Structural Design of Steel Bins and Silos

5/26/2018 Structural Design of Steel Bins and Silos

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The Structural Design of Steel Bins and Silos August, 01

1.1

1 INTRODUCTION

1.1 General

The storage of granular solids in bulk represents an important stage in the production ofmany substances derived in raw material form and requiring subsequent processing forfinal use. These include materials obtained by mining, such as metal ores and coal;agricultural products, such as wheat, maize and other grains; and materials derivedfrom quarrying or excavation processes, for example sand and stone. All need to beheld in storage after their initial derivation, and most need further processing to yieldsemi- or fully-processed products such as coke, cement, flour, concrete aggregates,lime, phosphates and sugar. During this processing stage further periods of storage arenecessary.

In the Southern African region, with its vast raw material resources, the storage of bulksolids plays an essential part in many industries, including coal and ore mining,

generation of electricity, manufacture of chemicals, agriculture, and food processing.The means of storage of these materials is generally provided by large storage vesselsor bins, built in steel or reinforced concrete, located at or above ground level.

1.2 Design

The functional planning and structural design of such containers represent specialisedskills provided by the engineering profession. Unfortunately there is a lack ofcomprehensive literature, covering all aspects of bin design, available to the practisingengineer. It is the purpose of this publication to present the necessary guidelines toenable the design function to be carried out efficiently and safely, as related to the wide

range of typical small, medium and fairly large storage containers or bins built in steel.

In the past the design of bins was based on static pressures derived from simpleassumptions regarding the forces exerted by the stored material on the walls of the bin,with no allowance for increased pressures imposed during filling or emptying. In thepresent text, advantage has been taken of a large amount of research work that hasbeen carried out during recent decades in various countries, especially the UnitedStates and Australia. It is hoped that the application of the better understanding of flowloads and the analysis of their effects will lead to the design of safer bins and theavoidance of serious and costly failures such as have occurred in the past.

1.3 Terminology

Regarding descriptive terminology applicable to containment vessels, it should be notedthat the word "bin" as used in this text is intended to apply in general to all suchcontainers, 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 notthey have a hopper bottom. More specific terms, related to particular shapes orproportions, are given below, but even here it must be noted that the definitions are notnecessarily precise.


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1.2

a) A bin may be squat ortall, depending upon the height to width ratio, Hm D, whereHm is the height of the stored material from the hopper transition level up to thesurcharged 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 lesserplan 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 silois 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 thevertical side and the sloping hopper bottom.

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

e) A hopper, where provided, is the lower part of a bin, designed to facilitate flowduring 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 acontinuous outlet or several discrete outlets.

f) A multi-cell bin or bunker is one that is divided, in plan view, into two or moreseparate cells or compartments, each able to store part of the materialindependently of the others. The outlets may be individual pyramidal hoppers (ieone per cell) or may be a continuous wedge hopper with a separate outlet for eachcell.

g) A ground-mountedbin 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.

1.4 Design procedure

The full design procedure for a typical steel bin would comprise a series of activities asdescribed in the ensuing text, but which can be summarised as follows:

a) Assessment of material properties

This involves an examination of the stored material with a view to determining itsproperties as affecting both the functional and the structural design of the bin. Theproperties include the density of the material, its compressibility, and its angle of

internal friction, angle of repose and angle of wall friction. For the majority of storedmaterials such as ores, coal, grain, etc these properties can be obtained from the

tables given in Chapter 2, but for unusual materials or very large silos theproperties should be determined from laboratory tests or by reference tospecialist materials handling technologists.


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1.3

b) Assessment of flow characteristics

Based on the material properties mentioned above, it is necessary to determinethe flow characteristics of the material and thus determine the optimum shape or

geometry of the bin to ensure satisfactory emptying and the prevention of hang-ups such as arching or bridging.

It should be noted that there are three main flow patterns when a bin is beingemptied, viz mass flow, funnel flow and expanded flow. These are discussed later,but the particular type of flow applicable to a bin depends both on the geometry ofthe bin and the flow characteristics of the material. Specialists should beconsulted in the case of uncommon or suspect materials.

c) Functional design of bin

The design of the bin from a functional or operating point of view, based on the

material characteristics described above, is usually undertaken by material flowtechnologists. This will involve the selection of the required depth, width and heightto accommodate the specified volume of material, the slope of the hopper bottom,location of hopper hip, size and location of outlets, etc. Some guidance is given inchapter 3.

d) Determination of pressures and forces

The normal and frictional forces exerted by the material on the inner surfaces orwalls of the bin are determined, considering the dynamic effects during filling, thestatic effects during storage and the dynamic effects during emptying, plus effectsdue to temperature, expansion of contents, etc, when present.

The magnitude and distribution of the wall forces will depend on the applicable flowmode, the effects of switch pressure in bins with hopper bottoms, and the effectsof eccentric discharge where applicable. Pressure diagrams showing themagnitude and distribution of pressure and frictional force are prepared for eachinner surface of the bin for the filling and emptying phases, for use in the structuraldesign of the bin.

e) Structural design

The structural design of the bin, including all of its components, can now be carriedout, for the various loads and load combinations applicable. Methods are given inthe text for the analysis of rectangular and circular bins, bunkers, hoppers and

silos, using conventional design practice or more recently developed methods.

1.5 Flow chart

A flow chart depicting the activities described above is given in Fig 1.1 for easyreference. The four main phases, viz (a) assessment of material characteristics, (b)functional design of bin, (c) determination of design loading, and (d) structural design,are clearly identified. The first two activities, may be undertaken by the client or by a


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1.4

specialist retained by him. The third and fourth activities would be the responsibility ofthe structural design engineer.

