Steel Silo Design

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STEEL SILO DESIGN

Jim Durack has a background in both academic and practicing engineering. He has worked with Aurecon

(formerly Connell Wagner) for the last eight years and is currently on sabbatical leave completing an engineering

doctorate through University of Southern Queensland. Jim is a specialist in the design of industrial structures

for bulk materials handling facilities. He has also worked internationally on the design and assessment of

large inverted cone silos as used primarily in the cement production industry. In 2007 ABHR published Jim’s

article on the implications for such silos of the then new Eurocode for silo loads, EN1991-4. Since then he has

presented three further conference papers in this field. Both Jim and Professor Tranberg have been involved in

the development of the USQ coursework based, Online delivered, Master of Engineering that has a significant

emphasis on industrial and marine structures.

In preparation for a planned course on silo design, Jim has extended his reinforced concrete silo research to a

speculative investigation of a steel solution for large inverted cone silos. His knowledge and experience with

concrete silos gives him fresh insight into this complex field. Jim considers that there may be a fundamentally newway of approaching steel silo design that is informed by the Eurocode but not limited by it. This paper provides

a relatively informal presentation of his ideas. He hopes that these may challenge steel silo designers to think

outside the square.

1. Context and background to researchSilos of one form and another are fundamental to the success of

most industrial projects. Ideally a silo will do its job with minimal

maintenance for many years. When a silo suffers some form of fail-

ure this may cause massive disruption of plant operations. There

is at least anecdotal evidence that silos suffer severe structural

failures more frequently than any other structure type with the

possible exception of retaining walls. Such structural failures arestill l ikely to be much less common than operating problems such

as flow interruptions. The operating performance of silos should

continue to be of prime concern to plant operators but those who

are “unlucky” enough to experience the structural collapse of a

key process silo will recognise the fundamental importance of

structural reliability.

Fundamental to structural design is a rational assessment of

the loads that are likely to develop during the lifetime of a pro-

posed structure. In 1895 Janssen developed the Janssen equation

that for the first t ime provided a rational method for assessment of

one aspect of the loads exerted by stored material on a silo wall.

It has always been acknowledged that “real silo loads” are more

complex than those predicted by this equation. “Traditional” code

methods for silo loads such as those of the ACI code and the nowsuperseded DIN code, used fairly simplistic “fudge factors” to

scale up the Janssen equation loads to account for the unknown

and perhaps unknowable complexities of real silo loading.

The Eurocode for silo load estimation EN1991 – 4 released in

draft form in 1995 is still based on the Janssen equation but speci-

fies a fundamentally different loading model. Research undertaken

by Durack and others generally concludes that while there remain

numerous unanswered questions, there is good evidence to sug-

gest that the Eurocode loading model is substantially correct. For

reinforced concrete silos, Durack has shown the Eurocode to be

considerably more onerous than earlier codes. More importantly, it

forces the designer to consider important structural issues that are

not evident when using earlier code defined loading models. Du-rack recommends that any contemporary structural designer of re-

inforced concrete silos should give consideration to the Eurocode

even if the final silo design is not strictly compliant with this code.

Durack has recently undertaken scholarship and finite ele-

ment modelling to investigate whether the Eurocode load may

have similar lessons for the designers of steel silos as he has found

it to have for reinforced concrete silos. The following represent

some key findings of this research:

• For the design of steel silos, the Eurocode for silo loads EN1991

- 4 is supplemented by the general design code EN1993 - 1 - 6

Strength and Stability of Shell Structures and the silo specific

EN1993 - 4 – 1 Design of Seel Structures - Silos.

• There is limited contemporary academic interest in theanalysis and design of reinforced concrete silos, but a huge

body of academic literature relating to various aspects of the

structural behaviour of steel silos. Much of the literature is

highly specialised in nature and of limited direct relevance

to practicing designers.

• Professor Michael Rotter is apparently the most highly pub-

lished academic working in the steel silo field. He has played a

leading role in the development of all three Eurocodes relevant

to silo design.

• Professor Rotter has published a text “Guide for the Economic

Design of Circular Metal Silos”. This text is specifically directed

to practicing silo designers. First published in 2001 it repre-

sents a general guide to steel silo design plus specific guidance

related to the application of the three silo Eurocodes.• Durack has reported that for reinforced concrete silos, the Eu-

rocode for silo loading is more conservative than earlier codes

by a factor in excess of 1.5. No such comparative review for

steel silos has been identified in the published literature.

