background discussion document for en 1991-4 · background discussion document for en 1991-4 june...

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CEN TC250/SC1/PT4

Background discussion document for EN 1991-4June 2001 - March 2002

prepared by Prof. J.M. Rotter, University of Edinburgh

This document has been prepared as a discussion paper indicating the basis ofchanges and amendments to the ENV 1991-4 undertaken by the Project Team. It ismostly a summary of discussions at the meetings in Copenhagen (June 2001) andBrussels (November 2001), together with reactions to comments on the August 2001draft received from several countries.

The meeting of the PT held in Copenhagen in June 2001 agreed a list of issues(CEN TC250/SC1/PT4 – 33) that needed to be considered, and this documentaddresses those issues.

List of issues1. Conservatism of the rules2. Principles and rules (what is compulsory and what is flexible)3. Main text and annexes: follow CEN rules. Materials testing? What are we

allowed to keep in annexes?4. Scope: may be OK for concrete silos5. Reliability classes6. Material variability7. Table of material properties8. Materials testing9. Mass flow and funnel flow bounds10. Terminology for maximum load magnifier11. Value of the maximum load magnifier and physical phenomena it represents12. Angle of internal friction (which one?)13. Angle of repose (needed for squat silos)14. The role of patch loads15. Separation of filling and discharge eccentricities16. Patch load rules for large eccentricities17. High eccentricity flow and pressures18. Extension of simple rules to wider range (don’t have the restriction of both

eccentricity of discharge and diameter limit to 5m)19. Simplified rules 5m restriction too small20. Internal ties in rectangular silos21. Rectangular silo pressures22. No distinction between concrete and steel: doesn’t the stiffness matter?23. Planar silos24. Coefficient for flat bottoms Cb: is 1.2 too low? Or should be omitted25. Hopper loads26. Corrugated walls27. Pressure strengthening effect for buckling28. Squat silos separated into squat and intermediate29. Squat silo rules30. Squat silos with high filling eccentricity

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31. Retaining silo rules (“magasins de stockage”)32. Actions due to thermal differentials33. Pressures on manholes34. Tanks requirements

Issues that are deemed outside the scope of the EN 1. Interaction of solid stiffness with structure2. Dust explosions3. Silage silos

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1. Conservatism of the rulesThe PT considered that it is important to devise at a standard that is more useful thanthe present draft ENV. In general the rules should not be more conservative than inthe existing code but a more realistic distribution of safety should be aimed at.

It has been suggested that the rules in ENV1991-4 are often more conservative thanthose of DIN1055.

The PT should consider:a) Whether example calculations demonstrate that this is true.b) What aspects of ENV1991-4 lead to the increased conservatism.c) How DIN1055 has produced safe designs without including material property

variation.

Comparative example calculations have been produced by members of the ProjectTeam and a number of different contributors. However, one of the key difficulties inmaking comparisons is to identify the source of the differences: substantivedifferences can arise from:a) different property values being adopted for the same solid in different standards.b) inclusion of material variability or the assumption of fixed values.c) magnitude of adopted discharge factors for normal pressures, wall friction and

bottom loads.d) the use of a patch load to locally increase pressures, producing a different

structural action that causes increased structural strength not simply related tonormal pressure. Differences in the definition of the patch load will also causedifferences between the standards, unrelated to items (a) to (c).

e) placement of safety margins in either the loading or the structures standard (asnoted below).

Unless the comparisons identify the chief source of the discrepancies, they do notassist in determining whether the draft EN is generally too conservative, or whetherthis is simply related to a difference of assumed material property value for aparticular solid.

The achievement of a certain level of conservatism in the design of structures comesfrom rules in both loading and structures standards. Thus, each national loadingstandard is intended for use with a particular national structural design standard, andthe total safety margin may be attributed more in loadings than in structures, or viceversa. Thus, it is not necessarily an appropriate comparison to compare the DIN silopressures with EN silo pressures, since the structures standards to be used afterwardsmay have different levels of safety. The only comparison that really counts is thedimensions of the final structure, and this comparison is difficult to make because somany design decisions and assumptions must be used in interpreting the standards.

2. Principles and rules (what is compulsory and what is flexible)Many of the ENV rules were marked as P (principle) when they were really rules. Anattempt has been made to correct all paragraphs to be aligned with CEN rules. ThePT should check all rules carefully to identify those that should be principles.

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3. Main text and annexes: follow CEN rules. Materials testing?What are we allowed to keep in annexes?On the understanding that alternative rules will be permitted to be placed in an annex,the PT resolved that they would use this arrangement to ensure that alternativetreatments of controversial items were all available within the standard.

4. Scope: this may be OK for concrete silosA careful review of the scope clauses should be undertaken.

Care should be taken with:a) Large diameter squat silos, which are increasingly common, but which have a

smaller experimental base of observations, and which were not considered whenmost rules in standards were devised;

b) Metal silos in which axial compressions develop in the walls due to both frictionand asymmetrical normal pressures;

c) Large eccentricities of discharge, for which many failures have occurred in slendersilos.

5. Reliability classesThe struggle between simplicity and the complexity required for safe design willpersist until designs are separated into categories of difficulty. The designers ofsimple structures want and need a simple code to permit designs to be done quicklyby hand, but large complicated designs require computer calculations and realisticallycomplicated load cases should be specified to guarantee the safety of these structures.This conflict is best met by introducing reliability classes. These allow simpleconservative rules to be used for simple cases, but demand more thorough treatmentfor cases where either less conservatism is sought (as in a design to be usedrepeatedly) or where the size, complexity and high risk mean that more design effortis both required and justified.

Since the reliability classes are already defined within ENV1993-4-1, it would beadvantageous to adopt the same definitions. The class boundaries are defined usingboxed values, so modifications to these boundaries could also be introduced.

The Reliability Class section of ENV1993-4-1 is given below:

2.3 Reliability differentiation

(1) Different levels of rigour should be used in the design of silo structures, depending on thereliability of the structural arrangement and the susceptibility to different failure modes.

(2) The silo design should be carried out according to the requirements of one of the following threeclasses of reliability used in this Part, which produce designs with essentially equal risk in the designassessment and considering the expense and procedures necessary to reduce the risk of failure fordifferent structures: Classes 1, 2 and 3.

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Table 2.1: Classification of design situations

Reliability Class Description

Reliability Class 3 Ground supported silos or silos supported on a complete skirt extending tothe ground with capacity in excess of 5000 tonnes

Discretely supported silos with capacity in excess of 1000 tonnes

Silos with capacity in excess of 200 tonnes in which any of the followingdesign situations occur:a) eccentric dischargeb) local patch loadingc) unsymmetrical filling

Reliability Class 2 All silos covered by this Prestandard and not placed in another class

Reliability Class 1 Silos with capacity between 10 tonnes† and 100 tonnes

† Silos with capacity less than 10 tonnes are not covered by Eurocode 3 Part 4.1.

(3) A higher Reliability Class may always be adopted than that required in table 2.1.

(4) The choice of minimum Reliability Class should be agreed between the designer, the client andthe relevant authority.

(5) Reliability Class 3 should be used for local patch loading, which refers to a stored solids loadingcase causing a patch load which extends round less than half the circumference of the silo, as defined inENV 1991-4.

(6) For Reliability Class 1, simplified provisions may be adopted.

NOTE: Appropriate provisions for Reliability Class 1 silos are set out in annex B.

6. Material variabilityDifferent materials have very different variability. The variability of each materialshould be explicitly defined, instead of having the same blanket range applied toeverything. A material that has a high variability places a greater demand on thestructure than one with low variability, since each part of the structure is heavilyloaded at a different property extreme, as shown in the following table.