Fig.1.1 Flow chart of bin design activities

(a) MATERIAL FLOWTESTS

(b) FUNCTIONAL DESIGN OF BIN

MASS FLOW FUNNEL FLOW EXPANDED FLOW

(c) DESIGN LOADING

FILLINGCONDITIONS

EMPTYINGCONDITIONS

ECCENTRIC DISCHARGECONDITIONS

(d) STRUCTURALDESIGN OF BINS

CIRCULAR BINS Plating,stiffeners, ring beams,columns, hoppers, skirt

plates

RECTANGULAR BINSPlating, stiffeners,

hoppers, support beamsand columns


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1.5

1.6 Scope of text

The contents of this publication are intended to serve as guidelines for the design of thevarious types of containment vessel built in steel for the storage of bulk solids, includingbins, bunkers, hoppers and silos. The subject matter presented covers the large

majority of such vessels of small, medium and fairly large size and of conventionalshape, containing materials with known or predictable properties and flowcharacteristics. It will thus be of assistance in the typical engineering design office andwill enable the structural design of bins to be carried out efficiently and safely.

As implied in the title of the publication, and as stated above, the text concentrates onthe structuralaspects of bin design, on the assumption that the functional or operatingaspects have been dealt with by a specialist materials flow technologist.

It must be emphasized that the text does not cover all aspects of bin design, because ofthe wide range of variables that may apply in the case of non-standard material types,bin geometries, etc. Such variables would include eccentric filling and emptying points,

asymmetric bin geometry, stored materials having unusual properties, etc.

Where any of these unusual circumstances are present, reference should be made tothe publications or papers dealing with the particular topic, as quoted in the text.Alternatively advice may be obtained from specialist sources locally, as mentioned inChapter 8.

Finally, it must be stated that the structural design of the bin must be undertaken bypersons suitably experienced in this class of work, and especially in the interpretation ofthe theories and methods employed. The overall responsibility for the structural designmust be taken by a registered Professional Engineer.


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The Structural Design of Steel Bins and Silos ... August, 01

2.1

2 PROPERTIES OF STORED MATERIALS

2.1 Introduction

Materials stored in bins have their own material flow characteristics which have to

be taken into account in the design of the bins and silos. These flow

characteristics govern the flow pattern during discharge and the loads on the

vertical and hopper walls are governed by the flow pattern.

Not taking account of the flow characteristics can lead to improper

functioning of the bin, and assumptions of loading conditions which are not

concurrent with the flow pattern occurring in the bin during discharge can

lead to serious problems.

The recommended procedure is to test the material for its flow characteristics,

perform the functional or geometrical design, ie establish the desired flow pattern

in the bin during discharge conditions, and only then establish all design loads for

the structural design.

Chapter 4 gives all of the equations necessary to determine the forces on the

vertical walls and hopper walls for mass flow and funnel flow conditions, as well as

filling (or initial) and emptying (or flow) conditions.

2.2 Material flow tests

In order to establish the flow characteristics of a stored material, a sample of the

material is tested by means of specially designed test equipment. In most

countries of the world equipment designed by Jenike and Johanson is used, and

tests are performed in accordance with the procedures and recommendations

developed by them.

The test procedures used are outlined in the publications Storage and Flow ofSolids, by Dr Andrew W Jenike, Bulletin No 123 of the UTAH Engineering

Experiment Station of the University of Utah, Salt Lake City, Utah.


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2.2

The following information is obtained from the tests:

Bulk density, ;

Angle of internal friction, ;

Effective angle of internal friction, ;

Angle of friction between the solid and the wall or liner material, w.

All of the above values are obtained by test under varying pressures.

Additional results may be derived from the tests, but these are not relevant to this

guideline because they are mainly used for the functional or geometrical design of

a bin or silo. (some guidance is given in chapter 3)

A report, reflecting all minimum requirements for continuous gravity flow conditions

derived from the test results, can be obtained from bulk solids flow consultants.

This report is used for the final geometrical or functional design of the bin, and the

chosen geometrical design governs flow patterns and subsequent loading

conditions.

2.3 Tables of material properties

Although it is advisable to test materials in order to establish their flow

characteristics, tables reflecting typical flow properties of various materials with

different moisture contents are provided at the end of this chapter.

These tables have been developed from averaged-out results derived from

numerous tests, and it should be noted that some of these material characteristics

show large variances.

The data provided should only be used for the loading assessment of small bins

with capacities not exceeding about 100 t. In order to eliminate arching, piping and

other related flow problems, the functional or geometrical design, ie the design

required for proper functioning of the bin, should always be based on test results.

For storage facilities with capacities in excess of 100 t, it is highly recommended

that the stored material be tested for its flow characteristics prior to the design of

the geometrical arrangement or the determination of the loading on vertical and

hopper walls.


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2.3

2.4 Flow patterns

Bins may be classified into three different types, each type having its relevant

vertical and hopper wall loads.

2.4.1 Mass flow bins (Type 1)

Mass flow bins are bins in which all of the stored material is in motion during

discharge. These bins are especially recommended for cohesive materials,

materials which degrade in time, fine powders, and material where segregation

causes problems. The smooth, steep hopper wall allows the material to flow along

its face and this will give a first-in, first-out pattern for the material. When material

is charged into a bin it will segregate, with coarse material located at the wall face

and fines in the middle of the bin. When material is discharged from a bin, it will

remix in the hopper and segregation is minimised. Fine powders have sufficient

time to de-aerate and so flooding and flushing of material will be eliminated.

Pressures in a mass flow bins are relatively uniform across any horizontal cross

section of the hopper. The bins should not have any ledges, sudden hopper

transitions, inflowing valleys, and particular care should be taken in assuring flow

through the entire discharge opening.