• Rotter’s text and the codes it supports are typical of code speci-

fied design methods. They allow a designer to undertake a de-

sign assessment of a proposed steel silo but they provide only

limited assistance in developing the form of understanding that

a designer needs in order to exercise responsible creativity in

achieving a reliable and economic design solution for a particu-

lar steel si lo application.

2. Focus of the current researchTo address the last of the previous dot point items, a combination

of finite element modelling and relatively simplistic first principles

analysis has been undertaken in order to explore structural phe-

nomena exhibited by steel silos in response to the Eurocode load

and related analysis and design issues.

A challenge for designers of steel silos

Australian Bulk Handling Review: July/August 2010

Jim Durack, engineering doctorate candidate USQ

Professor Charlie Tranberg – USQ


http://slidepdf.com/reader/full/steel-silo-design 2/685 Australian Bulk Handling Review: July/August 2010

STEEL SILO DESIGN

The research focuses on a 12 500 tonne capacity cement stor-

age inverted cone silo with a diameter of 18 metres and a storage

chamber height of 40 metres. This silo is not typical of most steel

silos that are likely to use a concentric discharge system and to

be smaller and more slender. The case study silo has been chosen

because of the author’s interest in reinforced concrete silos of

these proportions.

It should be noted that applicability of the Eurocode for siloloading specifically excludes the “inverted cone” discharge system

that is common in the cement industry. This discharge system uses

an inverted cone at the base of the silo that sheds the stored mate-

rial to sequentially operated discharge points located around the

silo perimeter. Despite this, the research is generally relevant to

the design of a steel silo of any sort.

3. The case study silo and its Eurocode loadingThe basic details of the case study silo are shown in Figure

1. This also gives a three dimensional representation of the

Eurocode loading.

In accordance with the Eurocode EN1991 – 4 Clause 5.2.4.3

and with z measured downwards from the top of the silo, the

loadings phse and phse – phce shown in Figure 2, that vary both cir-cumferentially and with height were input as follows:

phse

= 150.94 x (1 – 2.7813 ^ (-z / 14.56)) kPa

phse

– phce

= 150.94 x (1 – 2.7813 ^ (-z / 14.56)) – 40.4 x

(1 – 2.7813 ^(-z / 3.9)) kPa

4. Two dimensional structural phenomenaPrior to considering a three dimensional silo it is informative to

consider the behaviour of a two dimensional ring extracted from

such a silo. Figure 3 represents a 1 metre high ring extracted

from the case study silo with the loading corresponding to that

at a height of 15 metres above the base of the silo.

If the thickness of the 1 metre high ring is set to 25 mm then

it is obvious that these loads are very large. Despite this, we mayexpect that the uniform outward pressure should not create a

difficulty because this can only cause a uniform increase in the

circumference of the ring without inducing any bending. The

axial hoop tension can be calculated using the simple hoop ten-

sion equation:

T = Uniform pressure x Ring height x Radius (1)

= 123 kPa x 1 metre x 9 metres

= 1107 kN

The corresponding axial hoop stress around the circumfer-

ence is then:

f a = 1107 x 103 / (1000 x 25)

= 44.3 MPa

The differential pressure of +/- 85 kPa over the 30° (4.71 me-

tre arc length) flow zone and the two adjacent shoulder zone would obviously cause a problem if the load had to be carried

by bending action in the flexible 25 mm thick plate. Fortunately

this is not the case.

The hoop tension equation is commonly applied to uni-

form pressure situations but may also be applied to situations

where the pressure varies around the per imeter. It may be put

in the form:

T( θ ) = p( θ ) x r( θ ) (for unit ring height) (2)

Where T( θ ), p ( θ ) and r ( θ ) represent the values of the hoop

tension, radial pressure and ring radius at any location θ around

the perimeter of the ring. Equation (2) may be algebraically rear-

ranged as:

r( θ ) = T( θ ) / p( θ )It may readily be shown by FE modelling or consideration of

a small differential arc element of the ring, that for loading of the

type shown in Figure 2, the hoop tension T( θ ) remains constant

at the value given by equation (1). Thus, we may write:

r( θ ) = T / p( θ )

And substituting for T from Equation (1)

r( θ ) = (Uniform pressure / Pressure at position θ )

x Initial silo radius (3)

Equation (3) may be read as follows:

Provided the ring changes its shape in response to the load

such that at any angular location θ around the ring circumfer-

ence, the ring radius equals the ratio of the uniform pressure

to the pressure at θ, times the initial silo radius, then the load

will be carried by hoop tension action rather than by bending.This shape may be referred to as the “compliant shape”.