It would be helpful to include the different load cases defined in this table to aid thedesigner in identifying the property extremes that will govern in different stressresultant assessments and limit state verifications.

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Table 7.1 Values of properties needed for different wall loading assessments Load case Purpose Property extreme to be adopted Wall friction

coefficient µ Lateral pressure

ratio λ Angle of internal

friction φi For the barrel wall BN Maximum normal pressure on cylinder wall Lower Upper Lower BF Maximum frictional traction on cylinder wall Upper Upper Lower HF & HE Maximum vertical load on hopper Lower Lower Upper For the hopper wall Hopper wall

pressure ratio F

HF Maximum hopper pressures on filling Upper value forhopper

Lower Lower

HE Maximum hopper pressures on discharge Lower value forhopper

Upper Upper

The ENV rule insisted that the mean value of a property xm is reduced to 0,9xm andincreased to 1,15xm to allow for material variability.

Problems with the ENV rules include:a) Where materials are tested the same variability must be assumed as those in the

table: thus there is no advantage in testing to give a smaller variability.b) There is no requirement to include a wider variability than the simple values for

the materials in the table, so there is no advantage in testing.c) The use of variability of material properties ensures that different load cases (max.

hoop tensions, max wall axial compressions, max hopper loads) are all consideredwithin the direct calculations.

d) Once the variability has been taken into account, some amplification factors (likethe bottom load multiplier Cb) are probably only appropriate henceforth for specialcases that involve special phenomena, such as cohesive arching or mechanicalinterlocking. Other values for other amplification factors (like the discharge factorCo) will need to be modified in the light of the increased basic design loads arisingfrom including material variability.

It was agreed at the meeting of CEN TC250/SC1/PT4 that the principle of includingmaterial variability should be maintained, but that a better calibration of thevariability of individual materials is needed. This calibration should allow for theproper and appropriate values of the partial coefficients to be used in design.

The principles put in PrEN 1997-1 “Eurocode 7 Geotechnical design: Part 1 GeneralRules” Sections 2.4.3 and 2.4.5 have been adopted as far as possible. Concerningpartial factors γF, Eurocode 7 offers 3 different methods for the placement of thepartial factor within the calculation. The one adopted here is Design Approach 2(annex B), where the load is calculated in the basis of characteristic values of materialparameters and with the partial factor γF placed on the assessed load.

7. Angle of internal friction (which one?)The bulk solids handling community always use Jenike’s “effective angle of internalfriction” to represent the internal friction φ, whilst civil and structural engineers tendto use the soil mechanics value of a (c,φ) material. For a purely frictional materialstored in a silo, there is no difference. However, many powders and mildly cohesive

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solids are covered by this standard and it is important that the standard states clearlywhich value of internal friction is to be used, and gives reasons in the Annex.

In the existing Annex B, the procedure to determine two internal friction angles, φ andφc, is set out. The value of φ, used elsewhere in the standard corresponds to a soilmechanics normally consolidated or loading value of internal friction, not the Jenikeconstruction for the effective angle of internal friction.However, the notation (section 1.5) states that the value used in the standard is theeffective angle of internal friction.

The internal friction angle is used in this standard:a) to obtain the maximum load magnifier (section 7.4)b) for indirect determination of the lateral pressure ratio K (Annex B 9.2)

Both of these uses involve considerable empirical approximation, so the choice ofvalue does not seriously affect the outcome. However, it could be argued that theeffective angle of internal friction does not give a good measure for the lateralpressure ratio K through the formula K = 1,1 (1 – sinφ), so the soil mechanical valueshould be used.

It is recommended here that the notation section is changed to bring the value into linewith the Annex.

There should also be compatibility of notation with the rules for retaining walls givenin Eurocode 7.

It is also necessary that the values of internal friction angle in the table of materialproperties should be amended to give the simple soil-mechanical “internal frictionangle” and not the “effective angle of internal friction”, since the use of this parameterevaluating both the lateral pressure ratio λ or K and the discharge factor Co depend onthe simple internal friction angle.

8. Table of material propertiesIt is agreed that a larger table of material properties should be given in the standard torestrict designers’ bad habits of adopting inappropriate values from apparently similarmaterials. A possible table may be taken from Rotter’s Guide (23 materials) and wasplaced in the first revised version of the draft (EN version B). It has now beenmodified as described below.

The values in Table 5.1 can be used to show the variability of each solid. Thededuced variability (coefficient of variability) of the lateral pressure ratio for differentsolids is shown in the figure.

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Deduced CoV on lateral pressure ratio (data from AS3774)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Alumina

Barley

Cem

ent

Cem

ent c

linker

Coa

l: blac

k

Coa

l: bro

wn

Coa

l: pow

dered

Cok

e: bree

ze

Cok

e: petr

oleum

Con

crete

aggr

egate

Flour (

wheat)

Fly ash

Iron

ore p

ellets

Lime,

hydra

ted

Limest

one p

owder

Maiz

e

Phosphate

rock

Sand: c

oarse

dry

Sand: q

uartz

Slag: g

ranular

, dry

Soya b

eans

Sugar

Whea

t

Coe

ffic

ient

of v

aria

tion

AS implied valueENV value

The choice of a fixed value for the variability of these solids in theENV 1991-4 (1995) is quite unfortunate, since some solids are clearly much lessvariable than this (e.g. Flyash) leading to rather conservative designs, and some aremuch more variable (e.g. Coal) leading to an unsafe design procedure.

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First attempt

Table 5.1 Physical properties of bulk solids: characteristic values † Type of Bulk solid

Unit weight

γ

Angleof

repose φr

Effective angleof internal

friction φi

Lateralpressure

Ratio K or λ

Wall friction angle ‡ φw

(µ = tan φw)

Max. flowpressure

multiplier Co

γl γu φr φil φiu Kl, λl Ku, λu Wall type D1 Wall type D2 Wall type D3 Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper kN/m3 kN/m3 degrees degrees degrees degrees degrees degrees degrees degrees degrees Default material * 6.0 20.0 40 25 55 0.35 0.65 10 30 12 35 14 45 1.45 Alumina 10.0 12.0 27 25 40 0.42 0.53 20 25 25 30 30 35 1.40 Barley 7.0 8.5 20 26 33 0.50 0.63 15 24 18 27 25 32 1.35 Cement 13.0 16.0 28 40 50 0.45 0.58 20 25 23 28 28 33 1.40 Cement clinker 15.0 18.0 33 42 52 0.41 0.52 20 25 25 30 30 35 1.40 Coal: black 8.5 11.0 35 40 60 0.45 0.58 15 25 25 35 25 40 1.45 Coal: brown 7.0 9.0 33 45 65 0.35 0.45 18† 25† 25 35 35 45 1.45 Coal: powdered 6.0 9.0 38 40 50 0.35 0.45 20 24 24 28 27 32 1.45 Coke: breeze 7.0 8.0 40 35 45 0.35 0.45 22 27 26 33 28 35 1.45 Coke: petroleum 6.5 7.5 38 37 47 0.35 0.45 24 29 28 35 30 37 1.45 Concrete aggregate (to 28 mm, moist)

