tank structure, and discovering the influences of various thermal and

geometrical parameters on the buckling temperature of the tanks. A method which

facilitates understanding of tank behavior under fire environment will be performed to fill

this gap in current knowledge.

2.3 Methodologies:

The starting effort is put on the enhancement of the analytical solutions of stresses and

deformations in a cylindrical shell under an axisymmetric heating regime involving thermal

discontinuity at the liquid level. The thermal buckling behavior of tanks is then studied by

numerical simulations. First a solid flame model is chosen to represent the tank fire after

due consideration, and the heat transfer analysis is conducted using Abaqus to determine

the temperature distribution in the adjacent tank. The heat transfer analysis will be

followed by an extensive nonlinear finite element analysis of tanks under such scenarios.

The results from this study offers general understanding and provides useful information on

how serious the temperature gradient developed in the tank under such fire heating may

be for the thin-shell tank structure.

Being the first study on tank buckling under thermal loading, this study suffers some

limitations, especially the lack of direct experimental measurement, and also some

simplifications of both the fire model and tank model. However, results indicate clearly that

the fire loading is a major threat to the safety of adjacent tanks even if they are designed

satisfying all the requirements of current design standards.

2.4 Analytical Solutions:

Analytical solutions for problems of any complexity in shell structures are typically very

difficult mathematically. For this reason, the study began by developing an analytical

solution for the simplest known problem, to see whether this might possibly be extended to

more complex and realistic conditions. The simplest case, which does not appear to have

been studied before, is the condition of axisymmetric heating of a circular partially-filled

tank, which may be supposed to be caused by multiple other tanks on fire in the area round

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this tank. In addition, this study served the purpose of demonstrating the critically

important role of partial filling in producing discontinuities in the shell response, and also

showed that relatively small thermal changes could produce relatively large local stresses.

However, it was quickly realized that an extension of this analytical treatment to the more

complex conditions that occur in practical unsymmetrically heated tanks was not veryfeasible, so the study turned towards numerical solutions thereafter. Nevertheless, these

analytical solutions remain the only known ones for conditions of this kind, and there may

be applications for these solutions in problems unrelated to fire.

2.5 Heat Transfer Analysis:

A structural heat transfer analysis by using a proper fire model is next employed to explore

the temperature profiles in the tank. Oil tank fires are large pool fires. Methods of

estimating the thermal radiation from pool fires are available in many references. A semi-

empirical solid flame model is chosen for the pool fire in the oil tank in this thesis. The flame

is assumed to be a cylindrical blackbody and a homogeneous radiator with an average

emissive power.

This model provides a constant value of the radiation from the flame but does not give

information of fire evolution with time. It is deemed suitable for the current study of

exploring tank buckling behavior under fire heating. A steady state heat transfer analysis of

a typical oil tank exposed to an adjacent fire is then performed using the commercial

software Abaqus (Simulia 2008). Three heat transfer mechanisms - radiation, convection

and conduction are all taken into consideration in the simulations.

2.6 Proposition Of Empirical Models:

Two temperature distribution models are then proposed to describe the temperature

distribution developed in the tank obtained from the numerical heat transfer analysis.

Algebraic expressions are extremely useful to structural researchers and designers who

have no knowledge of heat transfer analysis but need to assess or design the structural

behaviour. Based on the fact that some idealizations and assumptions that have been made

in the solid flame model for heat transfer analysis, effort is put on seeking an expression

which can capture the most important temperature distribution features, but without

employing many curve fitting coefficients whose physical meanings are obscure. Eventually

two models with only a very few parameters which all possess physical meanings such as

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the diameter of the fire, location of fire and liquid level inside of the target tank are

proposed.

2.7 Thermal Shell Buckling Analysis:

Geometric and material nonlinear analyses are conducted in the finite element analysis

(FEA) software Abaqus (Simulia 2008) to investigate the buckling failure modes of an oil

tank under the fire heating regime and the influences of relevant parameters. A typical

fixed roof oil tank with uniform wall thickness is chosen to be the representative example

for investigation.

As the first attempt to analyzing the buckling failure of the tank, the arc-length method

(Riks subroutine in Abaqus) is employed, which is the conventional method used in shellbuckling analysis (Teng and Lou 1997). In the simulations, the proposed temperature

pattern is applied as the thermal loading. Although this method can accurately predict the

buckling temperature, the temperature loading has to reduce once the structure passes the

buckling point. While in reality, the post-Introduction buckling procedure of the structure

should be accompanied by either a constant or a continuously ascending temperature as

usually the thermal loading due to fire may often develop a much higher temperature than

the buckling temperature of a structure. To overcome this discrepancy, another nonlinear

static analysis method incorporating an artificial damping is used to make the simulation

able to continue after the first buckling occurs.