For the combination of loads defined in Figure 3 there are

three pressure zones and corresponding radii being:

The general area with phse = 123 kPa with:

r( θ ) = 123 / 123 x 9 = 9 metres

The high pressure shoulders with phse + (phse – phce )

= 208 kPa with:

r( θ ) = 123 / 208 x 9 = 5.32 metres

The low pressure flow zone with phse – (p hse – p hce )

= 38 kPa with:

r( θ ) = 123 / 38 x 9 = 29.13 metres

These compliant radii are dependent only on the pressure ratios

and are independent of both the thickness of the ring and the actualmagnitude of the pressures. Thus if the pressures are scaled up by

a load factor then there will be no change to the compliant shape

and corresponding radii. Figure 4 represents the FE Prediction of

the compliant shape for the ring subject to the combination of the

uniform and differential components of loading shown in Figure 3.

Figure 1 Basic silo details and a graphic illustration of the internal pressure on the silo walls.

Figure 2 The decomposition of the Eurocode load into uniform and differential components.

Figure 3 Two dimensional ring extracted from the 3D silo model.



It may be confirmed from the FE model that the numerically

predicted radii in the shoulder and flow zones are very close

to those predicted using Equation (3). The maximum radial de-

formations associated with moving to the compliant shape as

predicted by FE modelling are around 380 mm inwards in the

flow zone and 70 mm outwards in the shoulder zones.

The full story is not as simple as this. Firstly, rather than a

stepwise change from one radius to the next there is a smalltransition length from one radius to the next. Secondly, Graph

1 shows the radial displacement at the centre of the flow chan-

nel as predicted by FE modelling for a ring with a 10 mm thick-

ness, as the load factor on the combined loading increases

from 0 to 2.5. This represents the development of the compli-

ant shape for increasing load.

Graph 1 demonstrates that the stiffness of the ring is high-

ly non linear, exhibiting a huge increase in stif fness as the load

increases and the r ing moves to the compliant shape. (Durack

has reported on f ield measurement of the radial deformations

of a 10 000 tonne reinforced concrete silo during dischargeand the use of these measurements to infer the magnitude of

the loading necessary to cause such deformations. One conse-

quence of the non linear “tension stiffening” behaviour is that

this form of field testing cannot be used to determine unstiff-

ened steel silo wall pressures. As indicated in Graph 1, if the

measured radial d isplacement is say between 350 and 360 mm

then the pressures causing this displacement could be any-

where corresponding to that for a load factor between 0.1 and

2.5. Despite this limitation, the method should be excellent

for determining pressure ratios in the di fferent flow zones.)

Thirdly, the statement following Equation (3) states that

once the ring reaches the compliant shape, the combined load

is carried by hoop tension rather than by bending. This is notentirely correct. In moving to the compliant shape, bending

curvatures obviously must develop in order for the radii to

change to the required values. It may readily be shown that

the bending curvatures necessary to establish the compliant

radii in the flow and shoulder zones are given as:

1 / r bending = 1 / {[(Uniform phse ) / (Differential phse – phce )]

x initial silo radius} (4)

= 1 / (123 / 85) x 9

= 0.0768 m-1

In accordance with the engineers theory of bending, bending

strains will develop as a result of this curvature as:

εmax = y max / r bending (5)

Where y max is the maximum distance from the neutral axis ofthe wall of thickness t. Thus y max = t / 2. The bending stress as-

sociated with this bending strain for a material with a modulus of

elasticity E is then given as:

f max= E x εmax (6)

= +/- E x (t/2) / r bending (7)

The total stress due to the combination of axial hoop tension

and bending necessary to move to the compliant shape is then

given as (for a unit ring height):

f total.max = T / t +/- E x (t/2) / r bending (8)

Table 1 records maximum radial displacements and com-

pares the stress predictions of FE modelling with those of Equa-

tion 8 for ring thicknesses varying from 5 mm to 200 mm (with

T = 1107 kN and 1/r bending = 0.0768 m-1 and E = 200 x 103 MPa):

*Examination of the FE output for the very thin 5 mm plate suggests

that these values are unreliable.