2.4.2 Funnel flow bins or silos (Type 2)

A funnel flow bin is a bin in which part of the stored material is in motion during

discharge while the rest is stagnant. These bins are suitable for coarse, free

flowing, slightly cohesive, non-degrading materials and where segregation is not a

problem. The hoppers of these bins are not steep enough to allow material to flow

along their face. Material will flow through a central core and this will give a first-in,

last-out flow pattern for the material. Flow out of these bins can be erratic, and fine

powders can aerate and fluidize. If not properly designed the non-flowing solids

might consolidate and a pipe will form through which the material will flow while

the rest will remain stagnant.


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2.4

2.4.3 Expanded flow bins (Type 3)

An expanded flow bin is a combination of a mass flow and a funnel flow bin. Thelower part, eg the hopper, forms the mass flow section and the upper part, ie the

vertical walled section, represents the funnel flow section. These bins are used

especially for large storage capacities and where multiple outlets are required.

The flow patterns of the three types of bin are illustrated in Figure 2.1.

Type 1 Mass Flow Type 2 Funnel Flow Type 3 Expanded Flow


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3.1

3. ASSESSMENT OF FLOW CHARACTERISITCS AND FUNCTIONAL

DESIGN

3.1 Introduction

The design of the bin from a functional or operating point of view, based on the materialcharacteristics described in chapter 2, is usually undertaken by material flowtechnologists. This involves the selection of the required depth, width and height toaccommodate the specified volume of material, the slope of the hopper bottom, locationof the hopper hip, size and location of the outlets.

The engineer should never take responsibility for the functional design of the bin unlesshe/she is qualified to do so. It is better to pass this responsibility back to the client whowill employ a material flow technologist, or employ a material flow technologist himself

after discussion with the client.

3.2 Typical flow problems

There are a number of flow problems of which the designer should be aware. These aresummarised as follows:

No Flow condition

A stable arch forms over the discharge opening or a pipe (rathole) forms within the bulksolid above the hopper. This is caused by either the cohesive strength of the material orby the mechanical interlocking of the larger particles.

Erratic flow

Momentary arch formation/collapse within the bulk solid or partial/total collapse of arathole.

Flushing

Mainly a problem with powders which in funnel flow conditions aerate, fluidise and flushresulting in spillage, no control at the feeder and quality problems down the line due toirregular feed.

Inadequate capacity

Due to rathole formation or hangups in poorly designed hoppers a large proportion ofthe material remains dead in the silo, reducing the live capacity to a fraction of the totalvolume and requiring severe hammering, prodding or mechanical vibration to restoreflow of the material in the dead regions.


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3.2

Segregation

The different particle sizes within the bulk solid tend to sift through eachother causingaccumulation of fine particles in the centre of the storage facility and coarse particlesaround it. This problem causes serious effects on product quality and plant operationfor certain process applications

Degradation

Spoilage, caking, or oxidation may occur within bulk solids during handling and whenkept in a silo for too long a period. In first-in-last-out flow conditions through a silo(Funnel flow), some material may be trapped within the silo for extended periods andwill only come out when the silo is completely emptied.

Spontaneous combustion

Certain combustible bulk solids (coal, grains, sponge iron etc) subject to first-in-last-outflow conditions, where pockets of material are trapped for extended periods, may besubject to spontaneous combustion with disastrous consequences.

Vibrations

Vibrations caused by solids flow can lead to serious structural problems.

Structural failure

Drag forces on silo walls can exceed the buckling strength of the silo walls. This iscovered in more detail in chapter 5.

3.3 Variables affecting solids flowability

Before geometrical design of a silo commences, it is essential that the flowcharacteristics of the bulk solid have been established and the conditions the materialwill be subjected to inside the silo under operating conditions are adequately defined.

Variables affecting the flow of bulk solids include:

Consolidating Pressure

The magnitude of surcharge loads exerted by the material inside the silo has asignificant effect on the flowability of the material because it increases mechanicalinterlocking and cohesive arch formation.

Moisture Content

The flow of bulk solids is generally affected by the surface moisture content up to20% of the saturation point.

Temperature

Some bulk solids are affected by temperature or variation in temperature, such asthermoplastic powders or pellets.

Chemical composition

Chemical reaction of materials stored in a silo may change the flow characteristicsof the material


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3.3

Relative humidity

Hygroscopic materials are particularly sensitive to conditions of high relativehumidity with significant effect on flowability of the material, e.g. burnt lime,fertiliser, sugar etc.

Time under consolidation

Materials subject to consolidation pressure for extended periods of time maycompact with a resulting decrease in flowability.

Strain rate

Bulk solids with a viscous component need to be testes at various strain rates todetermine the effect on flow properties. ( Carnallite harvested from dead seabrines). The majority of bulk solids are however not strain rate sensitive.

Gradation

Particle size distribution and in particular fines content in many bulk solids canhave a significant effect on flowability of the material particularly if moisture ispresent

Effect of liner materials

Friction angles of the material against the liner change from one type of liner toanother.

3.4 Flow Testing

In addition to the testing of basic material properties such as bulk density, angle of wallfriction etc , specific tests can be done to determine the flowability of a material. Thesetests are beyond the scope of this guideline.

Facilities for flowability testing of bulk solids and the expertise for analysis andinterpretation of the results are available at Bulk Solids Flow S.A .


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3.4

3.5 Determination of Mass and Funnel flow

The following curves have been taken from the Institution of Engineers AustraliaGuidelines for the Assessment of Loads on Bulk Solids Containers

Please note that they are to be used as a guide and do not provide absolute values.

