51989151 din-1055-6-2005 silos

DIN 1055-6:2005-03

CONTENTS

Page

Foreword 7

1 scope 8

2 references to other standards 10

3 terms and symbols 11

3.1 terms 11

3.2 symbols 15

3.2.1 General 15

3.2.3 Latin letters, capital 15

3.2.3 Latin letters, small 17

3.2.4 Greek letters, capital 20

3.2.5 Greek letters, small 20

4 illustration and classification of actions 21

4.1 illustration of action in silos 21

5.6 principles of calculations for explosions 30

6 bulk material parameters 31

6.1 general 31

6.2 bulk material parameters 32

6.2.1 General 32

6.2.2 Determination of bulk material parameters 34

6.2.3 Simplified procedure 35

6.3 measurement of bulk material parameters in tests 35

6.3.1 Experimental determination 35

6.3.2 Bulk material density, γ 36

6.3.3 Coefficients of wall friction µ 36

6.3.4 Angle of inner friction, iϕ 36

6.3.5 Horizontal load ration,K 37

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6.3.6 Cohesiveness, 37 C

6.3.7 Bulk material correction value for the reference-surface load 37 opC

7 loads on vertical silo walls 38

7.1 general 38

7.2 slim silos 39

7.2.1 Fill loads on vertical silo walls 39

7.2.2 Discharge loads on vertical walls 44

7.2.3 Uniform increase of loads in place of reference-surface loads for fills and

discharges of the load-types for circular silos 49

7.2.4 Discharge loads for circular silos with large eccentricities during discharge 50

7.3 low silos and silos of medium slimness 55

7.3.1 Fill loads on the vertical walls

7.3.2 Discharge loads on the vertical walls 57

7.3.3 Large eccentricities for filling in of circular low silos and circular silos

of medium slimness 59

7.3.4 large discharge eccentricities for filling in of circular low silos and

Circular silos of medium slimness 60

7.4 silos with braced walls 61

7.4.1 Fill loads on vertical walls 61

7.4.2 Discharge loads on vertical walls 62

7.5 silos with fluidized bulk material 62

7.5.1 General 62

7.5.2 Loads in silos for storage of fluidized bulk material 62

7.6 temperature differences between bulk material and silo structure 63

7.6.1 general 63

7.6.2 loads due to a decrease in the surrounding atmospheric temperature 64

7.6.3 loads due to filling-in of hot bulk materials 64

7.7 loads in rectangular silos 65

7.7.1 Rectangular silos 65

7.7.2 Silos with internal braces 65

8 loads in silo hoppers and silo bottoms 65

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8.1 general 65

8.1.1 Physical parameters 65

8.1.2 General rules 67

8.2 horizontal silo bottoms 69

8.2.1 Vertical loads on horizontal silo bottoms in slim silos 69

8.2.2 Vertical loads on level silo bottoms in low silos and silos of

Medium slimness 69

8.3 steep hoppers 71

8.3.1 Mobilized friction 71

8.3.2 Fill loads 71

8.3.3 Discharge loads 71

8.4 flat hoppers 72

8.4.1 Mobilized friction 72

8.4.2 Fill loads 73

8.4.3 Discharge loads 73

8.5 hopper loads in silos with air-injection equipment 73

9 loads on tanks 74

9.1 general 74

9.2 loads due to stored fluids 74

9.3 parameters for fluids 74

9.4 suction loads due to insufficient aeration 74

Annex A (informative) Basis for the Planning of Structures

– Rules that complement DIN 1055-100 for silos and tanks 75

A.1 general 75

A.2 border limit for load capacity 75

A.2.1 part-safety correction value 75

A.2.2 Actions on structures - Actions in silos and tanks correction value

75

A.4 conditions for calculation and action-combinations for the

Requirement categories 2 and 3 76

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A.5 action-combinations for the

Requirement category 1 77

Annex B (normative) Actions, Part-Safety Factors and Composite

Correction Values for the actions on tanks 78

B.1 general 78

B.2 actions 78

B.2.1 loads from stored fluids 78

B.2.2 loads from internal pressures 78

B.2.3 loads from temperature changes 78

B.2.4 intrinsic loads 78

B.2.5 loads from insulation 78

B.2.6 distributed working loads 79

B.2.7 concentric working loads 79

B.2.8 snow 79

B.2.9 wind 79

B.2.10 low pressure due to insufficient aeration 81

B.2.11 seismic loads 81

B.2.12 loads due to connecting structures 81

B.2.13 loads due to non-uniform settlement 81

B.2.14 catastrophic loads 81

B.3 part-safety correction values for actions 81

B.4 combination of actions 81

Annex C (normative) measurement of bulk material parameters for

Determination of silo loads 82

C.1 general 82

C.2 application 82

C.3 symbols 82

C.4 terms 83

C.5 taking of specimens and their preparation 83

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C.6 determination of bulk material density γ 84

