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DESIGN AND

STABILITY OF LARGE

STORAGE TANKS AND

TALL BINS

PREPARED BY :

MUKESH M. CHAUHAN

BE-IV CHEMICAL

ROLL NO. 803

EXAM NO. 341

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THE MAHARAJA SAYAJIRAO UNIVERSITY OF BARODA

DEPARTMENT OF CHEMICAL ENGINEERING

FACULTY OF TECHNOLOGY & ENGINEERING,

BARODA.

Certificate

This is to certify that Mr. CHAUHAN MUKESH MOHANLAL.,

a student of B.E-IV Chemical has work on the Project entitled “Design

and Stability of Large Storage Tanks and Tall Bins” under my

guidance and herewith submits his report in partial fulfillment of the

degree of B.E. (Chemical) for the year 2011-12.

Dr. R. A. Sengupta

Head and Professor,

Chemical Engg. Deptt.

Faculty of Technology & Engineering

M.S.university of Baroda.

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Acknowledgement

I am extremely thankful to Dr. R. A. Sengupta, Head of Department of Chemical

Engineering and my guide for his excellent guidance, encouragement and support throughout

my dissertation work. His profound knowledge that he readily shared with me has helped me

overcome many difficulties. I cannot forget the innumerable time and effort to teaching me

both in this seminar and in writing it, that my work will never be able to match. His constant

support, encouragement, never ending enthusiasm and confidence in me has been a source of

motivation for me.

I would also like to express my heartfelt gratitude to Ms. N. H. Tahilramani, who

have personally paid attention in the progress of this work

Special thanks to library staff of T. K. Gajjar and A.C.E.S library for their kind co-

operation.

Finally, I express my deepest gratitude to all my family members for their constant

love and support and “God”.

Mukesh M Chauhan

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Contents

Chapter 1

Introduction to Storage tanks and Bins

1.1 Function of Storage Tanks and Bins …………………………………………………..01

1.2 Types of Storage Tanks and Bins……………………………………………………... 01

1.3 Design codes and Standards ………………………………………………………….04

Chapter 2

Design of Liquid Storage Tanks

2.1 Shell Design …………………………………………………………………………..05

2.2 Roofs …………………………………………………………………………………..09

2.3 Bottom plate …………………………………………………………………………...12

Chapter 3

Design and Stability of Storage Bins

3.1 Introduction ……………………………………………………………………………14

3.2 Functional Design of Bins ……………………………………………………………..14

3.3 Design of Bins-Loadings……………………………………………………………….17

3.4 Structural Design of bins……………………………………………………………….21

Chapter 4

Stability of Storage Tanks

4.1 Provisios for seismic loading…………………………………………………………..29

4.2 Overturning Stability against Wind Loads……………………………………………..41

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List of Figures

Figure 1.1 - Types of storage tanks

Figure 2.1 – Column supported framed roof

Figure 2.2 – Floating roof

Figure 2.3 – Joints in floor plates

Figure 2.4 – Bottom plate layout

Figure 3.1 – Flow patterns of materials in bins

Figure 3.2 – Graphical method for calculation of flow pattern

Figure 3.3 – Distribution of horinzontal and vertical pressure against depth of stored material

Figure 3.4 – Bin dimensions for use in Reinbert‟s and Janssens‟s equation

Figure 3.5 – Critical values of axial stresses for cylinders subjected to axial compression

Figure 3.6 – Cylinder to cone transition

Figure 3.7 – Forces on suspended bottoms

Figure 4.1 – Impulsive hydrodynamic pressure on wall

Figure 4.2 - convective hydrodynamic pressure on wall

Figure 4.3 – Typical stiffener ring section for ring shell

Figure 4.4 – Overturning check on tank due to wind load

List of Tables

Table 2.1 – Minimum thickness based on Diameter of the tank

Table 4.1 – Expressions for parameters of spring mass model

Table 4.2 – Importance factor-I

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Chapter 1 Introduction To Storage Tanks & Bins

1.1 Fuction of Storage tanks and Bins

1.1.1 Storage tanks

Storage tanks had been widely used in many industrial established particularly in the

processing plant such as oil refinery and petrochemical industry. They are used to store a

multitude of different products. They come in a range of sizes from small to truly gigantic,

product stored range from raw material to finished products, from gases to liquids, solid and

mixture thereof.

There are a wide variety of storage tanks; they can be constructed above ground, in ground

and below ground. In shape, they can be in vertical cylindrical, horizontal cylindrical,

spherical or rectangular form, but vertical cylindrical are the most usual used.

In a vertical cylindrical storage tank, it is further broken down into various types, including

the open top tank, fixed roof tank, external floating roof and internal floating roof tank. The

type of storage tank used for specified product is principally determined by safety and

environmental requirement. Operation cost and cost effectiveness are the main factors in

selecting the type of storage tank.

1.1.2 Storage Bins

The storage of granular solids in bulk represents an important stage in the production of many

substances derived in raw material form and requiring subsequent processing for final use.

These include materials obtained by mining, such as metal ores and coal; agricultural

products, such as wheat, maize and other grains; and materials derived from quarrying or

excavation processes, for example sand and stone. All need to be held in storage after their

initial derivation, and most need further processing to yield semi- or fully-processed products

such as coke, cement, flour, concrete aggregates, lime, phosphates and sugar. During this

processing stage further periods of storage are necessary.

1.2 Types of Storage tanks and bins

1.2.1 Storage tanks

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1.2.1.1 Open Top Tanks

This type of tank has no roof. They shall not be used for petroleum product but may be used

for fire water/ cooling water. The product is open to the atmosphere; hence it is atmospheric

tank.

1.2.1.2 Fixed Roof Tanks

Fixed Roof Tanks can be divided into cone roof and dome roof types. They can

be self supported or rafter/ trusses supported depending on the size.

Fixed Roof are designed as

Atmospheric tank (free vent)

Low pressure tanks (approx. 20 mbar of internal pressure)

High pressure tanks (approx. 56 mbar of internal pressure)

Figure 1.1 illustrates various types of storage tank that are commonly used in the industry

today.

Figure 1.1 Types of storage tank

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1.2.1.3 Floating Roof Tanks

Floating roof tanks is which the roof floats directly on top of the product. There are 2 types of

floating roof:

Internal floating roof is where the roof floats on the product in a fixed roof tank.

External Floating roof is where the roof floats on the product in an open tank and the roof

is open to atmosphere.