Figure 3.1 The boundaries between mass flow and funnel flow

(Coefficient of wall friction vs Half hopper angle)


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4.1

4 LOADING

4.1 Introduction

This chapter deals with the various live loads to which a typical bin structure is

subject. These may be summarised as follows:

Loads from stored materials:filling or initial loads;

emptying or flow loads.

Loads due to eccentric discharge conditions.

Loads from plant and equipment.

Loads from platforms and bin roofs.

Internal pressure suction

Wind loads.

Effects of solar radiation

Settlement of supports

4.2 Classification of bins Squat or tall

Regarding the loads imposed by the stored material, bins may be classified as

squat or tall, depending on their ratio of height to diameter or width. In the material

loading equations given later a distinction is made between the load intensities

applicable to squat bins and tall bins respectively. A squat bin is defined as one in

which the height from the hopper transition to the level of intersection of the stored

material with the wall of the bin is less than or equal to the diameter of a circular

bin, or the width of a square bin, or the lesser plan dimension of a rectangular bin.

A tall bin is one in which this height is greater than the above limit. This is

illustrated in Figure 4.1.

4.3 Loads from stored materials

The loadings applied by the stored material to the inner surfaces of a bin are

based on various theories, applicable to the initial and flow conditions and relating

to the walls of squat and tall bins and the hoppers, respectively. This is indicated

in the following sections.


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4.2

Fig 4.1: Bin classification Squat or tall

In all cases the pressures normal to the surfaces are obtained from the calculated

vertical pressures by use of a factor K, which is the ratio of horizontal to vertical

pressure. This factor is dependent on the effective angle of internal friction , and

since the latter has upper and lower limits for each type of stored material, K also

has maximum and minimum values.

The wall loads are furthermore dependent on the coefficient of friction between the

material and the vertical wall and hopper of the bin. This value also has upper and lower

limits for each type of stored material and type of bin wall or lining material.

4.3.1 Loads on vertical walls of squat bins

The method used for determining the loads during the filling or initial condition is based

on the Rankine theory. The maximum K and values derived from the lower limits for and .are used. The minimum K and values are used to obtain maximum loads on

the hopper walls and in cases where internal columns are used, to obtain extreme

maximum and minimum loads on these structural members.

For the emptying or flow condition the maximum K and values derived from the

upper limits for and . are used.

(b)Tall bin Hm D

Hm

D

Hm

D

(a) Squat bin Hm D (c) Plan Shapes


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4.3

4.3.2 Loads on vertical walls of tall bins

For the filling or initial condition, the Janssen theory is used for load assessment.

The maximum K and values, derived from the lower limits for and . , apply.

For the emptying or flow condition, the Jenike method, based on strain energy, isused. The wall loads depend on the flow pattern, viz mass or funnel flow (see

section 2.4). For this condition the maximum K and values, derived from the

upper limits for and . , apply.

4.3.3 Loads on walls of mass flow hoppers

Walker's theory is used in determining loads during the filling or initial stage.

Maximum K and values, derived from the lower limits for and . , apply.

For the emptying or flow condition, the Jenike method is used, with maximum values

of K and . derived from the upper limits for and . , apply. During flow an over-

pressure occurs on the hopper wall just below the transition, which has a peak value

at the transition level and extends downwards in a diminishing triangular pattern for a

distance of about 0,3 times the top width of the hopper (see section 3.6.2). This

localised pressure intensity is also referred to as 'switch pressure'.

4.3.4 Loads on walls of funnel flow hoppers

The methods used here, including the K and values, are the same as for massflow hoppers, except that no over-pressure occurs.

4.3.5 Examples of bin shapes and types of flow

Examples of various combinations of bin shape and type of flow are illustrated in

Figure 3.2. The bins are shown as either squat or tall, and the hopper wall slopes

are either steep (for mass flow of the contents during emptying) or not so steep

(for funnel flow). Also shown are bins having flat bottoms with hoppers having plan

shapes occupying less than the plan area of the bin (examples 4, 5 and 6); theseshapes apply mainly to concrete bins with slab bottoms, with either steel or

concrete hoppers.

In all cases the design of the bin and hopper walls would require consideration of

the initial or filling condition and the flow or emptying condition, the latter being

either the mass flow or the funnel flow condition.


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4.4

Shape Remarks

_ H D>1

_ The hopper is steep enough to allow

material to flow along its face

This is a MASS FLOW SILOHopper and vertical wall to be designed formass flow conditions.

_ H D1

_ Hopper top diameter smaller than the silodiameter

_ The hopper is steep enough to allowmaterial to flow along its face

This is an EXPANDED FLOW SILOThe hopper to be designed for mass flow,and vertical wall for funnel flow conditions.

_ H D>1

_ The hopper valley angles are steepenough to allow materil to flow along itsface.

_ Both hoppers are operational at the sametime

This is a MASS FLOW SILOHopper and vertical wall to be designed formass flow conditions.

Fig4.2a: Examples of bin shapes and types of flow

H

B

D

H

D

H

H

D


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4.5

B

H

Shape Remarks

_ H D>1

_ Hopper one is not steep enough to allowmaterial to flow along its face

_ Hopper two is steep enough to allow flowalong its face.

This is an EXPANDED FLOW BIN Vertical wall to be designed for funnel flowHopper 1 to be designed for funnel flowHopper 2 to be designed for mass flow.

- H B>1- Hopper valley angles are steep

enough to allow material to flow alongthe faces

This is an EXPANDED FLOW SILOThe hoppers to be designed for mass flow,and vertical wall to be funnel flow conditions.