C.6.1 short description 84

C.6.2 test apparatus 84

C.6.3 process / procedure 85

C.7 wall friction 85

C.7.1 general 85

C.7.2 co-efficient of wall friction µm for the determination of loads 86

C.7.3 angle of wall friction ϕwh for examining the flow behaviour 87

C.8 horizontal load ratio K 88

C.8.1 direct measurement 88

C.8.2 indirect measurement 89

C.9 stability parameters: cohesiveness c and angle of internal friction ϕi 89



C.10 effective elasticity module Es 93



C.11 determination of the upper and lower characteristic values for the bulk

Material parameters and the determination of the conversion factor a 96

C.11.1 testing principle 96

C.11.2 assessment methods 97

Annex D (normative) assessment of bulk material parameters for determination

Of silo loads 99

D.1 goal 99

D.2 assessment of the wall friction co-efficient for a corrugated wall 99

D.3 internal friction and wall friction of a coarse-grained bulk material

Without fine particles 100

Annex E (normative) details of bulk material parameters 101

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Annex F (normative) determination of the flow profile, mass flow

And core flow 102

Annex G (normative) seismic actions 103

G.1 general 103

G.2 symbols 103

G.3 conditions for calculation 103

G.4 seismic actions 104

G.4.1 silo bottom and foundations 104

G.4.2 silo walls 104

Annex H (normative) alternative rules for determination of hopper loads 106

H.1 general 106

H.2 terms 106

H.3 symbols 106

H.4 conditions for calculation 106

H.5 loads on hopper walls 107

H.6 determination of connecting forces at the hopper junction 108

H.7 alternative equations for the hopper load correction values Fe for

The load discharge 108

Annex I (normative) action due to dust explosions 109

I.1 general 109

I.2 application 109

I.3 additional standards, guidelines and rules 109

I.4 dusts of explosive nature and their parameters 109

I.5 ignition sources 110

I.6 protective measures 110

I.7 calculation of components 111

I.8 calculation of explosive overpressure 111

I.9 calculation of negative pressure 111

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I.10 securing the closing element of the discharge opening 111

I.11 recoil forces due to pressure release 111

Diagrams

Diagram 1 illustration of silo bins with nomenclature of geometric

Parameters and loads 9

Diagram 2 basic flow profile 26

Diagram 3 flow profile with pipe flow 27

Diagram 4 flow profile with mixed bulk material flows 28

Diagram 5 effects of slimness (height to diameter ratio) on the mixed bulk

material flows and the pipe flows 28

Diagram 6 customized arrangements for fill and discharge 29

Diagram 7 conditions under which pressures due to mass flow arise 32

Diagram 8 symmetric discharge loads around the vertical silo walls 40

Diagram 9 longitudinal and cross-sectional illustrations of the load diagrams of

reference-surface loads 42

Diagram 11 longitudinal and cross-sectional illustrations of the load

diagrams of reference-surface loads during discharge 47

Diagram 12 flow channels and pressure distribution during discharge

with large eccentricities 52

Diagram 13 loads in low silos or silos with medium slimness after the

fill (fill loads) 56

Diagram 14 fill pressures during eccentric filled low silos or silos with 59

medium slimness

Diagram 15 fill pressures in a braced-wall silo 62

Diagram 16 boundaries between steep and flat hoppers 66

Diagram 17 distribution of the fill pressures in a steep and flat hopper 67

Diagram 18 bottom loads in low silos and in silos with medium slimness 70

Diagram 19 discharge pressures in a hopper with a steep and a flat inclination 72

Diagram B.1 coefficients of pressure for wind loads in circular cylindrical tanks 80

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Diagram C.1 equipment for determination of γ 85

Diagram C.2 test procedure for determination of the coefficients of wall friction 87

