39513441 structural-design-of-steel-bins-and-silos

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 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.
In the Southern African region, with its vast raw material resources, the storage of bulk
solids 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 vessels
or 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 specialised
skills provided by the engineering profession. Unfortunately there is a lack of
comprehensive literature, covering all aspects of bin design, available to the practising
engineer. It is the purpose of this publication to present the necessary guidelines to
enable 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 simple
assumptions 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 the
present text, advantage has been taken of a large amount of research work that has
been carried out during recent decades in various countries, especially the United
States and Australia. It is hoped that the application of the better understanding of flow
loads and the analysis of their effects will lead to the design of safer bins and the
avoidance 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 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
– 1.2 –
bottom.
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.
1.4 Design procedure
The full design procedure for a typical steel bin would comprise a series of activities as
described 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 its
properties as affecting both the functional and the structural design of the bin. The
properties 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 stored
materials 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 the
properties should be determined from laboratory tests or by reference to
specialist materials handling technologists.

– 1.3 –
b) Assessment of flow characteristics
Based on the material properties mentioned above, it is necessary to determine
the 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 being
emptied, 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 of
the bin and the flow characteristics of the material. Specialists should be
consulted 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 flow
technologists. This will involve the selection of the required depth, width and height
to 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 in
chapter 3.
d) Determination of pressures and forces
The normal and frictional forces exerted by the material on the inner surfaces or
walls of the bin are determined, considering the dynamic effects during filling, the
static effects during storage and the dynamic effects during emptying, plus effects
due to temperature, expansion of contents, etc, when present.
The magnitude and distribution of the wall forces will depend on the applicable flow
mode, the effects of switch pressure in bins with hopper bottoms, and the effects
of eccentric discharge where applicable. Pressure diagrams showing the
magnitude and distribution of pressure and frictional force are prepared for each
inner surface of the bin for the filling and emptying phases, for use in the structural
design of the bin.
e) Structural design
The structural design of the bin, including all of its components, can now be carried
out, for the various loads and load combinations applicable. Methods are given in
the 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 easy
reference. 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

specialist retained by him. The third and fourth activities would be the responsibility of
the structural design engineer.
(a) MATERIAL FLOW
TESTS
(b) FUNCTIONAL DESIGN OF BIN
MASS FLOW FUNNEL FLOW EXPANDED FLOW
(c) DESIGN LOADING
Fig.1.1 – Flow chart of bin design activities
– 1.4 –
FILLING
CONDITIONS
EMPTYING
CONDITIONS
ECCENTRIC DISCHARGE
CONDITIONS
(d) STRUCTURAL
DESIGN OF BINS
CIRCULAR BINS Plating,
stiffeners, ring beams,
columns, hoppers, skirt
plates
RECTANGULAR BINS
Plating, stiffeners,
hoppers, support beams
and columns

1.6 Scope of text
The contents of this publication are intended to serve as guidelines for the design of the
various types of containment vessel built in steel for the storage of bulk solids, including
bins, bunkers, hoppers and silos. The subject matter presented covers the large
majority of such vessels of small, medium and fairly large size and of conventional
shape, containing materials with known or predictable properties and flow
characteristics. It will thus be of assistance in the typical engineering design office and
will 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 on
the structural aspects of bin design, on the assumption that the functional or operating
aspects 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 of
the 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 to
the publications or papers dealing with the particular topic, as quoted in the text.
Alternatively advice may be obtained from specialist sources locally, as mentioned in
Chapter 8.
Finally, it must be stated that the structural design of the bin must be undertaken by
persons suitably experienced in this class of work, and especially in the interpretation of
the theories and methods employed. The overall responsibility for the structural design
must be taken by a registered Professional Engineer.
– 1.5 –

The Structural Design of Steel Bins and Silos ... August, 01
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 of
Solids, by Dr Andrew W Jenike, Bulletin No 123 of the UTAH Engineering
Experiment Station of the University of Utah, Salt Lake City, Utah.
— 2.1 —