From Table 1, the following observations may be made:

• As the plate thickness increases from 5 mm to 40 mm there

is only a marginal 17% reduction in the maximum radial dis-

placement from 353 mm to 293 mm and the corresponding

bending curvature remains sensibly constant over this thick-

ness range with a value close to that given by Equation (4)

• For feasible thickness plates between 5 and 30 mm, the corre-

lation between Equation 8 and FE Modelling is very good. For

a plate thickness of 40 mm Equation 8 is overestimating the

maximum and minimum stresses by around 20%.

• The bending stress component of Equation (8) increases with

t/2. As predicted both by Equation (8) and FE modelling this,

perhaps surprisingly, leads to an increase in total stress as theplate thickness is increased!

• For a plate thickness of 200 mm it is clear that Equation 8 has

little relevance. The ring now has substantial flexural sti ffness

(similar to that of a typical reinforced concrete silo wall) and

is acting in an entirely different fashion. The small maximum

displacement of 24 mm indicates that the ring has not moved

to the compliant shape where hoop tension can carry the

load. Most of the load is now being carried in flexure with

high bending moments and shear forces.

5. Design implications of 2D structuralphenomena

It is to be expected that the behaviour of a three dimensionalsilo will include additional phenomena that are not evident in

a two dimensional ring extracted from such a silo. Despite this,

the findings of the previous section provide a suitable starting

point for understanding and have significant design implications

as summarised below:

STEEL SILO DESIGN

Figure 4 Two representations of the compliant shape.

Graph 1 The development of the compliant shape as the load increases.

FromFE FromFE FromFE

353 (327)* (117*)

357 204 17

350 210 - 99

340 232 -143

327 253 -179

293 276 -221

24 58 -46

Table 1 Maximum radial displacement and combined ring stresses for differing ring thicknesses.



• For feasible steel plate thicknesses and the non uniform Eu-

rocode loading, there is a good correlation between the pre-

dictions of simple hoop tension theory and results obtained

from FE modelling.

• A steel silo is dependent for its equilibr ium on moving towards

the compliant shape. Linear static analysis that assesses equi-

librium in the undeformed position (with a perfect circular

shape) will not give any meaningful prediction of the actualbehaviour of the silo. All of the previous FE results are based

on geometry non linear analysis.

• The Eurocode loading will cause large radial deformations of

an unstiffened steel silo. These large deformations develop at

quite low load factors but as the load increases they reach a

maximum value beyond which they will not further increase.

• Increasing the wall thickness of a silo will not significantly

reduce the magnitude of radial deformations (until the thick-

ness reaches very large values more typical of a reinforced

concrete silo).

• For a given non uniform load combination, increasing the wall

thickness of a silo will increase the total combined axial and

bending stress. A maximum stress in excess of the yield stress

should not be taken as an indication that the silo is approach-ing failure. It simply means that with thicker plates, some de-

gree of yield may be necessary to allow the silo to move to the

compliant shape.

• For low loads a silo will exhibit very low stiffness but as soon

as it approaches the compliant shape the stiffness will radical-

ly increase. For this reason it may be difficult to obtain conver-

gence of an FE solution for the first low increments of loading.

6. Three dimensional case study silo –horizontal effects

In Figure 5 the wall thickness has been kept constant to simplify

interpretation of stress information. There is no suggestion that thisthickness is adequate or appropriate for Eurocode loading. Figure

6 illustrates the overall behaviour of the three dimensional silo as

assessed using geometry non linear analysis for a load factor of 1.0.

There are “end effects” at the base and roof of the silo but in the

central region the silo is deforming in a similar fashion to the two

dimensional ring – pulling inwards in the low pressure flow zone

and pushing outwards in the high pressure shoulder zones.