17.0 19.0 34 30 40 0.35 0.45 15 25 18 30 25 35 1.40

Flour (wheat) 6.5 7.0 40 23 30 0.36 0.46 15 23 25 28 25 35 1.45 Fly ash 8.0 14.0 22 30 35 0.41 0.52 18 25 25 35 30 40 1.45 Iron ore pellets 19.0 22.0 35 35 45 0.35 0.45 20 25 26 33 28 35 1.40 Lime, hydrated 6.0 8.0 40 35 45 0.35 0.45 18 25 25 33 30 40 1.40 Limestone powder 11.0 13.0 30 40 60 0.35 0.45 15 25 23 30 28 40 1.45 Maize 7.0 8.5 30 28 33 0.45 0.58 15 25 20 30 25 32 1.40 Phosphate rock 16.0 19.0 27 35 55 0.35 0.45 19 25 22 30 25 32 1.40 Sand: coarse dry 14.0 17.0 30 30 40 0.41 0.52 15 25 22 28 25 35 1.40 Sand: quartz 15.0 17.0 30 35 40 0.35 0.45 15 22 15 22 20 26 1.40 Slag: granular, dry 10.5 12.0 40 35 38 0.36 0.47 16 22 20 25 24 28 1.40 Soya beans 7.0 8.0 23 25 32 0.47 0.60 10 15 12 18 14 20 1.30 Sugar 8.0 9.5 29 33 38 0.45 0.58 15 25 20 35 25 40 1.40 Wheat 7.5 9.0 20 26 32 0.50 0.63 15 25 18 30 25 32 1.30

† Where this table does not contain the material to be stored, testing should be undertaken. The “default material” is offered as a substitute for situations where the cost implications of using a wide property range for thedesign are minor, so that it is difficult to justify the cost of testing.

* Properties for a “default material” are shown here, for conditions where no data is available. For small installations, these properties may be adequate, but they will lead to very uneconomic large silos: testing is alwayspreferable.

‡ For Wall Type D4 (corrugated wall), see Appendix D4. † Values tabulated are for a polyethylene wall liner.NOTE: the lateral pressure ratios K for flyash and wheat were incorrect in the original table (taken from Rotter (2001)) and have now been corrected.

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Revised version of Table 5.1 Physical properties of bulk solids: characteristic values †

Type of bulk solid

Unit weight

γ

Angleof

repose φr

Effective angleof internal

friction φi

Lateral pressure Ratio

K or λ

Wall friction coefficient ‡ µ

(µ = tan φw)

Max. flowpressure

multiplier Co

γl γu φr φil φiu Km, λ m aλ WalltypeD1

WalltypeD2

WalltypeD3

aµ

Lower Upper Lower Upper Mean Factor Mean Mean Mean Factor KN/m3 KN/m3 Degrees degrees Degrees Default material * 6.0 20.0 40 25 55 0.35 1.6 0.32 0.39 0.50 1.60 1.45 Alumina 10.0 12.0 27 25 40 0.50 1.20 0.41 0.52 0.64 1.10 1.40 Barley 7.0 8.5 20 26 33 0.56 1.08 0.35 0.41 0.54 1.20 1.35 Cement 13.0 16.0 28 40 50 0.32 1.18 0.41 0.48 0.59 1.10 1.40 Cement clinker 15.0 18.0 33 42 52 0.29 1.19 0.41 0.52 0.64 1.10 1.40 Coal: black 8.5 11.0 35 40 60 0.24 1.46 0.35 0.57 0.63 1.25 1.45 Coal: brown 7.0 9.0 33 45 65 0.18 1.56 0.39 0.57 0.84 1.15 1.45 Coal: powdered 6.0 9.0 38 40 50 0.32 1.18 0.40 0.49 0.56 1.10 1.45 Coke: breeze 7.0 8.0 40 35 45 0.39 1.16 0.45 0.56 0.61 1.10 1.45 Coke: petroleum 6.5 7.5 38 37 47 0.36 1.16 0.50 0.61 0.66 1.10 1.45 Concrete aggregate 17.0 19.0 34 30 40 0.46 1.14 0.35 0.43 0.57 1.25 1.40 Flour (wheat) 6.5 7.0 40 23 30 0.61 1.08 0.34 0.50 0.57 1.20 1.45 Fly ash 8.0 14.0 22 30 35 0.51 1.06 0.39 0.57 0.70 1.15 1.45 Iron ore pellets 19.0 22.0 35 35 45 0.39 1.16 0.41 0.56 0.61 1.10 1.40 Lime, hydrated 6.0 8.0 40 35 45 0.39 1.16 0.39 0.55 0.70 1.15 1.40 Limestone powder 11.0 13.0 30 40 60 0.24 1.46 0.35 0.50 0.67 1.20 1.45 Maize 7.0 8.5 30 28 33 0.54 1.06 0.35 0.46 0.54 1.20 1.40 Phosphate rock 16.0 19.0 27 35 55 0.31 1.39 0.40 0.48 0.54 1.15 1.40 Sand: coarse dry 14.0 17.0 30 30 40 0.46 1.14 0.35 0.46 0.57 1.20 1.40 Sand: quartz 15.0 17.0 30 35 40 0.43 1.07 0.33 0.33 0.42 1.20 1.40 Slag: granular, dry 10.5 12.0 40 35 38 0.45 1.04 0.34 0.41 0.49 1.10 1.40 Soya beans 7.0 8.0 23 25 32 0.57 1.08 0.22 0.26 0.30 1.20 1.30 Sugar 8.0 9.5 29 33 38 0.46 1.07 0.35 0.50 0.63 1.25 1.40 Wheat 7.5 9.0 20 26 32 0.57 1.07 0.35 0.43 0.54 1.25 1.30

† Where this table does not contain the material to be stored, testing should be undertaken. The “default material” is offered as a substitute for situations where the cost implications of using a wide property range for thedesign are minor, so that it is difficult to justify the cost of testing.

* Properties for a “default material” are shown here, for conditions where no data is available. For small installations, these properties may be adequate, but they will lead to very uneconomic large silos: testing is alwayspreferable.

‡ For Wall Type D4 (corrugated wall), see Appendix D4.

NOTE: the lateral pressure ratios K for flyash and wheat were incorrect in the original table (taken from Rotter (2001)) and have now been corrected.

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The new version for the EN is therefore proposed with the relationships:

Max K = aK Km … (5.2)

Min K = Km / aK … (5.3)

Max µ = aµ µm … (5.4)

Min µ = µm / aµ … (5.5)

where Km is the mean value of K and µm is the mean value of µ.

It is supposed that:i) the value of aK depends on the material;ii) the value of µm depends on the wall surface type (thus several values of µm for a

given solid);iii) the value of aµ is proposed to be taken as a single value for all walls (this is not

a necessary assumption, but it simplifies the table and the process).

The values offered below are derived from upper and lower tabulated values given inthe Australian Standard (AS 3774-1996) assuming that the latter are 5%ile and 95%ilevalues (as indicated in that standard) but that the EN wishes to adopt 10%ile and90%ile values. The distributions were all assumed to be log-normal.

The resulting calculated variation factors aK and aµ for different solids are shownbelow.

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Lateral pressure ratio modifying factorFor lateral pressure ratio K, the tabulated values have been rounded to threesignificant figures (e.g. 1.07). There is no good reason to approximate these further.

Calculated modifying factor a k or a λ for lateral pressure ratio

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Aggreg

ate

Alumina

Barley

Cemen

t

Cemen

t clin

ker

Coal, b

lack

Coal, b

rown

Coal, p

owde

red

Coke,

breeze

Coke,

petro

leum

Flour (w

heat)

Fly ash

Iron o

re pe

llets

Lime,

hydra

ted

Limest

one p

owde

rMaiz

e

Phosph

ate ro

ck

Sand,

coars

e

Sand,

quart

z

Slag, fu

rnace

Soya b

eans

Sugar

Whe

at

Mod

ifyin

g fa

ctor

a

k o

r aλ

Values from AS3774-1996

ENV value

Source BPSTab16.XLS

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Wall friction modifying factorFor the wall friction, three values are given, corresponding to the three different wallsurface types D1, D2 and D3. However, in implementing the result, it has beensupposed that the variability of a given solid may be taken as a fixed amount, andsimplified values have been chosen in steps of 0.05 in the range 1.10 to 1.25.