The following information is obtained from the tests:
• Bulk density, γ;
• Angle of internal friction, φ;
• Effective angle of internal friction, δ;
• Angle of friction between the solid and the wall or liner material, φw.
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.
— 2.2 —

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.
— 2.3 —

2.4.3 Expanded flow bins (Type 3)
An expanded flow bin is a combination of a mass flow and a funnel flow bin. The
lower 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
— 2.4 —

3. ASSESSMENT OF FLOW CHARACTERISITCS AND FUNCTIONAL
– 3.1 –
DESIGN
3.1 Introduction
The design of the bin from a functional or operating point of view, based on the material
characteristics described in chapter 2, is usually undertaken by material flow
technologists. This involves the selection of the required depth, width and height to
accommodate the specified volume of material, the slope of the hopper bottom, location
of the hopper hip, size and location of the outlets.
The engineer should never take responsibility for the functional design of the bin unless
he/she is qualified to do so. It is better to pass this responsibility back to the client who
will 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 are
summarised as follows:
No Flow condition
A stable arch forms over the discharge opening or a pipe (rathole) forms within the bulk
solid above the hopper. This is caused by either the cohesive strength of the material or
by the mechanical interlocking of the larger particles.
Erratic flow
Momentary arch formation/collapse within the bulk solid or partial/total collapse of a
rathole.
Flushing
Mainly a problem with powders which in funnel flow conditions aerate, fluidise and flush
resulting in spillage, no control at the feeder and quality problems down the line due to
irregular feed.
Inadequate capacity
Due to rathole formation or hangups in poorly designed hoppers a large proportion of
the material remains dead in the silo, reducing the live capacity to a fraction of the total
volume and requiring severe hammering, prodding or mechanical vibration to restore
flow of the material in the dead regions.

Segregation
The different particle sizes within the bulk solid tend to sift through eachother causing
accumulation of fine particles in the centre of the storage facility and coarse particles
around it. This problem causes serious effects on product quality and plant operation
for certain process applications
Degradation
Spoilage, caking, or oxidation may occur within bulk solids during handling and when
kept 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 and
will 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-out
flow conditions, where pockets of material are trapped for extended periods, may be
subject 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 is
covered in more detail in chapter 5.
3.3 Variables affecting solids flowability
Before geometrical design of a silo commences, it is essential that the flow
characteristics of the bulk solid have been established and the conditions the material
will 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 a
significant effect on the flowability of the material because it increases mechanical
interlocking and cohesive arch formation.
Moisture Content
The flow of bulk solids is generally affected by the surface moisture content up to
20% of the saturation point.
Temperature
Some bulk solids are affected by temperature or variation in temperature, such as
thermoplastic powders or pellets.
Chemical composition
Chemical reaction of materials stored in a silo may change the flow characteristics
of the material
– 3.2 –

Relative humidity
Hygroscopic materials are particularly sensitive to conditions of high relative
humidity 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 may
compact with a resulting decrease in flowability.
Strain rate
Bulk solids with a viscous component need to be testes at various strain rates to
determine the effect on flow properties. ( Carnallite harvested from dead sea
brines). The majority of bulk solids are however not strain rate sensitive.
Gradation
Particle size distribution and in particular fines content in many bulk solids can
have a significant effect on flowability of the material particularly if moisture is
present
Effect of liner materials
Friction angles of the material against the liner change from one type of liner to
another.
– 3.3 –
3.4 Flow Testing
In addition to the testing of basic material properties such as bulk density, angle of wall
friction etc , specific tests can be done to determine the flowability of a material. These
tests are beyond the scope of this guideline.
Facilities for flowability testing of bulk solids and the expertise for analysis and
interpretation of the results are available at Bulk Solids Flow S.A .

3.5 Determination of Mass and Funnel flow
The following curves have been taken from the Institution of Engineers Australia
“Guidelines 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)
– 3.4 –

— 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.