By using the artificial damping method, extensive geometric and material nonlinear

analyses are carried out to simulate the tank behavior using the temperature distribution

obtained directly from the numerical heat transfer analysis. The influence of fire diameter,

location, liquid filling level and tank geometry are investigated. The accuracy of the

proposed temperature distribution model for predicting the structure behavior is also

evaluated by comparing its predictions with those using directly the temperature

distribution obtained from the numerical heat transfer analysis.

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3. Calculations:

Important Parameters:

X=axial co-ordinate of cylindrical shell-(m)

a=radius of middle cylindrical shell-(m)

h=thickness of cylindrical shell-(m)

L=length of cylindrical shell-(m)

=characteristic length of cylinder-(m-1

)

Y= -dimensionless co-ordinate of shell

w=radial displacement of the middle surface of the cylindrical shell, positive

inward-(m)

u=axial displacement of middle surface of cylindrical shell, positive in x direction-

(m)

p= Uniform internal pressure (Pa)

Q= Shearing force in cylindrical shell (N/m)

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D=Eh3

/12(1-2)flexural rigidity of axial strip of cylinder.(N-m)

N=Normal membrane force in cylindrical shells (N/m)

M=bending moment in cylindrical shells (N-m/m)

E= YoungsModulus of elasticity-(Pa)

=poison ratio of the material of the cylindrical shell

Cn=the four constants of integration c1, c2, c3and c4

=coefficient of thermal expansion (m/m.0C)

Fc=temperature function

b= Constant

d=b/-temperature parameter

=4aT0/d4+4 (m)

Cylindrical Shell Formulas:(F.J Stanek 1995)

1-SHELL CONSTANTS:

4=3(1-

2)/a

2h

2(1)

D=Eh3/12(1-) (2)

2-COORDINATE TRANSFORMATION:

Y=x (3)

CASE A:

Fc= T1+ T2X+T3X2+T4X

3 (4)

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Internal Bending Moments:

Mx=1/4a2CnMn =2Da(T3 +3 T4*y/) (5)

M=Mx (6)

Internal Membrane Forces:

Q=1/4a Cn Qn +6DaT4 (7)

Nx= (axial force)/2a = Constant (8)

N = - Cn Nn+ap (9)

Displacement of Middle Surface:

w=a/Eh (CnNn +Nxap)a*T1+T2(y/)+T3(y/)2+T4(y/)

3] (10)

dw /dx= a/Eh CnWna*T2+2T3(y/)+3T4(y/)

2] (11)

u= 1/Eh *u/4 CnQn+(Nx-ap)y +C5] (12)

CASE B:

Fc=T0e-bx (13)

d=b/q (14)

=4aT0/a4+4 (15)

Internal Bending Moments

Mx=(1/4a2)CnMn-Db

2e

-dy(16)

M=Mx (17)

Internal Membrane Forces

Q=(1/4a)CnQn-Db3e

-dy (18)

Nx=(axial force)/2a= constant (19)

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N=-CnNn+ap-(d4/d

4+4)EbT0e

-dy (20)

Displacement Of Middle Surface

w=a/Eh(CnNn+Nx-ap)-e-dy

(21)

dw/dx=a/EhCnwn+be-dy

(22)

u=1/Eh*/4CnQn+(NX-ap)y-aDb3e

-dy+c5] (23)

CASE A and B:

Internal Bending Stress

x=6Mx/h2 (24)

=6M/h2 (25)

Internal membrane stresses

mx= Nx/h (26)

m= N/h (27)

Total or principal stress (+ sign for outside surface andsign for inside surface)

x=Nx/h 6Mx/h2 (28)

=N/h 6M/h2 (29)

All The Above Equations Have Been Taken From TIMO SHINKO AND F.J.STANEK

1959.

3.1 PROBLEM STATEMENT

A storage tank having a uniform thickness of 10mm has a radius of its middle

surface of 10m.A radial outward shearing force of 17500N/m is applied at one

edge of the tank while the other edge is rigidly fixed. The length of storage tank

is 20m and its Poissons ratio is 0.3.If the temperature variation about the tank

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wall is assumed to be linearly distributed with base temperature of 00

C to 5000C at outer surface of tank. Find the circumferential membrane stresses at the

edge where the shearing force is applied and the axial bending stress at the

fixed edge. The material of the storage tank is carbon steel(mild steel).

Where Co-efficient of thermal expansion ==12*10-6 0

C

And Modulus of elasticity=E=2.1*1017

Pa

Solution

DATA

Thickness of cylindrical tank=h=10 mm

Radius of the cylindrical tank=a=10 m

Shearing force=Q=17500 N/m

Length of the tank=l=20 m

Poissons ratio==0.3

Internal membrane hoop stress=m=?

Bending stress across the axis=mx=?