Types of external floating roof consist of:

Single Deck Pontoon type ( Figure 1.4)

Double deck ( Figure 1.5)

Special buoy and radially reinforced roofs

1.2.2 Storage bins

Regarding descriptive terminology applicable to containment vessels, it should be noted

that the word "bin" as used in this text is intended to apply in general to all such

Containers, whatever their shape, ie whether circular, square or rectangular in plan,

Whether at or above ground level, whatever their height to width ratio, or whether or not

They have a hopper bottom. More specific terms, related to particular shapes or

Proportions, are given below, but even here it must be noted that the definitions are not

Necessarily precise.

a) A bin may be squat or tall, depending upon the height to width ratio, Hm/D, where Hm is

the height of the stored material from the hopper transition level up to the surcharged

material at its level of intersection with the bin wall, with the bin full, and where D is the

plan width or diameter of a square or circular bin or the lesser plan width of a rectangular

bin. Where Hm/D is equal to or less than 1,0 the bin is defined as squat, and when greater

as tall.

b) A silo is a tall bin, having either a flat or a hopper bottom.

c) The hopper transition level of a bin is the level of the transition between the vertical side

and the sloping hopper bottom.

d) A bunker is a container square or rectangular in plan and having a flat or hopper bottom.

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e) A hopper, where provided, is the lower part of a bin, designed to facilitate flow during

emptying. It may have an inverted cone or pyramid shape or a wedge shape; the wedge

hopper extends for the full length of the bin and may have a continuous outlet or several

discrete outlets.

f) A multi-cell bin or bunker is one that is divided, in plan view, into two or more separate

cells or compartments, each able to store part of the material independently of the others.

The outlets may be individual pyramidal hoppers (ie one per cell) or may be a continuous

wedge hopper with a separate outlet for each cell.

g) A ground-mounted bin is one having a flat bottom, supported at ground level.

h) An elevated bin or bunker is one supported above ground level on columns, beams or

skirt plates and usually having a hopper bottom.

1.3 Design Codes and Standards

The design and construction of the storage tanks are bounded and regulated by various codes

and standards. List a few here, they are:

American Standards API 650 (Welded Steel Tanks for Oil Storage)

British Standards BS 2654 (Manufacture of Vertical Storage Tanks with Butt welded

Shells for the Petroleum Industry

The European Standards

- German Code Din 4119 – Part 1 and 2 (Above Ground Cylindrical Flat Bottomed

Storage Tanks of Metallic Materials)

- The French Code, Codres – (Code Francais de construction des reservoirs

cylindriques verticauz en acier U.C.S.I.P. et S.N.C.T.)

The EEMUA Standards (The Engineering Equipments and Materials Users

Association)

Company standards such as shell (DEP) and Petronas (PTS)

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Chapter 2 Design of liquid Storage tanks

The design of vertical, cylindrical tanks for the storage of liquids can be divided into three

basic areas:

The shell

The bottom

The roof

The design of each of these is discussed in detail in this Chapter.

2.1 Shell Design

The cylindrical region of the tank is made up of a number of cylindrical shell courses or tiers,

each usually of same height. The courses are usually butt-welded although lap joints are

occasionally used. Each course is made up of number of equal length plates.

For calculating the thickness of courses two methods are available which are discussed

below.

2.1.1 Calculation of Thickness by the 1-Foot Method

The 1-foot method calculates the thicknesses required at design points 0.3 m (1 ft) above the

bottom of each shell course. This method shall not be used for tanks larger than 60 m (200 ft)

in diameter.

The required minimum thickness of shell plates shall be the greater of the value computed as

followed [API 650, 2007]:

Design shell thickness:

Hydrostatic test shell thickness:

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td = design shell thickness, mm

tt = hydrostatic test shell thickness, mm

D = nominal tank diameter, m

H = design liquid level, m

G = design specific gravity of the liquid stored

C.A = corrosion allowance, mm

Sd = allowable stress for the design condition, MPa

St = allowable stress for the hydrostatic test condition, MPa

2.1.2 Calculation of Thickness by the Variable-Design-Point Method

Note: This procedure normally provides a reduction in shell-course thicknesses and total

material weight, but more important is its potential to permit construction of larger diameter

tanks within the maximum plate thickness limitation.

Design by the variable-design-point method gives shell thicknesses at design points that

result in the calculated stresses being relatively close to the actual circumferential shell

stresses. This method may only be used when it is not specified that the 1-foot method be

used and when the following is true:

L = (500 D t)0.5

, in mm,

D = tank diameter, in m,

t = bottom-course shell thickness, excluding any corrosion allowance, in mm,

H = maximum design liquid level, in m.

Complete, independent calculations shall be made for all of the courses for the design

condition, exclusive of any corrosion allowance, and for the hydrostatic test condition. The

required shell thickness for each course shall be the greater of the design shell thickness

plus any corrosion allowance or the hydrostatic test shell thickness, but the total shell

thickness shall not be less than the shell thickness required by following condition.

The required shell thickness shall be the greater of the design shell thickness,

including any corrosion allowance, or the hydrostatic test shell thickness, but the shell

thickness shall not be less than the following:

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Nominal Tank Diameter Nominal Plate Thickness

(m) (mm)

D<15 5

15<D<36 6

36<D<60 8

D>60 10

Table 2.1 Minimum Thickness Based on Diameter

The calculated stress for each shell course shall not be greater than the stress

permitted for the particular material used for the course. No shell course shall be

thinner than the course above it.

2.1.2.1 The bottom-course thicknesses

Design shall thickness:

Hydrostatic test shell thickness:

2.1.2.2 Second-course thickness

To calculate the second-course thicknesses for both the design condition and the hydrostatic

test condition, the value of the following ratio shall be calculated for the bottom course:

Where,

h1 = height of the bottom shell course, in mm (in.),

r = nominal tank radius, in mm (in.),

t1 = calculated thickness of the bottom shell course, less any thickness added for corrosion

allowance, in mm (in.), used to calculate t2 (design). The calculated hydrostatic thickness of

the bottom shell course shall be used to calculate t2 (hydrostatic test).

If the value of the ratio is less than or equal to 1.375:

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If the value of the ratio is greater than or equal to 2.625:

If the value of the ratio is greater than 1.375 but less than 2.625,:

Where,

t2 = minimum design thickness of the second shell course excluding any corrosion allowance,

in mm (in.),

t2a = thickness of the second shell course, in mm (in.), as calculated for an upper shell course

as described in below section exclusive of any corrosion allowance. dn calculating second

shell course thickness (t2) for design case and hydrostatic test case, applicable values of t2a

and t1 shall be used.

2.1.2.3 Upper-course thicknesses

To calculate the upper-course thicknesses for both the design condition and the hydrostatic

test condition, a preliminary value tu for the upper-course thickness shall be calculated using

the formulas in 2.1.1 excluding any corrosion allowance, and then the distance x of the

variable design point from the bottom of the course shall be calculated using the lowest

value obtained from the following:

tu = thickness of the upper course at the girth joint, exclusive of any corrosion allowance, in

mm,

C = [K0.5

(K - 1)] / (1 + K1.5

),

K = tL / tu ,

tL = thickness of the lower course at the girth joint, except any corrosion allowance, in mm,

H = design liquid level (see 2.1.1), in m.

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So, the minimum thickness tx for the upper shell courses shall be calculated for both the

design condition (tdx) and the hydrostatic test condition (ttx) using the minimum value of x

obtained from above conditions.