- The hoppers are steep enough to allowmaterial to flow along their faces

- Both hoppers are operational at thesame time. (This is to prevent stable ratholing or piping in the stockpile.)

This is an EXPANDED FLOW SYSTEMThe hoppers shall be designed for massflow conditions.

- The hopper is steep enough to allowmaterial to flow along its face.

This is an EXPANDED FLOW SYSTEM

The hopper shall be designed for mass flowconditions.

Fig 4.2b: Examples of bin shapes and types of flow

D

H


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4.6

4.4 Equations for loading on walls Introduction

Equations for the determination of the forces acting on the inner surfaces ofthe vertical walls and hopper walls of bins are given in parts 3.5 and 3.6 of thischapter. The sequence of the clauses and sub-clauses is summarised in thefollowing table, for easy reference.

4.5 Loads on vertical walls

4.5.1 Initial loading Squat binsTall bins

4.5.2 Flow loading Squat bins4.5.3 Mass flow loading Tall bins4.5.4 Funnel flow loading Tall bins

4.6 Loads on hopper walls

4.6.1 Initial loading Squat binsTall bins

4.6.2 Mass flow loading Squat binsTall bins

4.6.3 Funnel flow loading Squat binsTall bins

The symbols used in the equations are defined in the list given at the beginning ofthe book.

The dimensional symbols are illustrated in the figure following the list.

Values of the hydraulic radius R for hoppers of different shapes and types are

given in Table 4.1.


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4.7

Table 4.1: Values of hydraulic radius R for hoppers (For surchargecalculations)

Silo Silo Silo Silo

Hopper Condition Type A Type B Type C Type D

Initial Di 4 Di 4 Da 4 ( )L xB

L Ba

a2 +

ConicalMass flow 4D4D ci =

Dc 4 Dc 4 Dc 4

Funnel flow 4D4D ci =

Dc 4 Dc 4 Dc 4

Initial Da 4 Da 4 Di 4 ( )L xB

L B

a

a2 +

Square

Mass flow D Da b4 4=

Db 24

Db 24

Db 24

Funnel flow D Da b4 4=

Db 2

4

Db 2

4

Db 2

4

Initial ( )L x B

L Ba

a2 + Da 4 Di 4 ( )

L xB

L Ba

a2 +

RectangularMass flow ( )

( )

L xB

L B

L x B

L B

a

a

a b

a b

2

2

+ =

+

0 252 2

, L Ba b+

0 252 2

, L Ba b+

0 252 2

, L Ba b+

Funnel flow ( )

( )

L xB

L B

L x B

L B

a

a

a b

a b

2

2

+ =

+

0 252 2, L Ba b+

0 25 2 2, L Ba b+

0 252 2

, L Ba b+

The characteristic hopper dimensions Db, Dc, Bb and L a are illustrated inFigure 4.3.

Note: For silo Type B, C and D material is flowing through a channel with adiameter equal to the top diameter of a conical hopper or the diagonal of square

or rectangular hopper.


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4.8

4.5 Loads on vertical walls

4.5.1 Initial loading

Squat bins

Ph = 1h K 2 (4.5.1)

where K2 is the greatere of:

a) 0,400

b)1

1

2

2

+

sin

sin

c)1

1

22

22

+

sin

sin

Sv = 2P h (4.5.2)


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4.9

hi

HaH

hi

Ha

TYPE A TYPE B TYPE C TYPE D

CONICAL

HOPP

ERS

SQUAREHOPPERS

RECTANG

ULAR

HOPPERS

Db Db Db D b

Bb

Bb Bb

La

La

La

La

Fig 4.3: Characteristic hopper dimensions for different bin shapes andhopper types

hi

Ha

hi

Ha

Dc Dc D c Dc

Bb


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4.10

Tall bins

Ph = ( )RhK2

1 22e1R

(4.5.3)

where R =Di

4

for circular bins

=Da4

for square bins

=( )a

a

BL

BL

+2for rectangular bins

Sv = 2P h (4.5.4)

4.5.2 Flow loading, squat bins

Ph = 1 1h K (4.5.5)

where K1 is the greater of:

a) 0,400

b)1sin1

sin1 1

+

c)

12

12

sin1

sin1

+

Sv = 1P h (4.5.6)

4.5.3 Mass flow loading, tall bins

For horizontal pressure Ph:

M = ( )12 (4.5.7)

where = 0,3 for axisymmetric flow

= 0,2 for plane flow

N =( )mM 12

1

2

(4.5.8)

where m = 0 for plane flow= 1 for axisymmetric flow

Kh =

1 (4.5.9)

x = ( )1

M RH h

m (4.5.10)


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4.11

So = ( )1 11 1

1 1

Ke K h R (4.5.11)

A =( ) ( )

( ) ( ) xmhxmhh

11

mxo

mh

e1MKe1MK

NKMeNS1MK

+

+ (4.5.12)

B = S N Ao (4.5.13)

Ph = ( ) !"

#$%

&

mMBA

R 1

1

1 1

(4.5.14)

In calculating the horizontal pressure Ph from the top of the vertical wall down

wards, a maximum value will be reached somewhat below mid point of the vertica

wall. This value shall be used for the remaining part of the vertical wall.

For frictional force U kN per linear m circumference:

M = ( )12 (4.5.7)

N =( )mM 12

1

2

(4.5.8)

Kh =

1 (4.5.9)

x =1 H

M Rm (4.5.15)

A =( )( ) ( )

( ) ( ) xmhxm

h

h

mxm

h

eMKeMK

NKMeNMK

+

+

11

1 1

1 (4.5.16)

B = A N (4.5.17)

U = !!"

#$$%

& ++

44

2

1 NeBeA

D

HD xxfor circular and square bins (4.5.17a)

=( ) ( )

( )!!"