Calculated modifying factor a µ for wall friction

1.00

1.05

1.10

1.15

1.20

1.25

1.30

Aggreg

ate

Alumina

Barley

Cemen

t

Cemen

t clin

ker

Coal, b

lack

Coal, b

rown

Coal, p

owde

red

Coke,

breeze

Coke,

petro

leum

Flour (w

heat)

Fly ash

Iron o

re pe

llets

Lime,

hydra

ted

Limest

one p

owde

rMaiz

e

Phosph

ate ro

ck

Sand,

coars

e

Sand,

quart

z

Slag, fu

rnace

Soya b

eans

Sugar

Whe

at

Mod

ifyin

g fa

ctor

aµ

Wall Type D1Wall Type D2Wall Type D3


ENV value

Source BPSTab16.XLS

Adopted modifying factor a µ for wall friction

1.00

1.05

1.10

1.15

1.20

1.25

1.30

Aggreg

ate

Alumina

Barley

Cemen

t

Cemen

t clin

ker

Coal, b

lack

Coal, b

rown

Coal, p

owde

red

Coke,

breeze

Coke,

petro

leum

Flour (w

heat)

Fly ash

Iron o

re pe

llets

Lime,

hydra

ted

Limest

one p

owde

rMaiz

e

Phosph

ate ro

ck

Sand,

coars

e

Sand,

quart

z

Slag, fu

rnace

Soya b

eans

Sugar

Whe

at

Mod

ifyin

g fa

ctor

aµ

All wall types:mean


ENV value

Source BPSTab16.XLS

For most solids, use of this data will increase the variability of solids assumed indesign. Thus the maximum design pressure will rise. If this is adopted, the overallconservatism of the complete calculation, involving discharge pressures, should bechecked. In particular, the Project Team should make sure that the adopted value ofthe discharge factor Co is adequately reduced to return the complete calculation toabout the same outcome as before.

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Material property data extracted from the CA-Silo study

The following tables content information on material properties based on differentsources and a set of recommended values. The recommended values should representphysical realistic values, but shall only be considered a first proposal which deservesmore consideration.

General remarks:Course grained materials (wheat) Has densities controlled mainly from method of fillingseem not very sensitive to test principle

Powders (cement) has densities controlled mainly from consolidation (pressure level)seem very sensitive to test principle (soil mechanics is used for the standard). Very

higt values of internal friction in the draft, version D are considered unrealistic.

Some materials (coal)- shall be seen rather a class of materials and therefore the variability may be verylarge.

CA-Silo ref.:Munch-Andersen J., L.O.Nielsen and J. Nielsen: ”Comparison of load parameters forstored materials”, Department of Structural Engineering and Materials, TechnicalUniversity of Denmark, Report S, no 1, 1997.

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WheatUnit weight Internal friction Lateral pressure

ratioWall friction

Draft, version D 7.5-9.0 26-32 0.57* or / by 1.07

0,35, 0.43, 0.54* or / by 1.25

DIN 9.0 0.60 0.25, 0.40, 0.60CA-silo 7.7-8.7 24-30 0.55-0.65 Steel: 0.28-0.40

Conc. : 0.40Proposal 8.0-8.8 24-30 0.55-0.65 Steel: 0.25- 0.40?

Conc: 0.30 – 0.45

CementUnit weight Internal friction Lateral pressure

ratioWall friction

Draft, version D 13-16 40-50 0.32* or / by 1.18

0,41, 0.48, 0.59* or / by 1.10

DIN 16 0.65 0.40, 0.45, 0.50CA-silo 16.0-16.8 34-39 0.40-0,49 Steel: 0.52-0.55Proposal 13-17 34-39 0.40- 0.50 Steel:?

Conc: ?

CoalUnit weight Internal friction Lateral pressure

ratioWall friction

Draft, version D 8.5-11.0 40-60 0.24* or / by 1.46

0,35, 0.57, 0.63* or / by 1.25

DIN 10.0 0.60 0.45, 0.50, 0.60CA-silo 7.1-11.2 26-42 0.36-0.61 Steel: 0.35-0.45

Conc. : 0.36Proposal 7.5-11.5 26-45 0.36-0.61 Steel: 0.35- 0.45?

Conc: 0.35 – 0.50?

9. Material testingThe testing of bulk solids should be always encouraged for designs in higherReliability Classes. The EN should provide an economic advantage in design to thedesigner or client who does undertake materials testing. It is important that a smallervariability can be deduced from the tests than the variability required to be used whenvalues are taken from the table of properties.

The variability of the material should be a major focus of the testing, and anappropriate statistical technique should be defined for deducing the characteristic

16


values from the measured values. Such a method is given in an Annex in theAustralian Standard and in Rotter’s Guide (2001).

10. Mass flow and funnel flow boundsThe distinction between mass flow and funnel flow in this standard must be only inrelation to the effect of the flow pattern on the wall pressures. In the ENV, the onlyeffect was in the pressures applied to the hopper, where mass flow caused larger localpressures in addition to those of funnel flow. Thus, in terms of design pressures, thedistinction to be drawn is not that of guaranteeing mass flow (as in the design foreffective function), but of identifying situations in which there is a risk of mass flow.The bounds traditionally drawn that separate mass and funnel flow are made to give asmall design zone within which mass flow is guaranteed. The figure in this standardshould, by contrast, indicate only the much larger zone in which there is a risk of massflow. Figure 5.1 has been amended accordingly.

11. Terminology for maximum load magnifierThe terminology of ‘maximum load magnifier’ is cumbersome and unclear. It wouldbe helpful to replace this with a different term.

The filling pressures are increased by a factor Co to represent discharge conditions.This factor was traditionally referred to in the literature as an “overpressure factor”,but other terms, as “flow pressure multiplier”, “discharge factor” have also been used.It would be helpful to reduce the term to two words, one of which should indicatedischarge in some sense. The Project Team has agreed that the term “dischargefactor” is probably the most suitable.

The ENV sought to clarify the fact that the value Co is only valid for slender silos byterming it the “maximum” load magnifier. Since this need remains, it is proposedhere that the lower value for squat and intermediate silos be termed instead the“reduced discharge factor”, which can be as low as 1.0.

12. Value of the discharge factor and physical phenomena itrepresentsThe discharge factor Co is used to translate the filling pressures into discharge valuesfor conditions in slender silos. Smaller values may be used in squat silos where thedischarge pressures are not so high.

The values used in the ENV were all empirical and are deemed to depend on thematerial being stored. For the TEN materials listed in the table of materials, values ofCo are given.

17


ENV 1991-4 (1995) values of discharge factor Co

1.25

1.30

1.35

1.40

1.45

1.50

Barley Cement Cementclinker

Dry sand Flour Fly ash Maize Sugar Wheat Coal

Dis

char

ge fa

ctor

or

Loa

d m

agni

fier

C o

a

For materials not listed in the table, section 7.4 gives the rule:

(3) For materials not listed in table 7.1, the maximum wall load magnifier may be obtained using:

For φ ≤ 30o, C0 = 1,35 … (7.4)

For φ > 30o, C0 = 1,35 + 0,02 (φ − 30o) … (7.5)

where:φ is the angle in internal friction measured in degrees.