Figure 6 also provides detailed information relating to the ring

level where the horizontal loading is identical to that for the two

dimensional ring previously considered. Referring back to Table

1 the following comparisons may be made between the 25 mm

thick two dimensional ring and the 25 thick ring forming part of

the three dimensional silo:• The maximum silo displacement at the ring level of 229 mm in-

wards is substantially less than the 340 mm for the two dimen-

sional ring. This means that in the two dimensional ring essen-

tially all of the load is carried by circumferential hoop tension,

but in the silo, some is being carried by an alternative load path.

• The hoop tension force varies around the perimeter of the silo

from 968 to 1252 kN/m. The average of these two figures is

very close to the constant hoop tension in the two dimensional

ring of 1107 kN/m.

• The maximum and minimum plate stresses (at the surface of

the plate) are 247 MPa and - 163 MPa compared to those for the

two dimensional ring of 236 MPa and – 148 MPa.

7. Three dimensional case study silo - verticaleffects

In addition to the horizontal loading on the silo wall, the stored

material also causes vertical loading as the stored material at-

tempts to slide down the inner face of the silo wall. This vertical

loading is referred to as the wall traction loading and at any depth

and radial position θ is equal to the horizontal pressure times

the assessed coefficient of friction between the stored material

and the silo wall. As with horizontal loading, traction loading

has been decomposed into a uniform traction component that is

constant around the perimeter and a differential component that

is downwards in the high pressure shoulder zones and upwards

in the low pressure flow zone.

The load path for these traction loads is straight down the silo wall. Figure 7 shows the analysis results for the uniform traction

component causing a steady increase in the vertical wall stress

from zero at the top to a maximum of - 62 MPa (compression)

at the base of the 25 thick wall. The differential traction com-

ponent produces a more complex stress variation that includes

both compression and tension areas but with maximum value of

only + 5.4 MPa and – 3.6 MPa this is clearly of secondary concern.

The surprise comes with Figure 8 that shows the vertical

wal l stresses assessed for the full Eurocode loading including

the uniform and differential components of both the horizon-

tal pressures and vertical tractions.

The view on the left of Figure 8 (a) indicates high stressesat the base of the silo in the region of the non uniform pres-

sures with maximum values of 237 MPa tension and 210 MPa

compression. These maxima are nearly four times the verti-

cal stresses due to just the vertical traction loads as shown in

Figure 7.

STEEL SILO DESIGN

Figure 5 First three dimensional silo analysis model.

Figure 6 Aspects of the behaviour of the Figure 5 silo focussing on the ring level.

Figure 7 Vertical wall stresses due to uniform and differential vertical traction taken separately.



The view on the right of Figure 8 (a) represents the same

stresses but with the plotting range limited to 50 MPa tension and

100 MPa compression. This shows that high vertical compression

(and tension) stresses exist high up the wall height. The maxi-

mum compression region is the low pressure flow zone. It can be

demonstrated that this increase in vertical stresses is a result of

the differential horizontal loading. It is difficult to come up with

a satisfactory intuitive understanding for this effect. One way ofthinking about it is to consider it to be a result of the curved silo

wall attempting to carry the differential horizontal loading by

spaning vertically from the base of the silo up to the roof. The

very high vertical stresses at the base of the wall correspond to a

rigid base to these vertically spanning wall elements giving rise

to high “negative moments” at the base of the wall. Despite the

difficulties in understanding the origin of this increase in vertical

stresses, they have to be accepted as being real.

The magnitude and extent of vertical stresses shown in Fig-

ure 8 is of great design significance as it has already been identi-

fied that in the flow zone where the compression stresses are

high, the horizontal pressures cause a local increase in the silo

wall radius as it moves towards the compliant shape. As dis-

cussed below this causes a reduction in the buckling capacity ofthe wall in this region.

Recall that the Euler critical lateral buckling stress for an ideal

axially loaded column with length l and radius of gyration r is:

σcr = 2E / [ (l/r)2 ] (9)

Now a very tall and slender silo could buckle laterally in this

fashion but it is much more common for a silo to exhibit local

buckling with a buckling shape as illustrated in Figure 9.

For uniform vertical loading only, applied to a cylinder of

radius r the formula to predict the development of the form of

buckling illustrated in Figure 9(a) with Poisson’s ratio of 0.25 is: σcr = 0.6 x E x t / r (10)

= 0.6 x 200 x 103 x 25 / 9000 (for the 25 thick wall and

the original 9 metre silo radius) = 333 MPa

Figure 9 (a) shows the FE buckling prediction for uniform ver-

tical traction loading only applied to the perfect circular silo. The

buckling stress prediction of 319 MPa shows excellent correlation

to Equation (10).