The steps described in 2.1.2.3 shall be repeated using the calculated value of tx as tu until

there is little difference between the calculated values of tx in succession (repeating the steps

twice is normally sufficient). Repeating the steps provides a more exact location of the design

point for the course under consideration and, consequently, a more accurate shell thickness.

2.2 Roofs

There are two main types of roof structures are used,

1). Fixed roof structures : They are most widely used roof structures,

1). Self supporting Framed Roof : This type of roof consist of a series of radial arms

overplated with roof sheeting resting on purlins placed over the radial arms.

2). Column supported Framed Roof : This type of roof consist of a shallow cone shape

with a slope of 1 in 16 supported at regular intervals on a series of vertical columns.

3). Self-supporting Frameless Roof : Fixed roofs of small diameter tanks (less than 12 m)

are prepared by joining plates without any supporting structure.

2). Floating Roof : Floating roofs are installed in oil storage tanks primarily to reduce

evaporation, handling losses, to decrease corrosion and to reduce fire hazards.

From the above types of roof column supported framed roof and floating roof are widely used

for large size storage tanks.

Figure 2.1 illustrates these types of storage tank roofs that are commonly used in the industry

for large storage tanks.

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2.1 Column supported framed roof

2.2 Floating roof

For large storage tanks design of column supported conical roof is as follows,

Column supported conical Framed Roof

When conical roof is used with structural support, slope of conical roof

recommended is 1/16.

For steel construction minimum thickness of 5 mm is recommended for the roof

plates

In this design roof plates are placed between the two rafters, but roof plates are

attached to rafters by intermittent lap joint welding. Hence roof plates are

supported by rafters & rafters are supported by Girders, central column &

periphery ring.

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Girders are supported by columns. Periphery ring is a top angle attached to shell

wall.

Design steps

1). Select minimum thickness of roof plate =5 mm + C.A. for structural steel.

2). Keep the slope of conical roof 1/16

3).Determine the pressure created by dead load & live load

P = trρm

+ 125 Where, tr = thickness of roof plate in meter

ρm

= Density of roof plates

4). Select the size of top angle or periphery ring 75mm × 75mm × 10mm

5). Determine the maximum rafter spacing on periphery ring.

l = tr 2f

P

Where, tr = thickness of roof plate

f = max allowable stress of roof plate material

6). Determine minimum nos. of rafters that must be provided in between outer most polygon

& periphery ring.

Min. nos. of rafters required

𝑛𝑚𝑖𝑛 = 𝜋𝐷

𝑙

Where, D = Diameter of storage tank

7). Determine the length of girder of the outer most polygon (girder = side of polygon) length

of Girder

L = 2R sin 360

2N

Where, N = Nos. Girders in polygon or nos. of the sides of polygon

R = radius of circle circum scribing polygon

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8). Determine the rafter spacing on girder

rafter spacing = Length of Girder

Nos. of rafters per Girder=

L

n/N

rafter spacing should be less than 2 m

If rafter spacing > 2. Then increase nos. of rafters.

9). Minimum nos. of rafters required between the two polygon is calculated by equation

𝑛𝑚𝑖𝑛 =2𝑁𝑅

𝑙× 𝑠𝑖𝑛

360

2𝑁=

𝑁𝐿

𝑙

Where,

L = Length of girder of the outer most polygon

R = Radius of circle circumscribing outer most polygon

N = nos. of Girders in Outer most polygon

l = Maximum allowable rafter spacing

Actual Nos. of rafters in between two polygon should be a multiple of nos. sides in both

polygon.

10). Minimum Nos. of rafters required in – between inner most polygon & central column is

also calculated by similar equation. In this case, actual nos. of rafters should be a

multiple of the Numbers of the sides in inner most polygon.

2.3 Bottom Plate

Bottoms of storage tank is constructed from rectangular standard plates. Rectangular plates

are joined to gather by single welded lap joint.

But, in large capacity storage tanks a ring of peripheral plates known as floor annular plates

are provided which have a circular outside circumference and usually a regular polygonal

shape inside the tank, and butt-welded together using backing strips.

Design criteria are shown below,

Bottom plate minimum thickness : 6 mm, excluding any corrosion allowance.

Minimum lap in Bottom plates : 5 x the plate thickness.

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Bottom plate extension beyond shell : 50 mm beyond shell.

Fig 2.3 Joints in floor plates

Annular Bottom Plate :

Width of the annular is determined by :

𝐿 = 215 𝑡𝑏

(𝐻𝐺)0.5

Where, tb = thickness of the annular plate in mm,

H = maximum design liquid level in m,

G = design specific gravity of the liquid to be stored.

Figure shows the bottom plate arrangement of large capacity storage tanks.

Fig 2.4 Bottom plate Layout

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Chapter 3 Design and stability of Storage bins

3.1 Intoduction

Bins are used by a wide range of industries to store bulk solids in quantities ranging from a

few tonnes to over one hundred thousand tonnes. Bins are also called bunkers and silos. They

can be constructed of steel or reinforced concrete and may discharge by gravity flow or by

mechanical means. Steel bins range from heavily stiffened flat plate structures to efficient

unstiffened shell structures. They can be supported on columns, load bearing skirts, or they

may be hung from floors. Flat bottom bins are usually supported directly on foundations.

Bin design procedures consists of two parts as follows:

a). functional design of bins –which includes Determine the strength and flow properties of

the bulk solid, then Determine the bin geometry to give the desired capacity, to provide a

flowpattern with acceptable flow characteristics and to ensure that discharge is reliable and

predictable.

b). Design of bins loading

c). Structural design of bin

Before the structural design can be carried out, the loads on the bin must be evaluated. Loads

from the stored material are dependent, amongst other things, on the flow pattern, the

properties of the stored material and the bin geometry while the methods of structural

analysis and design depend upon the bin geometry and the flow pattern. The importance of

Stages a). and b). of the design should not be underestimated.

3.2 Functional Design of bins

3.2.1 Shapes and types of bins

Bins are provided a storage function in the overall process systems and have to be designed

accordingly. The process requirements may range from a multiple silo proportioning system

to a single load- out silo. In any case the storage capacity of silos, and the required discharge

rate must be determined.

3.2.2 Shapes of outlets and hoppers

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The proper solution for selecting adequate and hopper is based on the analysis of the material

flow properties and conditions during material discharge outlet.

The relevant properties are :

-density

-angle of internal friction

-angle of wall friction(with corresponding values of static and kinetic co-efficient of friction)

-moisture content, etc.

3.2.3 Type of Flow

Two types of flow are shown in Figure 3.1. They are mass flow and funnel flow. Discharge

pressure is influenced by the flow pattern and so the flow assessment must be made before

the calculation of loads from the stored material. In mass flow bins, all the contents of the

bin flow as a single mass and flow is on a first-in first-out basis. The stored material in

funnel flow bins flows down a central core of stationary stored material and flow is on a

last-in, first-out basis.