It should be noted that:a) The values in the Table do not match the values given by this rule, so a material

similar to one in the table may be deemed to have two alternative values dependingon what it is presumed to be.

b) In view of (a), the values in the table should be brought into line with those foundusing the equation, by modifying either or both.

c) The Australian Standard deems the magnifier to be dependent only on thegeometry (slenderness) of the container and to increase progressively as the aspectratio becomes very large. This corresponds to higher overpressures being foundwhere the silo frictional phenomenon has a large effect on filling pressures and somatches French thinking that the wall friction coefficient may effectively fallduring discharge.

d) The DIN1055 standard makes the magnifier dependent on several parameters. e) The new revised DIN (Sept 2000) follows the ENV, but omits the material

variability. It adopts the same mean material properties as ENV, and so produces atotal load definition that is considerably less demanding of the structure. If thisnew DIN1055 is deemed to be safe, then the flow pressure multipliers for theEN1991-4 must be considerably reduced to bring them into line with each other.Otherwise the EN will typically define pressures and loads 10-15% larger thanDIN.

f) It should be noted that the total safety margin of a silo design depends on theassumed material variability, the load magnifier and the partial factor. It isimportant that the total safety margin does not become excessive by adopting a

18


large load magnifier (that is only weakly related to physical phenomena) togetherwith substantial material variability and substantial partial factors.

In relation to (a) and (b) above, the values of Co in the ENV material property table(taken from the ENV) are compared below with the values derived from the aboveEqs 7.4 and 7.5, using φ determined using K = 1.1(1 – sinφ). The equations 7.4 and7.5 were derived from this data, but the fit is poor, and either the K or the Co valuesshould be modified to make them match.

Comparison of discharge factors

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

28 30 32 34 36 38 40 42 44 46

Deduced internal friction angle phi (degrees)

Dis

char

ge fa

ctor

Co

ENV tabulated Co

Co from ENV equation

Co from ENV equation with AS3774 phi

If these equations are used with mean values of φ taken from the Australian StandardAS3774, the fit is very bad. This may be partly caused by the AS3774 values of φbeing effective angles of internal friction derived from Jenike tests (see below). Thischoice of internal friction angle tends to increase the apparent φ for powders andcohesive solids, leading to a higher derived Co and a lower deduced K.

Since most of the testing done in recent years has been undertaken by Jenike-stylelabs, it is difficult to obtain the correct data. Moreover, since most earlier testing wasinterpreted with slender reinforced concrete silos in mind, the earlier published valuesof K were not mean values but maxima and the corresponding φ values minima. It isnot easy to obtain reliable mean values of the soil mechanical internal friction anglefor a large range of different solids. The data on which to base the defined meanvalues of the material properties remains a significant problem for the PT.

19


ENV 1991-4 (1995) values of lateral pressure ratio

0.35

0.40

0.45

0.50

0.55

0.60

Barley Cement Cementclinker

Dry sand Flour Fly ash Maize Sugar Wheat Coal

Mea

n la

tera

l pre

ssur

e ra

tio

Km

13. Angle of repose (needed for squat silos)The angle of repose of a solid is not the same as the angle of internal friction. Theseangles are however similar, and older usage adopted the angle of repose as a quickmeasure of internal friction. The angle of repose was later removed from moststandards to ensure that this approximation was not continued, but there are otherreasons why the angle of repose is needed.

In squat silos, where the diameter is large and the wall height small, the total storagecapacity is much affected by the angle of repose. The point of highest contactbetween the solid and the wall is also generally governed by the angle of repose, sothe wall pressure rule requires this to be evaluated carefully. A determination of theequivalent surface in all silos also strictly needs the angle of repose to be defined first.It is therefore desirable that this material property be included in the table ofproperties.

It may be necessary to define two angles of repose, one for conical piles and the otherfor wedge-shaped piles, but these may be close enough for the conical pile value to besufficient.

The angle of drained repose is generally not required as part of a silo pressureassessment for worst case loading conditions.

14. The role of patch loadsThe patch load was devised for two purposes, as outlined here.

Silos that are either filled or discharged eccentrically to the vertical axis are subject tounsymmetrical pressures relative to that axis. These pressures are caused byasymmetries of solids packing and of solids flow.

Silos that are concentrically filled and discharged are also subject to unsymmetricalpressures, though these are generally smaller than those noted above. The asymmetryarises from geometric imperfections in the silo walls and minor asymmetries ofpacking that can cause disproportionately large asymmetries in the pressure pattern.

20


Where there are no eccentricities of the inlet or outlet, the patch load must serve toprovide a minimum level of asymmetrical load, to ensure that the silo is able to resistminor deviations from symmetry.

Where eccentricities exist, the patch load was also used to represent the increasingasymmetrical loads, though the loading pattern of the patch load is rather differentfrom that due to real eccentricities. For this reason, the ENV restricted the use of thistreatment to eccentricities that were less than 0.25dc, where dc is the characteristichorizontal dimension of the silo.

In the changes between the ENV and EN versions of this standard, the patch loadshould be adopted for those roles for which it is particularly suited, and other methodsused where it is less appropriate.

Filling patch loadThe patch load for filling conditions was not used in DIN 1055 (1987), but wasintroduced into the ENV because there is extensive experimental evidence thatunsymmetrical pressure patterns develop during the filling and storing process. Themagnitude of these unsymmetrical pressures is highly correlated with fillingprocedures, geometric imperfections on the silo wall, and anisotropy of the storedsolid after filling. The most important feature that can be easily captured in the designprocess is the effect of eccentricity in the trajectory of the falling solids, and this isnow represented in the EN by use of the eccentricity ef, the maximum eccentricityoccurring on the solids trajectory. This value is not restricted to any dimension.

It should be noted that powders are commonly aerated when they are placed in thesilo, leading to a level, or almost level top surface and a relatively homogenousparticle placement structure within the stored solid. For this reason, the EN permitsthe designer to ignore the filling patch pressure for powder solids.

The filling patch load is always superseded in design importance by the dischargepatch load, except in those silos that do not need to be designed for dischargepressures or the discharge patch load. This means that squat silos, silos withguaranteed internal flow and silos with mechanical discharge systems will be affectedby the filling patch pressure, but others will not.

The ENV used a rather heavy filling patch load because the variability of theproperties of stored solids was considerably underestimated. With a more realisticestimate of this variability now adopted into the EN, it has been possible andappropriate to reduce the magnitude of the filling patch load. The revised ruledemands a 10% increase in pressure when the eccentricity of filling is zero, and a20% increase if solids strikes the wall during filling.

Discharge patch loadThe discharge patch load was originally adopted into the ENV from the DIN 1055standard. The rule in DIN was based on a careful calibration against the results ofmany experiments on different solids. The rule in DIN was thought by the ENVproject team to be rather complicated, and several rather rough approximations weremade when it was introduced into the ENV. If these approximations were retained inthe EN, it would be difficult to achieve the same reliability in all silo designs, and

21


considerable discrepancies would persist between the requirements of DIN and thoseof the EN. It therefore seems appropriate to return to the more complicatedformulation used in DIN, now calibrated differently to account for the materialproperty variability that is properly recognised in the EN.

15. Separation of filling and discharge eccentricitiesThe effects of eccentricities of filling and discharge are quite different.

Filling eccentricities have two effects.

In squat silos, they have a very large effect because the difference between highestcontact points on the two sides of the silo diameter is great and the solid effectivelyapplies a large overturning moment on the silo. The nature of this loading is notrepresented at all well by a patch load.