#$$%

&++

+

+ NeBeA

BL

LBH

BL

LB xx

a

a

a

a

22

1 for rectangular bins (3.5.17b)

where D = Di = diameter of circular bin

= Da = width of square bin

Ba = width of rectangular binL = length of rectangular bin


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4.12

4.5.4 Funnel flow loading, tall bins

For horizontal pressure Ph:

=( )

tan

&

%$

#

"!1

12

D

H hfor circular and square bins (4.5.19a)

=( )

tan

&

%$

#

"!1

12

B

H h

a for rectangular bins (4.5.19b)

where D = Di= diameter of circular bin

= Da = width of square bin

= ( )( )11

1 cossin5,0 ww +

(4.5.20)

x =( )

!!"

#$$%

&+

+

1

sin

2sin

sin1

sin2

1

1

m (4.5.21)

y =( ){ }( ) ( ) ( )

( ) ( )

2 1

1

1 1

12

+ + + +

+

+

+

cos sin sin sin

sin sin

m m m

m (4.5.22)

where ( ) m+ 1 is in radians

q =( )( ) !

!"

#$$%

&

+1

sin1

sintan2

sin24

1

x

y (4.5.23)

Ka =( ) ( )

( )

24 1

16

1

1

tan sin tan

sin tan

+

+

q (4.5.24)

Ph = ( )K RK eaK h R

1

1 11 1 1 (4.5.25)

The minimum pressure at the outlet,( ) ( )!!

"

#$$%

&

= RHK

1

1h

11eiRx

P .

In calculating the horixontal pressures Ph from the top downwards, a maximum

value will be reached.

For the pressure calcultions, a straight line pressure diagram can be adopted from

the maximum achieved pressure downwards to the minimum pressure at theoutlet.

For frictional force U (kN per linear metre circumference) (As for mass flow loading

in 3.5.3):

M = ( )12 (4.5.7)


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4.13

N =( )m12

1M

2

(4.5.8)

Kh =

1 (4.5.9)

x =

1

H

M Rm (4.5.15)

A =

( )

( ) ( ) xmhxmhh

11

mxmh

e1MKe1MK

NKMeN1MK

+

+ (4.5.16)

B = A N (4.5.17)

U = !!"

#$$%

& ++

44

2

1 NBeAe

D

HD xxfor circular and square bins (4.5.18a)

=

( ) ( )

( )!!"

#$$

%

&++

+

+

NBeAe

BL2

BLH

BL2

BL xx

a

a

a

a1 for rectangular bins (4.5.18b)

where D = Di= diameter of circular bin

= Da= width of square bin

Ba= width of rectangular bin

L = length of rectangular bin

4.6 Loads on hopper walls

Note: In sections 3.6.1, 3.6.2 and 3.6.3 below, is the half hopper angle, ie the

inclination of the hopper wall to the vertical (for rectangular hoppers, =

inclination of wall under consideration, ie either side wall or end wall of hopper).

4.6.1 Initial loading

For normal pressure Pn:

K =+

=

tantan

tanofgreatertheK

2hmin or 0,400 (4.6.1)

n = ( ) !!"

#

$$%

&!"

#$%

& ++ 1tan

tan

11 2

min

hKm (4.6.2)

= half hopper angle

where m = 0 for plane flow

= 1 for axisymmetric flow


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4.14

Pn =!!!

"

#

$$$

%

&

!!"

#$$%

& !"

#$%

&

+

n

o

ooc

omin1

h

zh

1n

hh

1n

zhK (4.6.3)

where hc =1

1

Q

Ac

c

(4.6.4)

ho = based on section

Q

Ac

c

= 1 Ha for squat bins (4.6.5a)

= ( )RHK22

1 22e1K

R

for tall bins (4.6.5b)

For values of R for hoppers see Table 3.1

For shear force Sh:

Sh = h2P n (4.6.6)

4.6.2 Mass flow loading

For normal pressures nt and ntr:

= !!"

#$$%

&!!"

#$$%

& +

1

11

1sin

sinsin5,0

hh (4.6.7)

x = ( ) !"

#$%

&++

1

sin2sin

sin1sin2

1

1

m

(4.6.8)

y =( ){ }( ) ( ) ( )

( ) ( )

2 1

1

1 1

12

+ + + +

+

+

+

cos sin sin sin

sin sin

m m m

m (4.6.9)

where ( ) m+ 1 is in radians

ntr = Dx

y1

1

sin2

2cossin1

1

!!"

#$$%

& +

(4.6.10)

where D = Dc, Db, Bbor L a, as applicable; see Fig 3.3.

For rectangular hoppers, Bb is used when

considering the long sides of the hopper and

Lawhen considering the ends.

q = ( ) !!"

#$$%

&

++

!"

#$%

&

m1

1tantan

D

n2

tan

1

325,0 1h

1

trm

(4.6.11)


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4.15

nt =( ) ( )m1h

m

1c

c

trsin4,02tancossin

4Dq

A

Q3,3

n+

!!

"

#

$$

%

&!"

#$%

&

+ (4.6.12)

whereQ

A

c

c

= surcharge at top of hopper

= 1 Ha for squat bins (4.6.13a)

= ( )RHKeK

R111

11

1

for tall bins Type A (4.6.13b)

= ( )DandC,BTypes

binstallfore1

Ktan

R RHKtan

11

1 a11

(4.6.13c)

For values of R see Table 3.1

For distribution of pressures see figure at right.

Note: For bins of Types B, C and D the material flows through a channel withdiameter Dc. For square and rectangular bins it flows through a channel with adiameter equal to the diagonal of the top shape of the hopper.