(b)Tall bin Hm ≤ D
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 δ, 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 μ 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 μ values derived from the lower limits for δ
and .φ are used. The minimum K and μ 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 μvalues derived from the
upper limits for δ and .φ are used.
— 4.2 —
Hm
D
Hm
D
(a) Squat bin Hm ≤ D (c) Plan Shapes

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 μ values, derived from the lower limits for δ and .φ’, apply.
For the emptying or flow condition, the Jenike method, based on strain energy, is
used. The wall loads depend on the flow pattern, viz mass or funnel flow (see
section 2.4). For this condition the maximum K and μ values, derived from the
upper limits for δ and .φ, 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 μ values, derived from the lower limits for δ and .φ’, apply.
For the emptying or flow condition, the Jenike method is used, with maximum values
of K and μ. derived from the upper limits for δ and .φ’, 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 μ values, are the same as for mass
flow 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); these
shapes 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.
— 4.3 —

Shape Remarks
_ H D >1
_ The hopper is steep enough to allow
material to flow along its face
This is a MASS FLOW SILO
Hopper and vertical wall to be designed for
mass flow conditions.
_ H D <1
_ The hopper is not steep enough to allow
This is a FUNNEL FLOW BIN
Funnel flow conditions.
_ H D >1
_ Hopper top diameter smaller than the silo
diameter
_ The hopper is steep enough to allow
This is an EXPANDED FLOW SILO
The hopper to be designed for mass flow,
and vertical wall for funnel flow conditions.
_ H D >1
_ The hopper valley angles are steep
enough to allow materil to flow along its
face.
_ Both hoppers are operational at the same
time
This is a MASS FLOW SILO
mass flow conditions.
Fig4.2a: Examples of bin shapes and types of flow
— 4.4 —
B H D H D H D H

Shape Remarks
— 4.5 —
D H
B H
_ H D >1
_ Hopper one is not steep enough to allow
_ Hopper two is steep enough to allow flow
along its face.
This is an EXPANDED FLOW BIN
Vertical wall to be designed for funnel flow
Hopper 1 to be designed for funnel flow
Hopper 2 to be designed for mass flow.
- H B >1
- Hopper valley angles are steep
enough to allow material to flow along
the faces
This is an EXPANDED FLOW SILO
The hoppers to be designed for mass flow,
and vertical wall to be funnel flow conditions.
- The hoppers are steep enough to allow
material to flow along their faces
- Both hoppers are operational at the
same time. (This is to prevent stable rat
holing or piping in the stockpile.)
This is an EXPANDED FLOW SYSTEM
The hoppers shall be designed for mass
flow conditions.
- The hopper is steep enough to allow
material to flow along its face.
This is an EXPANDED FLOW SYSTEM
The hopper shall be designed for mass flow
conditions.
Fig 4.2b: Examples of bin shapes and types of flow

4.4 Equations for loading on walls – Introduction
Equations for the determination of the forces acting on the inner surfaces of
the vertical walls and hopper walls of bins are given in parts 3.5 and 3.6 of this
chapter. The sequence of the clauses and sub-clauses is summarised in the
following table, for easy reference.
4.5 Loads on vertical walls
4.5.1 Initial loading Squat bins
— 4.6 —
Tall bins
4.5.2 Flow loading Squat bins
4.5.3 Mass flow loading Tall bins
4.5.4 Funnel flow loading Tall bins
4.6 Loads on hopper walls
4.6.1 Initial loading Squat bins
Tall bins
4.6.2 Mass flow loading Squat bins
Tall bins
4.6.3 Funnel flow loading Squat bins
Tall bins
The symbols used in the equations are defined in the list given at the beginning of
the 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.