The second effect of filling eccentricities is quite different in slender silos: the solidthat lies immediately beneath the impacts of the filling process develops a closerpacking structure, anisotropy and a higher local density. If this denser material iscentrally located, there is little loss of symmetry. However, when the denser materialoccurs close to the wall at points well below the solid surface, highly unsymmetricalpressures may develop on the wall. The patch load provides a good representation ofthis phenomenon, but the eccentricity that matters is not the eccentricity of the top ofthe pile of solids when the silo is full, but the maximum filling eccentricity that occursduring the filling process.

silocentreline

α

ef

eo

β

θc

et

surfaceprofilefor full

condition

ec

For this reason the Project Team decided to divide the filling eccentricity into twoseparate factors governed by two differently assessed eccentricities (Fig. 1.1b). Thefirst, et, defines the centre of the top pile of solid: it is useful for squat silo eccentricfilling problems. The second, ef, is the maximum eccentricity of the top of the heapduring the entire filling process. It is useful for assessing the patch load to representunavoidable asymmetries in the loads.

These two eccentricities can only be determined by a calculation based on the solidstrajectory into the silo, and for this reason, these eccentricities are related to the chuteplacement and end slope.

22


Discharge eccentricities have a very large effect on very slender silos, where achannel of flowing material against the wall causes a serious local pressure reduction,leading to bending of the wall and large membrane stresses. Many failures due toeccentric discharge have occurred in recent years in both metal and concrete silos.The patch load does not represent this loading well.

In squat silos, moderate discharge eccentricities (eo < 0.25dc) have a rather smalleffect because the flow channel is internal. This eccentricity is therefore not soimportant in squat silos.

In view of the above, the PT divided the effects of filling eccentricities into twocategories and separated it from the discharge defined separate rules for eachsituation. The patch load is retained where it represents the silo pressure phenomenawell.

16. Patch load rule application for large eccentricitiesIf the above recommendation on filling and discharge eccentricities is adopted, thepatch load rule should be used only in relation to accidental asymmetries in anotionally symmetrical silo.

The effect of the eccentricity, either for filling or for discharge, is clearly dependenton the aspect ratio of the silo. It is therefore suggested here that the patch load beused wherever it represents the pressure pattern phenomenon well, and that specialrules are developed specifically for filling eccentricities and for dischargeeccentricities. These special rules should be particularly intended for use on silos inReliability Class 3, where the structural analysis requirements are more demanding,and the silos have been placed in this class because of their size and the difficulties ofdesign.

For silos in Reliability Class 1, no special treatment should be necessary and no patchis needed.For silos in Reliability Class 2, the patch load, and a simple treatment of highlyeccentric discharge pressures should be used.For silos in Reliability Class 3, the full treatment of patch loads with properlycalculated eccentric flow channel pressures should be used.

The special rule for filling eccentricities should focus on squat silos, with a rule thatcauses differential pressures across the diameter, leading to an overturning of thewhole silo, and increased vertical compression on the side where the filling pile ofsolid lies.

The special rule for discharge eccentricities should focus on slender silos, with aspecial load case representing a channel of flowing solid down one side. A sampleprocedure of this kind was devised by the American Concrete Institute committee,and similar rules can be developed. Large eccentricities in silos of significant sizerequire a finite element analysis (see ENV1993-4-1), so there is no advantage inmaking this load definition simple and suited for hand analysis.

If these two features are adopted, there is no need to restrict the eccentricity of theoutlet or of the filling spout.

23


17. High eccentricity flow and pressuresAs noted above, a special rule should be developed for high eccentricity dischargepressures for silos in Reliability Class 3. The Australian Standard AS3774 is the onlystandard in the world that currently has such a rule, though the American ConcreteInstitute has tried to gain acceptance for a rationally-based rule for some years.

A proposal has been made for the EN by Rotter, based on the method given in theGuide for the Economic Design of Circular Metal Silos and originally proposed in1986.

18. Extension of simple rules to wider range (don’t have therestriction of both eccentricity of discharge and diameter limit to 5m)For silos of small overall size (Reliability Class 1), simple rules can be produced thatpermit large eccentricities without complicated calculations.

For silos of moderate overall size (Reliability Class 2), simple rules can be used forconcentric filling and discharge cases, but silos with highly eccentric discharge outletsshould be treated as more complicated.

For silos of great size and complexity (Reliability Class 3), finite element analysis isrequired for design by ENV 1993-4-1 and there is no benefit in simplifying theloading case down to a rule designed for hand analysis.

19. Simplified rules 5m restriction too smallThis simplified rules that were previously used for silos of less than 5m diameter cannow be simplified even further for use with Reliability Class 1. In addition, somesimplifications may be possible for silos in Reliability Class 2.

Discussion should also focus on where the bounds on sizes should be between theindividual classes.

20. Rectangular silo pressuresThe pressures in rectangular silos are normally taken as equal to those in a circularsilo with the same cross-sectional area to perimeter ratio A/U. This is firmly based onJanssen’s equilibrium analysis. However, the pressure on the wall of a rectangularsilo is assumed to be constant at a given level (identical at the wall mid-side and in thecorner).

Recent research has shown that stiff-walled rectangular silos experience higherpressures at midside than in the corner, inducing larger bending moments in the wall.The pressure pattern should probably be amended to reflect this detrimental effect.

Much recent experimental and theoretical research on flexible walled rectangular siloshas shown that the pressures at the midside of the wall are much smaller than those inthe corners. This means that the bending moments developing in the walls andcorners are smaller than a uniform pressure design would suppose. If advantage istaken of this effect, the walls of flexible silos can be made lighter, making them evenmore flexible, and considerable improvement in design can be achieved.

24


Thus, for silos in Reliability Class 3, where considerable design effort is required,there should be two alternative design methodologies with different pressure regimesin a rectangular silo: a) stiff walled (concrete and stiffened metal silos)b) flexible-walled (unstiffened metal silos)

Patch loads Recent research on the effect of patch loads on rectangular silos suggests that theseloads make only a minor difference to the design, and that the complexity of designthat they introduce is not justified by the difference in outcome. It is not clear thatpatch loads are needed if the pressure distribution is made non-uniform according tothe proposal outlined above.

The revised rule now states that if the wall is subject to first order bending effectswhen the uniform Janssen pressures are applied, the patch load can be ignored. Sincethe patch load was only intended to induce a limited amount of bending, it can besafely ignored in this case.

21. Internal ties in rectangular silosInternal ties are covered by the rules of ENV1993-4-1, which have been adopted fromFrench practice (PT4-25, page 20). This is a structural problem more than a loadingcase, but some mention could be made of internal ties within ENV1991-4. The rulehas been limited to application to Reliability Classes 1 and 2 because the expressionsare not known to be valid for larger construction than 5m width and 20m height.

A new section has been added as “6.5 Loads in rectangular silos with internal ties” toprovide rules for this case. These rules should be carefully reviewed by the PT.

22. No distinction between concrete and steel: doesn’t the stiffnessmatter?The patch load was devised to represent unsymmetrical pressures that were observedin experiments. They are thus intended to act as substitute loads that induce stressresultants in the structure that are similar to those induced by the real phenomena,even though the latter are not at all well represented. Since the substitute load isintended to induce similar stress resultants, the relationship between local pressuresand induced stress resultants (the structural analysis) has a strong bearing on howthese patch pressures should be defined. In particular, thick-walled and thin-walledcylinders respond quite differently to local pressures, so a different definition isneeded according to the form of construction.