Figure 3.1 Flow Patterns

The flow type depends on the inclination of the hopper walls and the coefficient of wall

friction. Mass flow occurs in deep bins with steep hopper walls whereas funnel flow occurs in

squat bins with shallow hopper walls. Eurocode 1 gives a graphical method (shown in Figure

3.2) for determining the flow pattern in conical and wedge shaped hoppers for the purpose of

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structural design only. Bins with hoppers between the boundaries of both the mass and the

funnel flows should be designed for both situations.

Figure 3.2 Graphical method for calculation of flow pattern

3.2.4 Structural Material of bins

Most bins are constructed from steel or reinforced concrete. The main disadvantages of steel

bins are the necessity of maintenance to prevent corrosion, the steel walls may require lining

to prevent excessive wear, and the steel walls are prone to condensation which may damage

stored products such as grain and sugar, etc. which are moisture sensitive.

The selection of structural material for the wall may depend upon the bin geometry. A bin

wall is subject to both vertical and horizontal forces. The vertical forces are due to friction

between the wall and stored materials, while the horizontal forces are due to lateral thrust

from the stored materials. Reinforced concrete bins carry vertical compressive forces with

ease and so tend to fail in tension due to the high lateral thrusts. Steel bins, circular in plan,

usually carry the lateral forces by hoop tension. They are more prone to failure by buckling

under excessive vertical forces. The increase of horizontal and vertical pressure with depth is

shown in Figure 3.3. Increases in horizontal pressure are negligible beyond a certain depth

and therefore concrete bins are more efficient if they are tall, whereas steel bins tend to be

shallower structures.

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Figure 3.3 Distribution of horizontal and vertical

pressure against depth of stored material

3.3 Design of bins –Loadings

Material stored in a bin applies lateral forces to the side walls, vertical force (through friction)

to the side walls, vertical forces to the horizontal bottoms and both normal and frictional

forces to the inclined surfaces. The static values of these forces, resulting from materials at

rest, are all modified during the withdrawl of the material. In general, all forces will increase,

so that the loads during withdrawl tend to control the design.

The procedure for bins loading involves determining the static pressures and then multiplying

these forces by an “overpressure” factor to obtain the design pressures.

3.3.1 Static Loads

Two methods are generally used for determining of static pressure

1). Janssen‟s method

2).Reimberts‟s method

Before analyzing this method the pressure exerted by a stored pulverulent mass shall be

defined first.

When this material is poured onto a plane, it heaps up into a volume conical in shape, the

generatrices of which form a specific angle 𝜑 with the horizontal .

It exerts pressure on the walls and on the bottom of it, the resultant of which is the thrust.

This thrust has two component, one N normal to the wall considered, and other tangential T

parallel to the wall. If 𝜑′ is the angle of friction of the material on the wall, the corresponding

coefficient of the friction is tan𝜑′.

So, T is therefor the load balanced by the friction corresponding to the thrust N is :

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𝑇 = 𝑁 tan 𝜑

At given depth inside the bin, the load on the bottom or total vertical pressure, is the

difference between the total weight of the stored material and the total load balanced by the

friction of the material on the wall.

3.3.1.1 Janssens’s Method

The Vertical static unit pressure at depth z below the surface is :

𝑞 =𝛾𝑟

𝜇 𝑘 1 − 𝑒−𝜇 ′𝑘 𝑧/𝑟

Where,

𝛾 = weight per unit volume for stored material

r = Hydraulic radius of horizontal cross- section of the inside of the bin

𝜇′= coefficient of friction between stored material and wall = tan 𝜑′

k = ratio of p to q

Figure 3.4 Bin dimensions for

use in Reimbert’s and

Janssen’s equation

The lateral static unit pressure at depth z is

𝑝 =𝛾𝑟

𝜇′ 1 − 𝑒−𝜇 ′𝑘

𝑧𝑟 = 𝑞𝑘

Where k =𝑝

𝑞

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The ratio p/q is assumed by Jassen to be constant at all depths and has the value

𝑘 =𝑝

𝑞=

1 − sin 𝜑

1 − 𝑠𝑖𝑛𝜑𝑡𝑎𝑛2

𝜋

4−

𝜑

2

At the limit

pmax = qmax × k =γr

μ′=

γr

tan φ′

For circular bins,

𝑟 =𝑆

𝐿=

𝜋𝐷2

4 ×

1

𝜋𝐷=

𝐷

4

Whare

S = area of the bin

L = perimeter of the bin

D = diameter of the bin

3.3.1.2 Reimbert’s Method

The vertical static unit pressure at depth z below the surface is

q = 𝛾[𝑧(𝑍

𝐶+ 1)−1 +

𝑕𝑠

3]

The lateral static unit pressure at depth z is

p = 𝑝𝑚𝑎𝑥 [1 – (𝑍

𝐶+ 1)−2] = ∈ 𝑝𝑚𝑎𝑥

𝑝𝑚𝑎𝑥 is the maximum lateral unit pressure

C is the “characteristic abscissa”

𝑝𝑚𝑎𝑥 = 𝛾𝐷

4 tan 𝜑′

And

𝑐 = 𝐷

4 tan 𝜑′ tan2 𝜋4 −

𝜑2

− 𝑕𝑠

3

For polygonal bins or bins having more than four sides

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𝑝𝑚𝑎𝑥 = 𝛾𝑟

tan 𝜑′

And

𝑐 = 𝐿

𝜋

1

4 tan 𝜑′ tan2 𝜋4 −

𝜑2

− 𝑕𝑠

3

For rectangular bins- on shorter wall “a”

(𝑝𝑚𝑎𝑥 )𝑎 = 𝛾𝑎

4 tan 𝜑′

And

𝑐𝑎 = 𝑎

𝜋 tan 𝜑′ tan2 𝜋4 −

𝜑2

− 𝑕𝑠

3

For rectangular bins- on longer wall “b”

(𝑃𝑚𝑎𝑥 )𝑏 = 𝛾𝑎′

4 tan 𝜑′

And

𝑐𝑏 = 𝑎′

𝜇 tan 𝜑′ tan2(𝜋4−

𝜑2

)−

𝑕𝑠

3

Where

𝑎′ = 2 𝑎𝑏 − 𝑎2

𝑏

For design purposes, the granular material is usually assumed level at the top of the bin,

therefore 𝑕𝑠 = 0

It should be observed that theory developed by Reimbert takes into consideration the

variation of the ratio p/q with depth and also with the shape of the bins.

3.3.2 Static Forces –Vertical Friction

26 | P a g e

For circular, square and regular polygonal bins, the total static frictional forces per foot –

wide vertical strip of wall above depth z is approximetly:

By Reimbert‟s method :

𝑉 =(𝛾𝑧 − 𝑞)𝐴

𝐿

By Janssen‟s method:

𝑉 = 𝛾𝑧 − 0.8𝑞 𝐴

𝐿

Where

A = area of the horizontal cross- section of the bin

L = perimeter of the horizontal cross- section of the bin

3.3.3 Static pressure on silo Hoppers

The static horizontal pressures, p, and vertical q, on inclined hopper wall are calculated by

the Janssen or Reimbert formulas. The Hydraulic radius r, may be reduced with in the hopper

depth, but usually is assumed constant and equal to that of the bin. The static unit pressure

normal to the inclined surface, at depth z from the top of the fill is

𝑞𝛼 = 𝑝 𝑠𝑖𝑛2𝛼 + 𝑞𝑐𝑜𝑠2𝛼

Before, the stresses in the hopper bins were most easily calculated by graphic method or by a

combination of algebraic and graphical methods.