Table 4.1: Values of hydraulic radius R for hoppers (For surcharge
calculations)
Silo Silo Silo Silo
Hopper Condition Type A Type B Type C Type D
Initial Di 4 Di 4 Da 4 ( )
— 4.7 —
L xB
L B
a
2 + a
Conical Mass flow D 4 D 4 i = c Dc 4 Dc 4 Dc 4
Funnel flow Di 4 = Dc 4 Dc 4 Dc 4 Dc 4
L xB
L B
a
Initial Da 4 Da 4 Di 4 2 ( + a
)
Square
Mass flow Da 4 = Db 4 Db 2
4
Db 2
4
Db 2
4
Funnel flow Da 4 = Db 4 Db 2
4
Db 2
4
Db 2
4
L xB
L B
a
Initial ( )
L xB
L B
a
2 + a Da 4 Di 4 2 ( + a
)
L xB
L B
L xB
a
a
a b
a b
Rectangular Mass flow ( +
)
( L B
)
2
2
=
+
0,25 La2 +Bb2 0,25 La2 +Bb2 0,25 La2 +Bb2
L xB
L B
L xB
a
a
a b
a b
Funnel flow ( +
)
( L B
)
2
2
=
+
0,25 La2 +Bb2 0,25 La2 +Bb2 0,25 La2 +Bb2
The characteristic hopper dimensions Db, Dc, Bb and La are illustrated in
Figure 4.3.
Note: For silo Type B, C and D material is flowing through a channel with a
diameter equal to the top diameter of a conical hopper or the diagonal of square
or rectangular hopper.

— 4.8 —
4.5 Loads on vertical walls
4.5.1 Initial loading
Squat bins
Ph = γ1 h K2 (4.5.1)
where K2 is the greatere of:
a) 0,400
b) 1
1
2
2
−
+
sin
sin
δ
δ
c) 1
1
2
2
2
2
−
+
sin
sin
δ
δ
Sv = μ2 Ph (4.5.2)

hi Ha
— 4.9 —
H
hi Ha
hi Ha
TYPE A TYPE B TYPE C TYPE D
RECTANGULAR HOPPERS SQUARE HOPPERS CONICAL HOPPERS
Db Db Db Db
Bb
Bb Bb
La
La
La
La
Fig 4.3: Characteristic hopper dimensions for different bin shapes and
hopper types
hi Ha
Dc Dc Dc Dc
Bb

γ (4.5.3)
m H − h (4.5.10)
— 4.10 —
Tall bins
Ph = ( K h R )
1R 1− e−μ2 2
μ
2
where R = Di
4
for circular bins
= Da
4
for square bins
LB
2 +
= a
( L B
)a
for rectangular bins
Sv = μ2 Ph (4.5.4)
4.5.2 Flow loading, squat bins
Ph = γ1 hK1 (4.5.5)
where K1 is the greater of:
a) 0,400
b)
1 − sin δ
1
+ δ
1 sin 1
c)
1 − sin
δ
+ δ
1
2
1
2
1 sin
Sv = μ1 Ph (4.5.6)
4.5.3 Mass flow loading, tall bins
For horizontal pressure Ph:
M = 2(1−ν ) (4.5.7)
where ν = 0,3 for axisymmetric flow
= 0,2 for plane flow
N = ( m) M 2 1−
1
2
μ
ν (4.5.8)
where m = 0 for plane flow
= 1 for axisymmetric flow
Kh = ν
1− ν
(4.5.9)
x = μ1 ( )
M R

− −
K M 1 S N e M K N
− − − + μ − (4.5.12)
γ (4.5.14)
1 1
K M N e M K N
1 μ
− − − + −
γ D H x x for circular and square bins (4.5.17a)
LB x x
1 γ for rectangular bins (3.5.17b)
— 4.11 —
So = 1 (1 )
1 1
1 1
μ
μ
K
− e− K h R (4.5.11)
A = ( )( ) ( )
( m ) x
( m ) x
h
h
h
1
1
x m
o
m
h
K M 1 e K M 1 e
−
+ − −

B = So −N− A (4.5.13)
Ph = ( ) 
R A B 1
1
1 1 μ
μ
 − − M m

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 = 2(1−ν ) (4.5.7)
N = ( m) M 2 1−
1
2
μ
ν (4.5.8)
Kh = ν
1− ν
(4.5.9)
x = μ1H
Mm R (4.5.15)
A = ( )( ) ( )
( m ) x
( m ) x
h
h
h
m x m
h
K M e K M e
−
− −
+ − −
1 1
(4.5.16)

B = – A – N (4.5.17)
 U = −
Ae + Be + N

1   
−
2
D
4 4


H LB
= ( ) ( )( ) 
 