The patch load was devised in the context of stiff-walled concrete silos. The directapplication of this rule to thin-walled steel silos has not been demonstrated, and thedifferent form of patch load is intended to represent the effects of asymmetry in metalsilos quite well.

The above discussion of rectangular silos also suggests that the stiffness of thestructure is particularly important in rectangular silos. The rules should be amendedto reflect this difference.

25


For circular silos, it seems likely that the horizontally uniform component of pressureat any level will be similar for stiff and flexible walled silos, because thecircumferential stiffness is very high in both designs. However, the stiffness of theresponse to non-uniform or asymmetrical pressures is very different for thick-walledand thin-walled silos, and the patch loading rules should reflect this. The patch loaddefined in ENV1991-4 to be applied to a circular steel silo (pressure pattern pocosθ) isless demanding than the discrete rectangular patches used for stiff-walled silos toaddress this concern.

23. Planar silosRules should be included for planar silos if possible.

24. Coefficient for flat bottoms Cb: is 1.2 too low? Or does materialvariability cover this phenomenon so that Cb should be omittedThe earliest standards for silos were all primarily concerned with defining themaximum normal pressure against the wall of a tall concrete silo. This maximumpressure occurs when the wall is as smooth as possible and the lateral pressure ratio isas high as possible. The values of material parameters given in the tables reflectedthese extreme material property values.

However, a disadvantage of using these extremes (min µ and max K) was that thevertical stress in the solid was always underestimated. As a result, the total load thatwould regularly be applied to the hopper was underestimated. This was overcome byretaining the fixed (extreme) values of material properties relevant to the verticalwalls, but increasing the load on the bottom by using a bottom loading coefficient Cb.This coefficient raised the calculated bottom pressures to values seen in tests.

The justification given for this bottom load coefficient was often different, suggestingthat the increase in bottom load was caused by falling solid or impact, but there islittle evidence that static equilibrium was ever seriously in error, and it seems morelikely that the underestimate arose chiefly from the choice of values for the materialproperties.

There are a few solids for which falling solid, collapsing arches or impact arepotential events. These solids and the phenomenon concerned should be separatelyidentified and the rule made specific to them. Solids in this category might includehighly cohesive solids in slender silos and mechanically interlocking solids such ascement clinker. A draft rule has been suggested for these cases.

One bad feature of the bottom load multiplier Cb is that it makes no sense to have asingle value that is used on all bottoms. Where the silo has a moderately squatvertical-walled section above the hopper, wall friction on the vertical wall does notsupport much of the total weight of solids. The calculated vertical stress in the solidat the transition is then close to the total weight of solid. If this vertical stress is thenmultiplied by a factor of 1,2 or more, it can easily exceed the total weight of solids,suggesting that more load is applied to the hopper than can arise from the weight ofsolids. If some justification of this idea is attempted in terms of collapsing arches, itmay be noted that arching is least likely to occur in squat vertical wall geometries, and

26


most likely in very slender (tall) silos, so the justification is applied to entirely thewrong silo geometries.

By introducing the variability of material properties, the main problem of bottom loadmagnifiers is overcome. Two load cases are examined: one gives the maximumnormal pressure against the vertical wall; the other the maximum vertical stress in thesilo just above the hopper. The equivalent bottom load magnifier that arises fromthese two load cases using the material variability factors of 0,9 and 1,15 in the ENVis approximately 1,3. There is therefore no real case for introducing a bottom loadmagnifier for all but highly cohesive and mechanically interlocking solids.

25. Hopper loadsThe rules in ENV1991-4 were empirically based and lead to several strangeanomalies, some of which were pointed out by the comments on the ENV fromseveral countries. These rules should be substituted by rules with a more rationalbasis, that lead to similar structural designs for the typical cases that were consideredwhen the empirical rules were developed.

The method suggested as an alternative is based on the Dabrowski / Walker analysisof hopper pressures (converging equivalent to Janssen for vertical walls) with normalpressure ratios from Walker and the test results of a presented in Rotter’s Guide(2001) could be adopted by the PT as a basis for new rules in the EN.

Perhaps the DIN 1055 hopper method could be attached as an Annex to permit itscontinued use, but the weight of negative comments on this method from severaldifferent countries suggests that this is not a good choice to make for the EN.

26. Corrugated wallsThe PT indicated that it is important to include rules for silos with metal corrugatedwalls. Several different existing documents contain similar rules for such loads, andthe rule for the EN has been taken from Rotter (2001) which explains its sources.

27. Pressure strengthening effect for bucklingThin walled silos that are susceptible to buckling gain strength as a result of theinternal pressure within them. The design value of this internal pressure should be thelargest reliable co-existent pressure that is present when the buckling may occur. Forthis, it is necessary to ensure that a consistent set of material properties is used toevaluate both the axial compression in the wall and the coexistent internal pressure.

This matter is described quite fully in Rotter’s Guide (2001).

The ENV 1993-4-1 standard for silo structures has the paragraph:

(6) The elastic pressurised imperfection factor αpe should be based on the smallest local internalpressure (a value that can be guaranteed to be present) at the location of the point being assessed, andcoexistent with the axial compression:

αpe = αo + (1 − αo)

p̄

p̄ + 0,3

αo

... (5.14)

27


with:

p̄ = p r

t σxRc

where:p is the minimum reliable local value of internal pressure.

Thus, it is vital that EN 1991-4 defines the value of this “minimum reliable localvalue of internal pressure” for thin-walled silos.

This question is only covered by a note in Section 7 of the ENV 1991-4 which reads:

NOTE: For shell structures minimum (support) loads may be the unfavourable loads

This note is completely inadequate to deal with the need to specify:a) what material properties should be adopted for this calculationb) that the material properties should be consistent for a given load casec) that it is the largest reliably present pressure (which is generally the smallestcalculated pressure) that must be used for the buckling calculation

The best arrangement would be to move Section 7 towards the front of the standard,and to close this new section with a statement of the different property extremecombinations that must be used, together with a clear statement that each set ofproperty extremes should constitute a separate load case for structural design.

28. Squat silos separated into squat and intermediateThe ENV 1991-4 separates silos into slender and squat silos, but then has twocategories of geometry for squat silos. These are the truly squat, for which specialrules are given, and then silos between the limit of truly squat and the limit of slendersilos. It would be a much neater arrangement to define these into three categories:slender, intermediate and squat. Simple rules for slender and squat silos can then bewritten, and the intermediate category can be taken as a blend of the two, as in theENV rule.

The definitions of geometry then become:

a) Slender silos A silo in which the overall aspect ratio of the stored solid hb/dc exceeds 1.50. b) Intermediate aspect ratio silos A silo in which the overall aspect ratio of the stored solid hb/dc lies between 1.00 and1.50. c) Squat silos A silo in which the overall aspect ratio of the stored solid hb/dc is less than 1.00.

This proposal has been drafted into the revised EN version.

28


29. Squat silo rulesThe design rule for very squat silos involves a two-part pressure distribution. Atsmall depths below the highest wall-solid contact, the normal pressure is deemed toincrease linearly with depth, until it reaches the same value as would be obtained fromthe Janssen equation for slender silos.

ph

h

zhLJ

Equivalent surfaceho

The approximate rule in ENV 1991-4 looks fine for normal pressures, and using handcalculations, but this is not the only load case of importance. The rule presentsconsiderable problems when the vertical load in the wall is to be evaluated.