For shear forces Sh:

Sh = h1 n tr (4.6.14)

Sh = h1 n t (4.6.15)

4.6.3 Funnel flow loading

For normal pressure Pn:

Ph = ( )111 hHK a+ for squat bins (4.6.16a)

= ( )( )RhHK aeR 11111

1 +

for tall bins Type A (4.6.16b)

= ( )( )RhHK aeR 111tan1

1 1tan

+

for tall bins Types B, C and D (4.6.16c)

Pn = !!

"

#$$

%

&+!!

"

#$$%

&+

cossin

4cos

sin1

2

1

2

hhD

r

KP (4.6.17)

where r = horizontal distance from centre of hopper to point on hopper wall

where pressure Pnapplies (see below),

and D = Dc, Db, Bbor L a, as applicable; see Figure 3.3

For rectangular hoppers, Bb is used when considering the long sides of the

hopper and Lawhen considering the ends.


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4.16

For values of R see Table 3.1.

For shear force Sh:

Sh = ( )!!"

#$$%

&+!!

"

#$$%

& 221

1

sincos2

cossin11

hhD

r

KP (4.6.18)

Switch Pressures

Switch pressures are only occurring where mass flow hopper meets with the

vertical wall of an overall man flow silo, so where a mass flow hopper is a part of

an expanded flow design, there are no switch pressures occurring.

Some judgement in the calculation and use of switch pressure should also be

taken in account as with very steep hoppers, the switch pressures tend to be very

high.

The judgement should be based on a vertical wall design approach, taking

account of the hopper loads with a modified switch pressure.


30/36


4.17

4.7 Eccentric discharge

When the discharge opening at the bottom of a circular bin is displaced laterally in

plan from the vertical centroidal axis of the bin, eccentric discharge conditions are

introduced. The material flows through an eccentric channel as shown in

Figure 4.4. The ratio of the horizontal pressure in the flow channel to the

horizontal pressure in the rest of the bin is in direct proportion to that of the radii of

the flow channel and the bin respectively, ie Po Ph= r R (Ref ...A W Jenike).

Using Jenike's moment equations, the moment per unit length due to eccentric

discharge is

M = K R2P (4.7.1)

where K =( )!

!

"

#$$

%

&

1

2

cos

sin1

tansin

w

(4.7.2)

R = radius of bin

= eccentricity angle

w1 = maximum angle of friction between material and wall

P = normal pressure

The value of recommended for use in the above equation is 21, although larger

values may occur.

Because of the large difference between the pressures Poand P, deformation of

the cylindrical shell in plan tends to occur, and strengthening of the shell becomes

necessary. For this reason, eccentric discharge outlets should be avoided if at all

possible in circular bins.


31/36


4.18

Fig4.4: Eccentric discharge of circular bins

4.8 Corrugated steel sheet bins

Circular bins or silos made from corrugated steel sheets (with the crests and

valleys of the corrugations running circumferentially) are usually mounted on flat

concrete bases, and so are subject to funnel flow during emptying.

The vertical friction forces at the walls are not generated by the sliding of the

contents against the walls, but by the sliding of the contents against the static

material trapped in the corrugations. The coefficient of friction is therefore not

but tan , where is the effective angle of internal friction of the material.

Thus in calculating lateral pressures Phand frictional forces S vand U for the vertical

walls under initial and emptying conditions, equations (4.5.2), (4.5.3), (4.5.4), (4.5.6),

(4.5.18) and (4.5.25) may be used, but with the effective angle of internal friction

substituted for w , and the tangent of this angle substituted for .


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4.19

4.9 Wind loading

The wind loading on bin structures can be assessed by reference to SABS 0160

(Ref ...), where force and pressure coefficients are given for structures of square,

rectangular and circular shape in plan, for various height to width ratios.

Since wind loading is usually only significant in tall bins, and as such bins are often

located in unprotected sites, it is recommended that the terrain be assumed as

category 2.

Wind loading on square or rectangular bins is usually not critical (but must of course

be allowed for), because the bin shape is inherently stable and stiff, and has properly

stiffened plate elements.

Circular bins, on the other hand, are very sensitive to wind loading because of the

varying pressure/suction distribution of the wind loading around the circumference,

and the lack of stiffness of the shell in resisting this loading. The required thickness of

plate in the upper strakes of a circular bin is often determined by the wind loading.

Wind buckling is characterised by the formation of one or more buckles on the

windward face of the shell. Wind also produces an overturning moment on a tall bin,

which induces a vertical compressive stress in the leeward face; this reached a

maximum at the base of the bin, where the shell needs to be checked against

buckling.

The distribution of pressure around a cylindrical structure is given in Table 14 ofSABS 0160, in terms of external pressure coefficients Cpe. Force coefficients, for

calculating the total wind force on the bin, are given in Table 1 of the code for circular

structures and in Figure 6 for square and rectangular structures.

The great majority of circular bins exposed to the weather are furnished with covers or

roofs, which serve the dual purpose of protecting the interior of the bin and of

maintaining the circular shape of the top of the shell. In the case of a bin exposed to

wind loading and having an open top, however, internal suction forces are generated

that aggravate the non-uniform loading pattern referred to above. Such bins are much

more subject deformation, and require special consideration to cater for this severe

form of loading.

What has been stated above applies to single or isolated bins. Where a row or

group of closely-spaced circular bins is located across the wind direction the wind

resistance per bin is much higher than if the bins were widely spaced because the

free flow of air around each bin is inhibited. Where a single row of bins is located


33/36


4.20

parallel to the wind direction the windward bin would probably be subject to wind

loadings as determined above, but the down-wind bin or bins would be largely

shielded by the windward one. It is not possible to suggest actual load factors for

these conditions because of the number of variables involved and advice should

be sough from wind loading specialists if wind loading is thought to be critical.