+ +
+
−
+
Ae Be− N
L B
L B
a
a
a
a
2 2
where D = Di = diameter of circular bin
= Da = width of square bin
Ba
= width of rectangular bin
L = length of rectangular bin

4.5.4 Funnel flow loading, tall bins
For horizontal pressure Ph:
1 0,5 sin cos w w φ ′ + − φ ′ (4.5.20)
m − m +
m
cos sin sin sin
− + + + ⋅ +
β θ β θ θ β β θ
+
sin sin
m (4.5.22)

y (4.5.23)
tan sin tan
θ π δ θ

h i e 1 1 P x R .
— 4.12 —
D
H h
θ = tan−
( −
) 
 

 
1
2 1
for circular and square bins (4.5.19a)
B
H h
= tan−
( −
) 
 

 
1
2 1
a for rectangular bins (4.5.19b)
β = ( 1
( )) 1
x = ( )

 

 
+ +
m δ
2 sin
−
1
β θ
sin 2
sin
1 sin
1
1
θ
δ
(4.5.21)
y =
( { ( )}) ( ) ( )
( ) ( )
2 1
1
1 1
1
2
− +
δ β θ
where (β +θ )1−m is in radians
( )
q = θ δ
( )  

 
−
−
+ 1
1 sin
2 tan sin
24sin
1
θ
θ
π
x
( 24 + )( 1
−
)
Ka = ( )
16
1
sin tan
δ θ
1
+
q
(4.5.24)
Ph = K R ( )
γ K h R
μ
1 μ
1 1
a e
K
1− − 1 1 (4.5.25)
( 
)( ) 
The minimum pressure at the outlet,  
−
μ
γ
= μ K H R
1
1
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 the
outlet.
For frictional force U (kN per linear metre circumference) (As for mass flow loading
in 3.5.3):
M = 2(1−ν ) (4.5.7)

K M 1 N e M K N
− − − + μ − (4.5.16)
γ D H x x for circular and square bins (4.5.18a)
LB x x
H LB
γ Ae Be− N
1 a for rectangular bins (4.5.18b)
= width of rectangular bin
L = length of rectangular bin
K the greater of tan
= α
min or 0,400 (4.6.1)
m K (4.6.2)
— 4.13 —
2
N = 2(1 m)
μ −
1M
ν (4.5.8)
Kh = ν
1− ν
(4.5.9)
x = μ1H
Mm R (4.5.15)
A = ( )( ) ( )
( m ) x
( m ) x
h
h
h
1
1
m x m
h
K M 1e K M 1e
−
− −
+ − −

B = – A – N (4.5.17)
 U = −
Ae + Be + N

1   
−
2
D
4 4


 
= )( ) ( )(  
+ +
+
−
+
2 L B
2 L B
a
a
a
Ba
4.6 Loads on hopper walls
Note: In sections 3.6.1, 3.6.2 and 3.6.3 below, α is the half hopper angle, ie the
inclination of the hopper wall to the vertical (for rectangular hoppers, α =
inclination of wall under consideration, ie either side wall or end wall of hopper).
4.6.1 Initial loading
For normal pressure Pn:
K =
φ′ + α
tan tan
h2

  

 ′
φh
1 1 tan 2
n = ( + ) + − 1

 

min α
tan
α = half hopper angle
where m = 0 for plane flow
= 1 for axisymmetric flow

 −
K h z 
h z
(4.6.3)
γ for tall bins (4.6.5b)
φ φ h
h (4.6.7)
m − m +
m
cos sin sin sin
− + + + +
β α β α α β β α
+
sin sin
m (4.6.9)
tan tan 1
D
0,25 h1
— 4.14 —
Pn =

  


γ −
  


 
 



h h
−
+ −
−
n
o
o o
c
o
1 min n 1
n 1
h
where hc = 1
γ1
Q
A
c
c
(4.6.4)
= based on section
ho
Q
A
c
c
= γ1Ha for squat bins (4.6.5a)
= R ( − −μ
K H R)
1 1 e 2 2
K
2 2
μ
For values of R for hoppers see Table 3.1
For shear force Sh:
Sh = μh2 Pn (4.6.6)
4.6.2 Mass flow loading
For normal pressures nt and ntr:



 ′
0,5 sin sin
β =  

 

 
 
′ + −
1 1
1
1 sin
δ
 ( x = β + α
) 
+


m δ
2 sin
−
1
sin 2
sin
1 sin
1
1
α
δ
(4.6.8)
y =
( { ( )}) ( ) ( )
( ) ( )
2 1
1
1 1
1
2
− +
δ β α
where (β +α )1−m is in radians
ntr = D
x
 +
−
y
1

δ β
1 sin cos2
1
1
2sin
γ
α
 
 
(4.6.10)

 where D = Dc, Db, Bb or La, as applicable; see Fig 3.3.
For rectangular hoppers, Bb is used when
considering the long sides of the hopper and
La when considering the ends.


q = ( )  
+
α + φ′ −
α γ


 π

1 m
2n
1
tan
3
1
tr
m
(4.6.11)


3,3 Q
c
q D 4
A

 

 




π

− γ
+ (4.6.12)
nt = ( )( )m
γ − − for tall bins Type A (4.6.13b)
R tan K H R
1 1
γ
1 − − φ1 1 a
φ
γ for tall bins Type A (4.6.16b)
γ for tall bins Types B, C and D (4.6.16c)


sin α +cos α 4 μ sinα cosα
P (4.6.17)
— 4.15 —
h1
m
1
c
tr
sin cos tan 2 0,4sin
n
α+ α φ′ − α
where Q
A
c
c
= surcharge at top of hopper
= γ1Ha for squat bins (4.6.13a)
= ( e K H R )
R 1 1 1
1 1
1 μ
μ
K
( for tall bins
= 1 e
) Types B, C and D
tan K
(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 with
diameter Dc. For square and rectangular bins it flows through a channel with a
diameter equal to the diagonal of the top shape of the hopper.
For shear forces Sh:
Sh = μh1 ntr (4.6.14)
Sh = μh1 nt (4.6.15)
4.6.3 Funnel flow loading
For normal pressure Pn:
Ph = ( )1 1 1 K H h a γ + for squat bins (4.6.16a)
= R( e K (Ha h ) R ) 1 1 1 1
1 − −μ +
μ
1
= R ( e K (Ha h ) R ) tan 1 1 1
1 1
tan
1
− − φ +
φ


2
Pn =  

 
h D h

+  
 
1
2
1
r
K
where r = horizontal distance from centre of hopper to point on hopper wall
where pressure Pn applies (see below),
and D = Dc, Db, Bb or La, as applicable; see Figure 3.3
For rectangular hoppers, Bb is used when considering the long sides of the
hopper and La when considering the ends.

1 1 sin cos 2 cos sin
P (4.6.18)
— 4.16 —
For values of R see Table 3.1.
For shear force Sh:




Sh = ( ) 

 
h D h

− +  
 
− α α μ 2α 2α
1
1
r
K
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.

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 R2 P (4.7.1)


θ
θ θ
sin tan 1 sin
where K = ( ) 
— 4.17 —
 
′ −
−
φ θ
π
1
2
cos
w
(4.7.2)
R = radius of bin
θ = eccentricity angle
θ′w1 = maximum angle of friction between material and wall
P = normal pressure
The value of θ recommended for use in the above equation is 21º, although larger
values may occur.
Because of the large difference between the pressures Po and 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.

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 μ
but tan δ, where δ is the effective angle of internal friction of the material.
Thus in calculating lateral pressures Ph and frictional forces Sv and 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 δ
substituted for φ′w, and the tangent of this angle substituted for μ.
— 4.18 —

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 of
SABS 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
— 4.19 —

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 40ºC above the ambient shade temperature.
— 4.20 —

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.
— 4.21 —

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 γi 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 Ψi should
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 Ψi 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 various
types of load are given in Table 4.2.
— 4.22 —

Table 4.2: Partial load and load combination factors, ultimate limit state.
— 4.23 —
Type of load
Partial
load
factor γi
Load
combination
factor Ψi
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 supports 1,3 0

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