3.4 Structural Design of Bins

Once the different pressures acting on the walls of the bin have been defined, designer is

ready to determine the thickness of the bin‟s walls. To provid stabitity to the bins against

various loads acting due to wind loads and materials to be stored. Stiffeners are provided on

the walls of the bins which is also discussed in this section.

3.4.1 Cylindrical Shells

The calculation of the size of the vertical walls of cylindrical bins does not present special

difficulties. Beyond the self weight of the walls, they are acted upon by two main forces: the

27 | P a g e

lateral pressure and the vertical friction force due to the frication of the material on the walls,

which generates vertical compression stresses on the walls.

If 𝑝𝑧 is the lateral pressure and r the internal radius of the bin, the thickness of the wall must

designed to withstand a circumferential tensile or hoop stress of;

𝑓𝑡 = 𝑝𝑧 𝑟

𝑡

For small bins, stiffeners may not be required. For large and deep bins, because the

cylindrical wall may buckle under vertical compressive loads, and may bend under bending

moments induced from uneven distribution of the wall pressure due to dynamic effects and

due to eccentrically located outlets, etc,. ring stiffeners or rings and vertical stiffeners are

recommended.

After calculation of the hoop stress as mentioned before the vertical pressure will be

calculated.

The longitudinal compressive stress is, following Reimbert‟s theory:

𝑓𝑐 = 𝑉

𝑡=

(𝛾𝑧−𝑞)𝜋𝑟 2

2𝜋𝑟𝑡=

𝛾𝑧 –𝑞 𝑟

2𝑡

It should be noted that the above Equation applies only when 𝛾𝑧 > 𝑞

To find the maximum stress in the plate at the level considered, ft and fc may be combined in

the form:

ft‟ = ft + v fc

fc‟ = fc + v ft

Where

v = 0.3, poisons ratio for steel

ft ‟ = maximum tensile stress in the plate

fc‟ = max. Compressive stress in the plate

ft = circumferential tensile stress or hoop stress

fc = longitudinal compressive stress

28 | P a g e

For max. compressive stresses in the bin walls, considerations must be given to the portions

of bin walls at the stiffener and to those portions of bin walls which lie between stiffeners.

The load distribution and their corresponding stresses may be calculated as follows :

𝑞𝑠 = 𝐴𝑠 + 2𝑏𝑒 𝑡 𝐹𝐶𝑆

𝐴𝑠 + 2𝑏𝑒 𝑡 𝐹𝐶𝑆 + 𝑏 − 2𝑏𝑒 𝑡𝐹𝑐𝑢

𝑞𝑢 = 𝑞 − 𝑞𝑠

𝑓𝑐𝑠 =𝑞𝑠

𝑛(𝐴𝑠 + 2𝑏𝑒𝑡)

𝑓𝑐𝑢 =𝑞𝑢

𝑛(𝑏 − 2𝑏𝑒)𝑡

Where

Fcs , Fcu = allowable compressive stress of stiffened and unstiffened shell respectively

fcs , fcu = vertical compressive stress of stiffened and unstiffened shell respectively

b = horizontal spacing of vertical stiffeners

be = effective width of the plate

n = no. of vertical stiffeners

3.4.1.1 Stiffened shells

The portions of bin shells near the stiffeners have greater load – carrying capacity. If “n” is

the total no. of equally spaced vertical stiffeners, and be is the effective width of the shell on

each side of the stiffeners, as cshown in figure 4.1, the effective width be will be :

𝑏𝑒 = 0.95𝑡 1 − 0.475𝑡

𝑏

𝐸𝑠

𝐹𝑐𝑠 𝐸𝑠

𝐹𝑐𝑠

𝐹𝑐𝑠 is the allowable stress of the stiffener and plate column determined by the appropriate

column formula with the vertical spacing 𝑙 of the horizontal stiffeners as the column length.

Since, the allowable stress 𝐹𝑐𝑠 and the effective width 𝑏𝑒are interdependent it is necessary to

use a trial- and -error method by assuming 𝑏𝑒 ,to calculate 𝐹𝑐𝑠 , or vice versa . After𝐹𝑐𝑠 and

𝑏𝑒have been determined, the capacity of the stiffened shells of the bin can be calculated as :

𝑞𝑠 = 𝑛 𝐹𝑐𝑠(𝐴𝑠 + 2𝑏𝑒 𝑡)

29 | P a g e

For quick and approximate evaluation, 𝑏𝑒 may be assumed to be 30 to 40 t, where t is the

thickness of the plate.

It should be noted that the above effective width is taken as approx. equal to that of a flate

plate. In the case of a cylindrical panel the load carrying capacity will be increased Due to its

curvature. Let λ1 be the slenderness ratio of the stiffener and shell column, and λ2 =20 𝑟

𝑡 ,

Where “r” is the shell radius in feet, and “t” the wall thickness in inches, then the combined

slenderness ratio can be calculated by :

λ =λ1λ2

λ12+ λ2

2

3.4.2 Stiffeners

Due to the effect of wind pressure, arching of material, and uneven distribution of lateral

pressure in the horizontal section during filling and emptying are possible, stiffeners are

always recommended vertical spacing of the horizontal stiffeners of 10 to 15 ft, and

horizontal spacing of the vertical stiffeners of 4 to 10 ft may be recommended as the normal

practice.

The vertical stiffeners can be designed as a portion of a stiffener and shell column, as

discussed in stiffened shells. The horizontal stiffeners should be designed to support the

vertical stiffeners against buckling. The minimum width of such a horizontal stiffener to be

recommended here is one- hundredth of the diameter of the bin, with a central filling or

central discharging device. For bins with non- central fillings or non- central discharging

devices, The horizontal stiffeners should be designed for one sided pressure effect. The

recommendation by many designers for the design of each horizontal stiffener is:

𝑀 = 0.04 𝛾𝑟2 𝑑𝑒 𝑙 tan 𝜑 , for 𝑙 < 2 r tan 𝜑

𝑀 = 0.08 𝛾𝑟3 𝑑𝑒 𝑙 tan2 𝜑 , for 𝑙 > 2 r tan 𝜑

Where

𝑑𝑒 = the eccentric distance of the outlet from the centre of the bin, and

M = the moment in the stiffeners

30 | P a g e

In no case , shall the width of the horizontal stiffener be less than one-hundredth of the

diameter of the bin, as recommended for bins with central filling or central discharging

devices.

3.4.3 Hoppers

The shells of the silos are terminated at their lower part, by hoppers, their shape being usually

that of a truncated cone in the case of cylindrical shell, in order to permit complete discharge

of the stored material through the discharge trap placed at the lowest point.