4.10 Loading from plant and equipment

Items such as pumps, blowers, filters, conveyor head pulleys and drive units, etc,

are often mounted on the roofs of storage bins. The loading imposed can usually

be catered for quite simply in the design of the roof support beams, but there are

certain aspects of conveyor loading that need special attention. If the conveyor

belt tensions at the head pulley are to be resisted by the bin (ie if the tensions are

not carried back into the conveyor stringers), then the bin roof structure will need

to be proportioned to resist this extra loading and the bin as a whole be checked

for the overturning effects.

Likewise if the conveyor is housed in a gantry and the head end of the gantry is

supported on the top of the bin, the bin structure should be designed to cater for

all of the conveyor loading components, including side wind on the gantry. A

situation to be specially allowed for is where the gantry (or series of gantries) is

anchored at its lower end and is not provided with a sliding bearing at its support

on the bin roof. Here, differential thermal expansion of the bin caused by solar

radiation on one side of the bin will result in horizontal displacement of the top,

which in turn will induce a compressive or tensile force in the gantry structure, with

a corresponding horizontal reaction at the top of the bin. Tall circular bins are

particularly sensitive to these effects.

A suitable means of avoiding the above situation is to have the gantry head end

supported on sliding bearings and for the conveyor belt tensions to be transmitted

back into the gantry; in this way only vertical loading will be applied to the bin.

4.11 Effects of solar radiation

All bins in exposed situations are subject to the effects of solar radiation as

described above, even where conveyor loading is not present. If it is necessary to

investigate this aspect, it is suggested that the temperature of the wall exposed to

the sun be taken as 40C above the ambient shade temperature.


34/36


4.21

4.12 Live loads on roofs and platforms

Where the top cover of a bin serves simply as a roof and not as a platform (ie

where it is non-trafficable), the live loading may be taken as specified for roofs in

SABS 0160, Clause 5.4.3.3, ie a distributed load varying from 0,3 kPa to 0,5 kPa

depending on the loaded area, or a point load of 0,9 kN, whichever is more

severe. For trafficable roofs the loading may be taken as given in Clause 5.4.3.2,

ie a distributed load of 2,0 kPa or a point load of 2,0 kN. If material spillage or

excessive dust collection is a possibility it should be allowed for in addition to the

above loading.

The live loading on access platforms and stairways in industrial structures is not

specified in the code, but it would be good practice to allow for a distributed load

of 3,0 kPa or a point load of 3,0 kN.

4.13 Internal pressure suction

In the case of bins having pneumatic discharge systems, positive internal

pressures are generated by the blowers, but as safety vents are usually provided

the full blower pressure is not likely to be realised. The maximum pressure exerted

should be obtained from the supplier of the system and the pressure acting on

localised areas of the bin wall be taken as say 80% of the specified pressure.

Rapid discharge of bulk solids having low permeability to gases can cause

negative air pressure in a bin. Circular bins, and especially their upper parts

(including the roof), are particularly sensitive to this effect. Safety vents may be

installed to limit the negative pressure, but in any case the pressure required to

open the vent should be ascertained.

4.14 Settlement of supports

Most bin structures, especially cylindrical ones, are very stiff in the vertical

direction because of their great depth and fully-plated construction. Consequently,

settlement of one support point whether a beam, a column or a foundation may induce high stresses in the shell structure and also cause a re-distribution of

load on the remaining supports. In the extreme case of the complete failure of one

column say due to vehicle impact under a bin supported on four columns,

the load on each of the two remaining load-bearing columns is doubled.


35/36


4.22

Even relatively small settlements of foundations can cause significant

redistribution of load at the remaining supports, and it would therefore be prudent

to introduce an overload factor for these.

4.15 Load combinations

When designing bin structures by the limit-state method, the partial load and load

combination factors as laid down in SABS 0160, Table 2, should be used, but

certain variations as mentioned below may be advisable.

Since the bulk density of the stored material is usually well-defined, and in any

case its upper limit value is used in design, a partial load factor i of 1,3, as

specified for stored fluids, would seem reasonable for this material when at rest,

eg in the design of the support. But since the maximum material loading may well

be present when other live loads are active, the load combination factor ishould

be taken as 1,0. Thus where the effects of initial material loading and wind

loading, for example, are cumulative, the partial load and load combination factors

would be taken as 1,3 and 1,0 respectively, for both the material load and the wind

load. For the emptying or flow condition, however, a i factor of 1,6 on the

material loading would be advisable. On the other hand, where the effects are not

cumulative, the material load or the wind load combination factor would be taken

as zero, as applicable.

Suggested values of partial load and load combination factors for the varioustypes of load are given in Table 4.2.


36/36


4.23

Table 4.2: Partial load and load combination factors, ultimate limit state.

Type of loadPartialload

factor i

Loadcombination

factor i

Loads from selfweight of structure

Maximum, acting in isolation 1,5

Maximum, acting in combination 1,2 1,0

Minimum 0,9 1,0

Loads from stored material:

Gravity (material at rest) 1,3 1,0

Initial (filling) condition 1,6 1,0

Flow (emptying) condition 1,6 1,0

Dead loads from plant and equipment 1,5 1,0

Loads from conveyors:

Dead load 1,5 1,0

Live load 1,6 1,

Loads from internal external pressure in bin 1,6 1,0

Wind load 1,3 0

Loads from vehicle impact 1,3 0

Loads from differential settlement of supports1,3 0

Structural Design of Steel Bins and Silos

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