The situation for non uniform loading is more complex. It

has already been noted that proper assessment of silo behaviour

requires non linear analysis – but finite element buckling analy-

sis by definition, is linear and thus cannot directly predict the

onset of buckling due to non uniform loading with its inherently

non linear characteristics. The analytical Equation (10) is strictly

speaking only applicable to uniform loading but it is informa-

tive to apply it in the flow zone region where, for non uniformloading, the silo moves (almost) to the compliant shape. The FE

model predicts a final silo radius in this region of 24.8 metres.

We then have: σcr = 0.6 x 200 x 103 x 25 / 24 800

= 121 MPa

Figure 9(b) represents the FE buckling prediction, again for

uniform traction loading only but for a model that is initially de-

formed to the shape illustrated in Figure (6) with the final ge-

ometry non linear, 24.8 metre silo radius in the critical region.

The FE prediction of 132 MPa buckling stress is very close to

that of Equation (10) with some increase due to averaging of the

peak stress and the stabilising effect of the adjacent small radius

shoulder regions.

Thus it appears that for this silo, the non uniform Eurocodeloading is causing:

• High vertical stresses near the base of the silo

• Vertical compression stresses around 100 MPa reaching well

up the height of the silo (compared to a

• maximum of 62 MPa at the base of the silo for the uniform

traction loading only)

• A substantial reduction in the buckling capacity of the wall in

the flow zone as evidenced by a reduction in the critical buck-

ling stress from 319 MPa down to 132 MPa due to the increase

in the silo radius as it moves towards the compliant shape.

8. Working around the problem

It appears that the Eurocode load, when applied to steel silos,may be considerably more onerous in comparison to earlier

codes that considered only uniform loading. It can probably be

shown that while there have been an unacceptable number of

failures of steel silos, there are many that are performing well but

do not comply with the requirements of the new loading code.

It would be easy to start criticising the Eurocode for silo loading

that could be seen as being unnecessarily conservative.

The author’s research on reinforced concrete silos indicates

that the Eurocode for silo loading probably represents a good

model of actual silo loads. A more creative way around the prob-

lem is to consider whether some modification to the traditional

silo structural system may allow the development of a Eurocode

conforming silo without the need for significant additional cost

while providing signif icantly enhanced structural reliability.One possibility is the use of some form of corrugated wall-

ing or of multiple vertical or circumferential s tiffeners - or both.

The author considers that this approach may have its applica-

tions in some areas but that in general is unlikely to produce sig-

nificant benefits. The structural efficiency of a steel silo comes

largely from the flexibility of the thin steel wall and its ability

to move to the compliant shape. Stiffeners wil l inevitably cause

high stress concentrations as they attempt to fight against the

flexibility of the wall.

A second possibility is illustrated in Figure 10 (b). This makes

use of a single relatively massive stiffener at about one third

height. The idea behind this stiffener started with an acceptance

of the tendency of the silo to attempt to carry some of the nonuniform load by spaning vertically, resulting in high compression

stresses in the high radius flow zone. The stiffener represents

an attempt to provide an internal support for this vertical load

path thus increasing its efficiency in carrying some of the non

uniform components of the load.

STEEL SILO DESIGN

0.0

Figure 8 Vertical wall stresses due to the full Eurocode loading.

Figure 9 Typical buckling mode shapes for uniform and non uniform loading.



9. Design comparisonTo explore the potential advantages of the silo illustrated in Fig-

ure 10 (b) compared to the simpler reference silo of Figure 10

(a), a design assessment was undertaken for the two silos. Both

silos were taken as being of Grade 450 steel with elastic plastic

behaviour using the Von Mises yield criterion and with E = 200

x 103 MPa and Poisson’s ratio = 0.25. Both silos were of identical

geometry and subject to the same loading defined in Figure 2. A decision was made to use a form of design by advanced

analysis using geometry and material non linear analysis. The

primary decisions necessary for such design assessment involve

setting the magnitude and shape of the imperfections to be in-

corporated in the analysis model and the choice of an appropri-

ate failure criterion to identify the collapse load. Such decisions

require extensive sensitivity analyses and comparative trialling

against other accepted design methods. The following decisions

were adopted with l imited trialling and are intended only to al -

low for rational comparison of the stiffened and unstiffened silos

on an equal basis.