Co efficient of thermal expansion==12*10-6

oC

Modulus of elasticity=E=2.1*1011

Pa

Temperature range=00C-500

0C

Proposed temperatures

T1=0 0C

T2=166.60C

T3=333.260C

T4=5000C

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CHARACTERISTIC LENGTH

2=1.6523/ah

=1.6523/10*0.01

=(16.523)0.5

=4.06 m-1

DIMENSIONLESS COORDINATE

Yl=*L

Yl=81.2

CALCULATIONS @ y=0

MOMENT ABOUT THE AXIS

Mx=(1/4a2)*(CnMn-2aD)*(T3+3T4*y/)

M1=-2e-y

cosy @y=0 (Timo Shinko)

M1=-2

M2=-2e-y

siny (Timo Shinko)

M2=0

We dont have the value of D which is flexural rigidity so solving for

Flexural rigidity

D=(Eh3/12*(1-2))

D=18935.97N-m

@ y=0 and Mx=0

0=(1/4*10*4.062) *[-2C1+0]-2*(0.192*10

11)*10*12*10

-6

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0=-3.03*10-3

C1-1535662080

C1=-499355.094

SHEARING FORCE CALCULATIONS

Q=(1/4a) *(QnCn+6DT4)

Q1=-2e-y

(cosy + siny) (Timo Shinko)

Q1=-2

Q2=-2e-y

(siny - cosy) (Timo Shinko)

Q2=2

Now calculating for C2

17500=(1/a*10*4.06) *(-499355.094*(-2)+2C2)+6*(18935.97)(12*10-6

)(10)(500)

0=-4533.356+0.01231C2

C2=368266.1251

NORMAL STRESS TANGENT TO THE MIDDLE SURFACE

N=-CnNn+ap

N1=e-y

siny (Timo Shinko)

N1=0

N2=e-y

cosy (Timo Shinko)

N2=1

N=-(-499355.094*0+368266.1251C 1) + 10*1.01*105

N=1378266.125 N/m

m=1378266.125/0.01 N/m2

m=137826612.5 Pa

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m=137.8266 MPa

CALCULATIONS @ y=81.2

MOMENT ABOUT THE AXIS

Mx=(1/4a2) *[CnMn-2aD(T3+3T4y/)]

M1=-2e-y

cosy

M1=-2*e-0.812

cos(812.2)

M1=1.663*10-36

N-m

M2=-2e

-ysiny

M2=-2*e-81.2

sin(81.2)

M2=-5.03414*10-36

Now solving for Mx

Mx=(1/4*10*4.062) *(-99355.094*(-1.663*10

-36) +[368266.125*(-5.03414*10

-36) -

=2(10)(1.2*10-6

)(18935.91)(333.26+3(500)(81.2/4.06)

Mx=-1.55226*10-33

-137855.0735

Mx=-137855.0735 N-m/m

BENDING AXIAL STRESSES

bx = 6Mx/h2

Putting the values in above equation we get

bx= 6 *(-137855.074)/ 0.012

bx = - 8271304410 Pa

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bx=-8271.3 MPa

CIRCUMFERNTIAL BENDING STRESSES

b= 6M/h2

Where M= *Mx

Thus M= 0.3*(-137855.0735)

M= -41356.52205 N-m/m

Now for

b= 6*(-41356.52205)/0.012

b= -2481391323 Pa

b=-2481.391 MPa

MAXIMUM YIELD STRESS

y /2 =(bx+b)/2 (3.1)

y=10752.69MPa

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Fig 3-1 Table of Properties of Steel (Mechanics of Material By F.P Beer and

Johnson)

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3.2 Conclusion:

In our calculation we have obtained the value of stress from Eq 3.1. It is much higher than

the ultimate strength of the steel as in the Fig.3.1 . So at assumed temperature profile

points T1, T2, T3, T4the design will fail due to high thermal stresses developed. This

conclusion is complying with the guide line of API 650 Appendix M (Requirements for Tanks

Operating at Elevated Temperatures) that tank temperature should not exceed 260oC.

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4. References:

1.API 650 2007). Welded steel tanks for oil storage. American Petroleum Institute

2.Atallah, S., and Allan, D. S. (1971). "Safe separation distances from liquid fuel fires." Fire

Technology, 7(1).

3.Baker, W. E., Cox, P. A., Westine, P. S., Kulesz, J. J., and Strehlow, R. A. (1982). "Explosion

hazards and evaluation."

4.Beyler, C. L. (2004b). "Industrial fire protection engineering." Fire Technology.

5. Board, B. M. I. I. (2010). "Buncefield investigation".

http://www.buncefieldinvestigation.gov.uk/index.htm.

6. Chang, J. I., and Lin, C. C. (2006). "A study of storage tank accidents". Journal of Loss

Prevention in the Process Industries, 19(1): 51-59.

7.Teng and Lou 1997 and DiNenno 1995

8.Ying Liu thesis 2011 "Thermal buckling of metal oil tanks subject to an adjacent fire " .

9.Timo and Shinko Theory Of Plates And Shells.

10.Mechanics of Material 6th

Edition by F.P. Beer And Russell Johnston.