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Silo Loads
Guest Article by David Stuart-Dick, Powder Engineering Systems
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There are unique relationships between the flow pattern of
a product in a silo, the stresses in the flowing product and the loads the product applies
to the silo walls. The contents of a silo, like any bulk granular material with internal
friction, have ‘active’ and ‘passive’ states of stress. These active
and passive states develop in the bulk solid as it flows in a flow channel.
Pressure Fields
When flowing in a parallel-sided channel with no
convergence the solid generally moves as a plug. It behaves elastically and there is
little if any relative movement between the particles. The pressure on the solid increases
with depth below the surface. The major principal stress in the solid is vertical and the
minor principal stress horizontal. This is called an active pressure field.
In a converging hopper section where the cross section of
the flow channel is reducing the solid must deform. It is forced to contract horizontally
and expand vertically. The major principal stress aligns horizontally and the minor
principal stress aligns vertically. This is called a passive pressure field.
The vertical stresses are highest at the bottom of the
parallel walled section. At the top of the hopper section the high stresses are
transferred to the walls since the solid starts contracting horizontally and the major
principal stress is horizontal. Further down in the hopper the vertical stresses are low
since most of the weight of the solid is supported in the upper part of the hopper. In
fact, the pressure distribution in the lower part of the hopper is independent of head of
solid in the silo. This has major implications on how the silo operates.
In a mass flow silo all the product in the silo is in
motion whenever any is withdrawn. Product slides on the hopper wall and the convergence is
defined. In funnel flow the product forms its own flow channel within stagnant material
and there is often no convergence. Therefore, while the pressures at the outlet of a mass
flow hopper are low and independent of head, the pressure at the outlet of a funnel flow
silo are not independent of head and may be high.
Cohesive solids can develop strength and the strength is a
function of compacting pressure. In a mass flow hopper the outlet size can be designed
based on known, low outlet pressures. The loads on mass flow feeders, density of
discharged product, particle attrition, wear on feeder parts etc. are all low and
constant.
Stresses
There is a fixed relationship (K) between the major and
minor principal stresses in a flowing solid. Equilibrium of the mass allows us to
calculate the pressures applied to the walls of a silo. In general the relationship K is
taken as a constant - somewhat dependent on the properties of the product but strongly
dependent on the flow conditions. For example, during initial fill conditions K is usually
taken as 1 for design purposes. For flow conditions K is between 0.2 and 0.6 in the
parallel-sided cylindrical section of a silo. In the converging hopper section K may be as
low as 1.5 or as high as 10. High values apply for relatively incompressible solids in
steep hoppers. In a diverging section K is usually taken as 0.2.
Many codes of practice for silo design were formulated
before flow patterns were well understood. Consequently, the methods given in codes are
usually based on the elementary theory of Janssen with factors applied to account for
different conditions. A common approach of modern designers is to calculate loads as
accurately as possible but check that the design is adequate for all the major codes of
practice. An accurate calculation will often predict higher loads than the codes.
Dynamic, Fluidized and Eccentric Loads
Other loads that must be considered are dynamic loads,
loads due to fluidized product and loads due to eccentric flow. Under normal conditions
dynamic loads will not occur in mass flow silos. Dynamic loads in funnel flow may be due
to collapsing ratholes, stuck product releasing from one side of the silo or collapsing
bridges. Each of these phenomena has caused numerous silo failures.
Fluidization can only occur when handling a fine product
(particle sizes generally less than 200 micron). However, at least one silo has failed due
to fluidization with larger particles. This happened when a very moist compressible
product was squeezed under the weight of product until all the void spaces were filled
with moisture. The product lost its angle of internal friction and became a liquid with
suspended solids. The loads were higher than the hopper could support and it let go
spilling the contents of the silo onto the ground.
Normally a fine powder will adopt the properties of a fluid
when it is handled at too high a rate. The powder does not have enough time to de-aerate
and when it reaches the outlet, if the pressure is high enough it will fluidize. Sometimes
aerating nozzles, designed to encourage flow will provide enough gas to push a marginal
situation into a fluidized condition. Apart from the high loading condition fluidization
will often cause flooding of downstream equipment. It is a condition that should be
avoided.
An eccentric load due to eccentric flow channels is also a
condition that will not normally be found in mass flow silos. The relatively thin skin of
a silo is very efficient in resisting the tensile loads imposed by uniform product
loading. When non-uniform, due to an eccentric flow channel, an additional horizontal
bending moment is introduced. If the silo skin is not designed to resist horizontal
bending, it wrinkles or cracks. Some concrete silos are designed with walls thick enough
to resist bending but very few steel silos would be designed this way.
Thanks to David for his contribution. He can be reached in
the UK at:
- Powder Engineering Systems
- Carrington Business Park
- Manchester, M31 4YR
- United Kingdom
- Phone: +44 161 667 4523
- Fax: +44 161 667 4524
- http://www.powderengineering.com
Help others by posting your comments, suggestions and
experiences with bulk solids feeding or any other materials handling concerns you may have
on our On-Line Help Forum. For
past Ask Joe ! Articles, visit the Ask Joe! Archived Articles.
Guest articles for the Ask Joe! Column are always welcome,
for more information please contact Joe Marinelli directly at his email address:
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