The nominal geometric construction tolerance on the silo ra-

dius was taken as being +/- 30 mm with a magnifier of 3.0 to in-clude for non geometric imperfections such as residual stresses.

Thus the maximum deviation from a perfect cylinder prior to

load application was 90 mm. The deformation due to the non uni-

form loads is not included as an imperfection as this deformation

is determined directly by the geometry and material non linear

analysis. The shape of the imperfections was different for each

silo being set to that corresponding to the lowest mode buckling

shape for each silo subject to the uniform traction load only but

with an initially deformed shape corresponding to the full Eu-

rocode load.

The failure criterion was taken as the load beyond which a

convergent solution was no longer obtained. This represents a

non conservative failure criterion and some might argue for a

more conservative criterion such as first yield – but it has alreadybeen identified that for steel silos that must adopt their compli-

ant shape, yield is not a good indicator of an approaching failure

mechanism.

It was found that both silos reached convergence for Load

Factors up to 3.2 with no convergent solutions beyond this point.

Figure 11 compares the Von Mises strain at the outer surface of

the silo for load factors of 1.67 and 3.2. The plotting range for

strain is limited to the yield strain for Grade 450 steel so white

regions represents regions where yield has developed at the plate

surface.

In principle, a load factor of 1.5 / 0.9 = 1.67 represents the

minimum necessary load factor for code compliance. At this load

factor there is no yield in the heavier unstiffened silo and onlysmall regions of yield for the lighter stiffened silo. With this slight

exception, both silos achieve the necessary collapse load as as-

sessed using the very conservative first yield failure criterion.

At a load factor of 3.2 as must be expected, the thinner sti ff-

ened silo, with extensive regions of yield, is working harder than

the heavier unsti ffened one. Despite this, examination of the Von

Mises stress at the mid plane shows no yield for the heavier silo

and only limited regions of yield for the stiffened silo.

It may be concluded that more detailed investigation is likely

to confirm that both silos are code compliant as assessed using

design by advanced analysis - probably with a considerable mar-

gin of safety and some possibility of reductions in plate thick-

nesses. No attempt has been made to identify whether eitheror both of these silos comply with the design requirements of

EN1993 - 4 - 1 Design of Seel Structures – Silos.

10. Disclaimer and overall conclusionsThis paper has simplified some matters and omitted considera-

tion of significant design issues other than those central to its fo-

cus. The paper is not intended to demonstrate a definitive design

approach for steel silos.

It is hoped that this paper will provide some general under-

standing of steel silo behaviour and design for interested engi-neers and that specialist steel silo designers may find it to be pro-

vocative of discussion and perhaps robust criticism. Some will

continue to question the credibility of the Eurocode silo loading.

As has been shown, field measurements of steel silo wall defor-

mations allowing determination of pressure ratios in flow and

shoulder zones could readily provide further proof or otherwise

as to the correctness of the Eurocode load.

It is not claimed that the silo system incorporating a single

relatively massive stiffener necessarily represents a step forward

with regard to the design of steel silos. It is suggested that steel

silo designers should accept the challenge of considering new

options for achieving more reliable and economical steel silo de-

signs based on a solid understanding of the implications of the

Eurocode loading.

KEY REFERENCESDurack, J. McKay, H. 2007. Implications of the new Eurocode EN1991-4

to cement and raw meal silo design. Australian Bulk Handling Review

Vol 12 Nos 2 and 3.

Durack, J. McKay, H. 2007. Measured wall movements during

discharge compared to Eurocode predictions for an inverted cone silo.

International Bulk Materials Handling Conference. University of

Newcastle.

Durack, J. 2008. Observations of the performance of existing inverted

cone silos. Bulk Materials Handling Conference, Brisbane.

Durack, J. 2008. The analysis and design of reinforced concrete silos.

20th Australian Conference on the Mechanics of Structures and Materials. University of Southern Queensland.

STEEL SILO DESIGN

Figure 10 A modified structural system for a steel silo.

Figure 11 Comparative design assessment for the two silos.

Contact: James Durack, email – [email protected]

Steel Silo Design

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