In calculating the thickness of the walls of hoppers, it is assumed that the stored pulverulent

materials transmit to the walls of the hoppers the vertical pressure which they exert at the

level of the connection to the vertical walls, i.e., at the level of the junction of the walls of the

shells to the walls at these hoppers.

The following loads are considered :

a). The vertical pressure exerted by the stored material at the lower level of the vertical walls.

b). The weight of the stored material filling the hopper.

c). The weight of the devices fixed onto the hopper (if any).

The plates forming the cone will be subjected to both the hoop tension and the meridional

tension. Janssen‟s or Reimbert‟s expressions for both lateral and horizontal pressure may be

used, but some modifications of a minor nature will be necessary.

For application, we will use Janssen‟s expressions.

The mean hydraulic radius “r” should be replaced by half the appropriate cone radius 𝑟1

2 and

the co-efficient of friction on the wall 𝜇‟ by the corresponding internal friction coefficient, 𝜇.

Those modifications take into account the fact that in this area the material is sliding against

the material located outside the radius 𝑟1 , instead of sliding against the bin wall,

The lateral pressure would therefore be :

𝑃 =𝛾𝑟1

2𝜇 1 − 𝑒−2𝜇𝑘𝑧 /𝑟1

Giving a hoop tension of :

31 | P a g e

TH = P𝑟1

Resulting in a hoop stress of :

𝑓𝐻 =𝑃𝑟1

𝑡

Similarly, the longitudinal tension would take the form :

𝑇𝐿 =𝑊1𝑐𝑜𝑠𝑒𝑐 𝜑

2𝜋𝑟1

In above equation

𝑊1 = 𝑞𝜋𝑟12 + 𝛾𝑟1

2𝜋𝑍′

3+ 𝑠𝑒𝑙𝑓 𝑤𝑒𝑖𝑔𝑕𝑡

𝑞𝜋𝑟12 = vertical pressure of stored material at lower level

Where

𝑞 =𝛾𝑟1

2𝜇𝐾 1 − 𝑒−2𝜇𝑘𝑧 /𝑟

𝛾𝑟12 = weight of the stored material

Self weight = weight of the hopper

Resulting in a meridional stress of :

𝑓𝐿 =𝑊1𝑐𝑜𝑠𝑒𝑐 𝜑

2𝜋𝑟1𝑡

Both 𝑓𝑕 and 𝑓𝐿 will be a maximum at the waist, and a minimum at the outlet.

3.4.4 Roofs

The roof should be a self supporting structure. It may be flat, or in the form of a cone or

dome. However, in view of the fact that a partial vacuum may develop, above the stored

material due to the arching action, larger vents should be provided to prevent any inward

buckling of the silo walls or of the roof, itself, from this cause.

3.4.5 Buckling

32 | P a g e

In the horizontal planes, both circular and rectangular steel bins are under axial tension and

there is no danger of buckling.

In vertical planes, the uniformly distributed compressive loading due to the own weight of

bin walls, the frictional force of the stored material and roof and equipment loads, buckling of

the bin walls may occure at a certain value of the comp. load.

3.4.5.1 Cylindrical Bins

The buckling stress for cylindrical bins is given by the classical solution for axially

compressed cylinders.

𝜎𝑐𝑟 = 𝐸𝑕/𝑎

[3 1 − 𝑣2 ]12

Where h is the wall thickness and 𝑎 is the avg. surface radius, (with h<< 𝑎)

The critical values of axial stresses for cylinders subjected to axial compression are

conveniently expressed as a function of the so- called Batdorf parameter Z

𝑍 =𝐿2

𝑎𝑕(1 − 𝑣)

12

With the corresponding values of factor Ka, as shown in Figure

𝐾𝑎 =𝐿2𝑕

𝜋2𝐷𝜎𝑐𝑟

Figure 3.5 Critical values of axial

stresses for cylinders

subjected to axial compression

33 | P a g e

𝐷 = 𝐸𝑕

12 1 − 𝑣2

For thew values of Z > 2.85, long cylinders, the values of 𝑣𝑐𝑟 given by above fig. and

equation for 𝜎𝑐𝑟 are the same.(Z < 2.85 represents the short cylinders).

3.4.5.2 Compression ring between cylinder and hopper

When the transition from a cylinder to a cone is made abruptly, a compression ring must be

provided to resist the horizontal inward pull from the cone, as shown in fig.

Figure 3.6 Cylinder to cone transition Figure 3.7 Forces on suspended bottoms

This steel ring should be designed for an allowable stress of 10000 psi. This relatively low

value is used to minimize deflection and hence the secondary bending stress. But, the

compression ring must be checked particularly for buckling. Using a factor of safety of 3, in

Levy‟s formula for buckling of a ring under uniform pressure:

𝑇𝐻𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙=

3𝐸𝐼

𝑅𝑟3

Where

𝑇𝐻 = horizontal component of T2

Where T2 = meridional force Fig.

Rr = centroidal radius of a ring

E = Young‟s modulus

I = minimum moment of inertia

Using this steps structural design of bins can be done.

34 | P a g e

Chapter 4 Stability of storage tanks

The stability of Storage tanks and tall bins are mostly affected By the

seismic loadings and Due to wind loading acting on their structure. So, this storage structures

must be designed for with stand this loadings to remain stable.

Wind load and seismic load on the tall bins causes vibration in the vessel due to the wind and

sudden acceleration in earth‟s crust.

Under these conditions the vessel under this loading acts as a cantilever beam and starts

vibrating same as the cantilever beam. Slender columns are more able to absorb seismic

forces. On the other hand, the reverse is true under the influence of wind forces. If the column

is rigid, it will with stand higher wind forces. So, stability consideration is taken for wind

load only in the Tall Bins.

4.1 Provisions for Seismic Loading

Storage tanks

The seismic design of the storage tank is accordance to API 650 (2007) There are three major

analyses to be performed in the seismic design, and they are:

i) Overturning Stability check - The overturning moment will be calculated and

check for the anchorage requirement. The number of anchor bolt required and the anchor

bolt size will also be determined based on the overturning moment.

ii) Maximum base shear

iii) Freeboard required for the sloshing wave height – It is essential for a floating roof tank to

have sufficient freeboard to ensure the roof seal remain within the height the tank shell.

4.1.1 - General

Hydrodynamic forces exerted by liquid on tank wall shall be considered in the analysis in

addition to hydrostatic forces. These hydrodynamic forces are evaluated with the help of

spring mass model of tanks.

4.1.2 - Spring Mass Model for Seismic Analysis

35 | P a g e

When a tank containing liquid vibrates, the liquid exerts impulsive and convective

hydrodynamic pressure on the tank wall and the tank base in addition to the hydrostatic

pressure. In order to include the effect of hydrodynamic pressure in the analysis, tank can be

idealized by an equivalent spring mass model, which includes the effect of tank wall – liquid

interaction. The parameters of this model depend on geometry of the tank and its flexibility.