Unfortunately the intersection point hLJ cannot be defined using a simple equation:the distance hLJ is the solution of:

hLJλzo

+ e-hLJ /zo = 1 +

hoλzo

Whilst this may not seem to be a problem when normal pressures are beingconsidered, it leads to a complicated evaluation for the vertical force developing in thesilo wall, since the expression for the vertical force depends on a depth which cannotbe written explicitly and is not easily evaluated. A better treatment of the wall pressures in squat silos is to use the semi-empiricalexpression of the Reimbert theory [1976], suitably generalised to accommodate amore general expression for the natural lateral pressure ratio λ of the solid [Rotter,1983b, 2000b]. The normal pressure is then given by:

phf = pho

1 −

z − ho

zo − ho + 1

-2

and the frictional traction on the wall at any level is given by:

pwf = µ phf

where pho and zo have the same meaning as in Janssen’s equation, and ho is the valueof z at the highest solid-wall contact, which for a symmetrically filled circular silo ofradius r is given by:

ho = r3 tanφr

where φr is the angle of repose of the solid.

29


The above leads to simple expressions for the hoop and vertical forces in the wall:

nθ = r pho

1−

z−ho

zo−ho+1

-2

nx = − µ pho (z − ho)2

( )z + zo − 2ho

The above generalised Reimbert equation leads to the same result as Janssen atgreater depths, but generalised Reimbert provides a most useful conservative estimateof pressures near the surface in squat silos, whilst satisfying all the equilibriumrequirements and boundary conditions. It is recommended that the Reimbert equation is used for squat silos.

30. Squat silos with high filling eccentricityAs noted above, a high eccentricity of the top pile after filling of a squat silo leads tounsymmetrical pressures that induce large vertical forces in the wall, which areparticularly important in thin-walled metal silos (especially where these are large andvery light constructions). A new rule has been devised for this condition. Thepressures down any meridian are deemed to follow the pattern of the Reimbert theory(which gives zero pressure at the top contact between the solid and wall), and theeccentric filling pressures are determined according to the theory of Rotter (1983).The membrane theory of shells is used to deduce the vertical force developing in thesilo wall down the most filled side. This is added to the vertical force due to wallfriction. It should be noted that the most filled side has pressures that are effectivelythe same as if the silo were symmetrically filled to the same level, so the effect ofunsymmetrical filling has no impact on the design normal pressures on the wall.

dc

et

zs

Highest wallcontact with solid

Figure 5.5 Filling pressures in an eccentrically filled squat or intermediateslenderness silo

The new rule is given by the following:(4) The resulting additional vertical force (compressive) in the wall nz(z) per unitlength of circumference at any depth z below the point of highest wall contact is:

nz(zs) = 0,04 pho zs tanφr (et / r) (Z2 - 7Z - 6) … (5.77)

30


in which:

pho = γµ

AU =

γ r2µK … (5.78)

Z = zsB … (5.79)

B = r

2µK – ho … (5.80)

ho = r tanφr [1 - (et / r)2] / 3 … (5.81)

wherezs is the depth below the highest point of solid contact with the wall φr is the angle of repose of the particulate solidr is the radius of the circular silo wall et is the radial eccentricity of the top of the filling pile (figure 1.1b and 5.5)The above equation is only empirical in that the polynomial function of Z attempts tomatch the actual variation of axial force with depth. The fit of the empirical fit to theactual variation with depth is shown in the following images:

Variation of axial membrane stress at z/A = 1 with eccentricity

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Dimensionless eccentricity of fill: tan(phi)*Re/A

Nz/

Nzo

ApproxNz/Nzo

Variation of best fit cubic coeffs with T

y = 0.04x

y = -0.248x

y = -0.2892x

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Value of T

Coe

ffic

ient

s a1-

a3

a1a2a3Linear (a3)Linear (a1)Linear (a2)

Reference:Rotter, J.M. (1983) “Structural Effects of Eccentric Loading in Shallow Steel Bins”, Proceedings,Second International Conference on the Design of Silos for Strength and Flow, Stratford upon Avon,Nov., pp 446-463.

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31. Retaining silosRules for these extremely squat (hc/dc < 0,4) structures, known in France as“magazins de stockage” were requested by French mirror group in March 2002. ThePT discussed what term should be used in English, since this structural form is notknown to have a name in English. They considered “stock silos”, “stockage stores”and similar terms, before deciding that the walls had more in common with retainingwall structures than anything else. They therefore chose the term “retaining silos”.

The key consideration in the development of the proposed rule was that it shouldblend smoothly with the rules for retaining walls given in EN 1997, and with the rulesfor squat silos. The adopted rule gives a linear pressure variation with depth that is inagreement with the result that would be obtained by application of soil mechanicstheory. It is in accordance with EN 1997 Section 9.5.2.

The normal pressure against a vertical wall is given by:pn = K (1 + sinφr) zs where zs is the depth below the highest stored solid contact with the wall and φr is theangle of repose.

32. Actions due to thermal differentials

During consideration of the final draft of EN 1991-1-5 “Thermal actions”, it becameevident that the provisions in that standard do not cover the principal problems ofthermal differentials in silos. The critical missing element was the fact that thermaldifferentials in silos lead to large pressures as a result of the stiffness of the storedsolid. If appropriate rules were to be introduced into EN 1991-1-5, then it wouldrequire extensive information to be given concerning the assessment of the stiffness ofparticulate solids and methods of measuring that stiffness. It was therefore proposedthat these rules should be placed within EN 1991-4, where phenomena associatedwith particulate solids are located.

Two problems are known in this regard: the shrinkage of a thin metal silo structureonto a stiff thermally inert stored solid following a sudden fall in ambienttemperature; and the temperature differential associated with the filling of a silo withhot solids, leading to severe local bending of the wall near the solid surface. Bothproblems are given a brief treatment, and it is hoped that these rules will be improvedwith time.

The rule for shrinkage of a thin metal silo onto a thermally inert solid is taken fromthe Australian Standard (AS 3774), which adopted the analytical treatment ofAndersen (1966). Whilst this treatment does not account for the effects of changes inthe mobilisation of wall friction, which can have a drastic effect, it is satisfactory forrelatively squat silos with relatively small thermal differentials.

Andersen, P.F. (1966) “Temperature Stresses in Steel Grain Storage Tanks”, Civil Engineering, ASCE,Vol. 36, No. 1, pp 74-76.

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The rule for silos filled with hot solids remains a principle at the present time, until aquantitative rule can be developed.

33. Pressures on manholes

Local pressures on manholes are now included, with the local pressure increased by afactor of 2 for the manhole design only. This rule has been placed in Section 3.3.

34. Tanks requirementsAnnex A in the steel structures code for tanks ENV 1993-4-2 could be adopteddirectly into EN1991-4, as intended by the drafting project team for the tanksstandard.

Issues that are deemed outside the scope of the EN

1. Interaction of solid stiffness with structureThere are two issues in relation to this:a) In relation to buckling, the PT thought it is too difficult to develop a sound andsafe rule, but a couple of sentences should be written into the EN to indicate the effectof solid stiffness on the buckling strength,

b) For rectangular silos, the PT thought that the effect of the pressure distributionshould be addressed. The comments outlined in the section on rectangular silos abovedeals with this question.

2. Dust explosionsThe PT considered that it is too difficult to set out complete rules for dust explosions,but warnings and advice should be included within the EN. Following a contributionfrom Prof. Eibl and Dr Ruckenbrod, an annex has been added for special explosiveaspects in relation to silos.

3. Silage silosThe PT considered that it is too difficult to set out complete rules for silage silos, butwarnings and advice should be included within the EN.

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background discussion document for en 1991-4 · background discussion document for en 1991-4 june...

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