Ground supported tanks can be idealized as spring-mass model shown in Figure 1. The

impulsive mass of liquid, mi is rigidly attached to tank wall at height hi (or hi* ). Similarly,

convective mass, mc is attached to the tank wall at height hc (or hc*

) by a spring of stiffness

Kc . Equations are given below,

Table 4.1 Expression for parameters of spring mass model

36 | P a g e

4.1.3 – Time Period

4.1.3.1 – Impulsive Mode

For a ground supported circular tank, wherein wall is rigidly connected with the base slab,

time period of impulsive mode of vibration Ti , in seconds, is given by

Ci = Coefficient of time period for impulsive mode. Value of Ci can be obtained from

h = Maximum depth of liquid,

D = Inner diameter of circular tank,

t = Thickness of tank wall,

E = Modulus of elasticity of tank wall, and

ρ = Mass density of liquid.

4.1.3.2 – Convective Mode

Time period of convective mode, in seconds, is given by

Where, Cc = Coefficient of time period for convective mode. Value of Cc can be

obtained by

D = Inner diameter of tank

For tanks resting on soft soil, effect of flexibility of soil may be considered while evaluating

the time period. Generally, soil flexibility does not affect the convective mode time period.

However, soil flexibility may affect impulsive mode time period.

37 | P a g e

4.1.4 – Damping

Damping in the convective mode for all types of liquids and for all types of tanks shall be

taken as 0.5% of the critical. Damping in the impulsive mode shall be taken as 2% of the

critical for steel tanks and 5% of the critical for concrete or masonry tanks.

4.1.5 – Design Horizontal Seismic Coefficient

Design horizontal seismic coefficient, Ah shall be obtained by the following expression,

Where

Z = Zone factor

I = Importance factor given in table,

R = Response reduction factor (2.5 - 3.0)

Sa/g = Average response acceleration coefficient

Table 4. 2 – Importance

factor,I

4.1.6 - Base Shear

Base shear in impulsive mode, at the bottom of tank wall is given by

and base shear in convective mode is given by

where,

(Ah)i = Design horizontal seismic coefficient for impulsive mode,

(Ah)c = Design horizontal seismic coefficient for convective mode,

mi = Impulsive mass of water

Type of liquid storage tank I

Tanks used for storing drinking water, non-volatile

material, low inflammable petrochemicals etc. and

intended for emergency services such as fire

fighting services. Tanks of post earthquake

importance.

1.5

All other tanks with no risk to life and with

negligible consequences to environment, society

and economy.

1.0

38 | P a g e

mw = Mass of tank wall

mt = Mass of roof slab, and ; g = Acceleration due to gravity.

Total base shear V, can be obtained by combining the base shear in impulsive and convective

mode through Square root of Sum of Squares (SRSS) rule and is given as follows

4.1.7 – Overturning Moment at the Base

For obtaining bending moment at the bottom of tank wall, effect of hydrodynamic pressure

on wall is considered.

Overturning moment in impulsive mode to be used for checking the tank stability at the

bottom of base slab/plate is given by

and overturning moment in convective mode is given by

where

hw = Height of center of gravity of wall mass, and

ht = Height of center of gravity of roof mass.

mc =Convective mass of liquid

mi= Impulsive mass of liquid

mt = Mass of roof slab

mw = Mass of tank wall

hc *= Height of convective mass above bottom of tank wall (considering base pressure)

hi* = Height of impulsive mass above bottom of tank wall (considering base pressure)

Mc*= Overturning moment in convective mode at the base

Mi* = Overturning moment in impulsive mode at the base

t b = Thickness of base slab

39 | P a g e

4.1.8 – Hydrodynamic Pressure

During lateral base excitation, tank wall is subjected to lateral hydrodynamic pressure and

tank base is subjected to hydrodynamic pressure in vertical direction

4.1.8.1 – Impulsive Hydrodynamic Pressure

The impulsive hydrodynamic pressure exerted by the liquid on the tank wall and base for the

circular tanks Lateral hydrodynamic impulsive pressure on the wall, piw , is given by

Where

ρ = Mass density of liquid,

φ = Circumferential angle, and

y = Vertical distance of a point on tank wall from the bottom of tank wall.

Coefficient of impulsive hydrodynamic pressure on wall, Qiw (y) can be obtained from

Figure.

Fig. 4.1 Impulsive Hydrodynamic Pressure on wall

40 | P a g e

Impulsive hydrodynamic pressure in vertical direction, on base slab (y = 0) on a strip of

length l', is given by

Where x = Horizontal distance of a point on base of tank in the direction of seismic

force, from the center of tank.

4.1.8.2 – Convective Hydrodynamic Pressure

The convective pressure exerted by the oscillating liquid on the tank wall and base shall be

calculated as follows:

Lateral convective pressure on the wall pcw , is given by

The value of Qcw (y) can be read from the graph

Fig 4.2 Convective Hydrodynamic Pressure on wall

41 | P a g e

Convective pressure in vertical direction, on the base slab (y = 0) is given by

4.1.9 – Effect of Vertical Ground Acceleration

Vertical ground acceleration induces hydrodynamic pressure on wall in addition to that due to

horizontal ground acceleration. In circular tanks, this pressure is uniformly distributed in the

circumferential direction. Which will cause One of the most important type of damage is the

„elephant foot ‘ buckling of the lowest course of the tank wall.

Hydrodynamic pressure on tank wall due to vertical ground acceleration may be taken as

where

y = vertical distance of point under consideration from bottom of tank wall, and

Sa / g = Average response acceleration

The maximum value of hydrodynamic pressure should be obtained by combining pressure

due to horizontal and vertical excitation through square root of sum of squares (SRSS) rule,

which can be given as

4.1.10 – Sloshing Wave Height

To provide sufficient free board to eliminate damage during earthquake sloshing wave height

is calculated.

Maximum sloshing wave height is given by

42 | P a g e

where

( Ah )c = Design horizontal seismic coefficient corresponding to convective time period.

Free board to be provided in a tank may be based on maximum value of sloshing wave

height. This is particularly important for tanks containing toxic liquids, where loss of liquid

needs to be prevented. If sufficient free board is not provided roof structure should be

designed to resist the uplift pressure due to sloshing of liquid.

4.1.11 – Anchorage Requirement

As mentioned above during seismic loading tanks are subjected to many pressure loads and

overturning moments. So for stability of storage tanks anchorage is provided using anchor

bolts.

Circular ground supported tanks shall beanchored to their foundation (Figure)when

If we Consider a tank which is about to rock (Figure ).

Let Mtot denotes the total mass of the tank-liquid system,

D denote the tank diameter, and (Ah )i g denote the peak

response acceleration. Taking moments about the edge,

Thus, when h / D exceeds the value indicated above, the tank should be anchored to its

foundation.

4.2 Provisions for Wind Loading

43 | P a g e

Wind loading and presence of vacuum in the tank are external pressures and tend to

destabilise the tank geometry resulting in collapse by buckling. In fixed roof structures fixed

roof provides some stabilising effect.

But, In open top and external floating roof tanks do not have the benefit of this shell rigidity

and therefore a circumferential stiffeners are provided at the top of the shell & also at

regular intervals.

4.2.1 Top Stiffener and Intermediate Wind Girder Design

4.2.1.1 Top Stiffener/ Top Wind Girder

Stiffener rings of top wind girder are to be provided in an open-top tank to maintain the

roundness when the tank is subjected to wind load. The stiffener rings shall be located at

or near the top course and outside of the tank shell. The girder can also be used as an

access and maintenance platform. There are five numbers of typical stiffener rings

sections for the tank shell given in API 650 (2007) and they are shown in Figure 2.5 [API

650, 2007].

Fig 4.3 Typical stiffener

ring section for ring

shell

The requirement in API 650 (2007) stated that when the stiffener rings or top wind girder are

located more than 0.6 m below the top of the shell, the tank shall be provided with a

minimum size of 64 x 64 x 4.8 mm top curb angle for shells thickness 5 mm, and with a 76 x

44 | P a g e

76 x 6.4 mm angle for shell more than 5 mm thick. A top wind girder in my tank is designed

to locate at 1 m from the top of tank and therefore for a top curb angle of size 75 x 75 x 10

mm is used in conjunction with the stiffener detail a) in Figure 2.5. The top wind girder is

designed based on the equation for the minimum required section modules of the stiffener

ring [API 650, 2007].

Where

Z = Minimum required section modulus, cm³

D = Nominal tank diameter, m

H2 = Height of the tank shell, in m, including any freeboard provided above the maximum

filling height

V = design wind speed (3-sec gust), km/h

The term (𝐷2𝐻

17) on the equation is based on a wind speed of 190 km/h and therefore the

𝑉

190

2

term is included in the equation for the desire design wind speed.

Accordance to API 60 (2007) clause 5.9.5, support shall be provided for all stiffener rings

when the dimension of the horizontal leg or web exceeds 16 times the leg or web thickness

[API 650, 2007]. The supports shall be spaced at the interval required for the dead load and

vertical live load.

4.2.1.2 Intermediate Wind Girder

The shell of the storage tank is susceptible to buckling under influence of wind and internal

vacuum, especially when in a near empty or empty condition. It is essential to analysis the

shell to ensure that it is stable under these conditions. Intermediate stiffener or wind girder

will be provided if necessary.

To determine whether the intermediate wind girder is required, the maximum height of the

un-stiffened shell shall be determined. The maximum height of the un-stiffener shell will be

calculated as follows [API 650, 2007]:

45 | P a g e

Where

H1 = Vertical distance, in m, between the intermediate wind girder and top wind girder

t = Thickness of the top shell course, mm

D = Nonimal tank diameter, m

V = design wind speed (3-sec gust), km/h

As stated in earlier, the shell is made of up diminishing thickness and it makes the analysis

difficult. The equivalent shell method is employed to convert the multi-thickness shell into an

equivalent shell having the equal thickness as to the top shell course. The actual width of

each shell course in changed into a transposed width of each shell course having the top shell

course thickness by the following formula [API 650, 2007]:

Where

Wtr = Transposed width of each shell course, mm

W = Actual width of each shell course, mm

tuniform = Thickness of the top shell course, mm

tactual = Thickness of the shell course for which the transpose width is being calculated, mm

The sum of the transposed width of the courses will be the height of the transformed shell

(H2).

If the height of transformed shell is greater than the maximum height of un-stiffened shell,

intermediate wind girder is required. The total number intermediate wind girder required can

be determined by simply divide the height of transformed shell with the maximum un-

stiffened shell height.

Similarly, minimum required section modulus of the intermediate wind girder has to be

determined. The same equation in the top wind girder can be used, but instead of the total

shell height H2, the vertical distance between the intermediate wind girder and top wind

girder is used.

46 | P a g e

4.2.2 Overturning Stability against Wind Load

The overturning stability of the tank shall be analyzed against the wind pressure, and to

determine the stability of the tank with and without anchorage. The wind pressure used in the

analysis is given as per API 650 (2007).

The wind load (Fs) on the shell is calculated by multiplying the wind pressure ws to the

projected area of the shell, and the wind load (Fr) on the roof will be zero as the roof will be

floating on the liquid into the tank, where there will be no projected area for the roof.

Figure 4.4 Overturning check on tank due to wind load

As per API 650 (2007), the tank will be structurally stable without anchorage when the below

uplift criteria are meet [API 650, 2007].

Where

Mpi = moment about the shell-to-bottom from design internal pressure (Pi) and it can be

calculated by the formula

Mw = Overturning moment about the shell-to-bottom joint from horizontal plus vertical wind

pressure and is equal to Fr.Lr + Fs.Ls. Fr and Fs is the wind load acting on the roof and shell

respectively and Lr and Ls is the height from tank bottom to the roof center and shell center

respectively.

47 | P a g e

MDL = Moment about the shell-to-bottom joint from the weight of the shell and roof

supported by the shell and is calculated as 0.5 D. WDL. The weight of the roof is zero since

the roof is floating on the liquid.

MF = Moment about the shell-to-bottom joint from liquid weight and is equal to

48 | P a g e

References

1. API Standard 650, “Welded Steel Tanks For Oil Storage” American Petroleum

Institute, Eleventh Edition, (June 2007).

2. Bob Long and Bob Garner, “Guide to Storage Tank and Equipment “, volume 1,page no.1-

173 Professional Engineering Publishing, UK (1977).

3. K. Rajagopalan, “Storage Structure”. McGraw-Hill, New York (1989).

4. Antonio Di Carluccio." Dynamic Behavior of Atmospheric storage tank,” Chapter 4, in

"Structural Characterisation and Seismic Evaluation of Steel Equipments in Industrial

Plants", (2007).

5. Indian Institute of Technology Kanpur, Gujarat State Disaster Management Authority.

“Guidelines for seismic design of Liquid storage tanks”, (October 2007).

6. Gerard L. Xavier, “Structural Design of steel bins” Chapter 1-4, (1979)

7. Kuan, Siew Yeng, “Design, Construction and Operation of the Floating Roof Tank

Page 46-79, (October 2009).

8. Brownell L.E. and Young, E.H., “Process Equipment Design”, John Wiley, New

York, 1959.

9. B.C. Bhattacharyya, “Chemical engineering equipment design”, CBS Publishers

(2001)

10. No author identified, no date. “structural design of bin” Retrieved from

http// www.fgg.uni-lj.si/kmk/esdep/master/wg15c/l0400.html [Accessed 14/1/12.]

11. J. W. Carson and R. T. Jenkyn, “Load development and structural Considerations in

silo design”, Jenike & Johansan incorporated, page 1-16.

12. Bureau of Indian Standards, “Criteria for design of steel bins for storage of bulk

materials IS : 9178 (Part 1), Edition 1.2 (1992-08)