Diagram C.3 test procedure for determination of Ko 88

Diagram C.4 test procedure for determination of the angle of the internal

Friction ϕi and ϕc and the cohesiveness based upon the tension

Created by pre-compression 90

Diagram C.5 test procedure for determination of the elasticity module during

loading and unloading 94

Diagram D.1 measurement of the profiling of the wall surface 100

Diagram F.1 demarcation of mass and core flow conditions in conical and

cuneiform hoppers 102

Diagram G.1 possible rearrangements oat the bulk material surface due to

Seismic actions 103

Diagram G.2 seismic actions on the substructure (e.g. braces) 104

Diagram G.3 cross-section through the vertical silo shaft with details of

the additional horizontal loads due to seismic actions 105

Diagram H.1 alternative rules for the hoppers 108 Tables

Table 1 classification of conditions for calculation 23

Table 2 relevant parameters for different load estimates 25

Table 3 categories of wall surfaces 34

Table A.1 composite correction values 77

Table C.1 test parameters 91

Table C.2 typical values for the coefficients of variation for the bulk

Material parameters 98

Table E.1 bulk material parameters 101

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Foreword

This standard was compiled in the NABau-AA 00.20.00 “Actions on Buildings”

(Spiegelausschuss zu CEN/TC/ 250/SC 1).

This standard is part of the new series DIN 1055 Actions on Structures, which consists of

the following parts:

Part 1:

Part 2:

Part 3:

Part 4:

Part 5;

Part 6;

Part 7:

Part 8:

Part 9:

Part 10:

Part 100:

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References to standards belonging to the series DIN 1055, contained in this standard,

refer exclusively to the above-mentioned new series DIN 1055.

This standard was developed by the Work Committee NABau 00.20.00 on the basis of

DIN V ENV 1991-4 and conforms largely to the draft manuscript prEN 1991-4.

Any deviations of this standard from the above-mentioned manuscript prEN 1991-4

conform by and large with possible commitments to the national safety standards so that,

in the case of an eventual ratification of EN 1991-4, this standard can be compatible in

the national context.

Revisions Vis-à-vis DIN 1055-6:1987-05 the following revisions have been made:

a) structural adaptation in line with the EN 1991-4

b) terminology adaptation in line with the EN 1991-4

c) adaptation of the calculation and safety concepts in line with the EN 1991-4

d) incorporation of regulations for actions due to dust-explosions

e) incorporation of regulations for actions due to earthquakes

f) incorporation of regulations for actions due to bulk material properties

Earlier Editions

DIN 1055-6: 1964-11, 1987-05

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1. Scope

1) This standard contains general principles and information relating to the influences

for the design and calculations of silos for storage of bulk materials and for tanks.

It is to be applied in association with the other parts of the series DIN 1055.

2) This standard also contains stipulations for actions on silos and tanks which

extend beyond the direct action caused by the stored bulk material or fluids (e.g.

effects of temperature differences).

3) While applying the rules for calculations made for silo bins and silo structures the

following geometric limitations should be kept in mind:

--- The cross-sections of the silo bins are limited to the instances shown in diagram 1d.

Smaller deviations are allowed under the condition that the possible effects on the silo

structures due to the pressure changes resulting from these deviations will be taken into

account.

--- The foll. Limits will apply for the geometric measurements:

10<c

b

dh

mhb 100<

mdc 60<

--- The transition from the vertical silo shaft into the hopper takes place in a simple

horizontal plane (also possible in several steps) (see diagram 1a).

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--- The influences on the silo pressures due to inbuilt things or customized restrictions

and inbuilt things such as discharge cones, discharge girders, consoles and spots, etc.,

are not covered (apart fro discharge hoppers).


following limits should be kept in mind with regard to the stored bulk material:

--- The calculation for a particular property of the bulk material has to be made for every

single silo.

--- The bulk material is free flowing or it can be ensured that in special cases it behaves

as free flowing material (see 3.1.12 and Annex C).

--- The maximum grain size of the bulk material is not more than (see diagram

1d).

cd03.0

NOTE If the bulk material particles are large in comparison with the thickness of

the silo wall, the effects of the contact of individual large particles with the wall are to be

regarded as a form of a deposit of individual loads.


following limits should be kept in mind with regard to the operational conditions

during filling and discharging:

--- During filling the action of the forces of inertia and impact are very slight and may be

ignored

--- in case of use of discharge aids (e.g. transporting equipment (feeders) or central well

with absorption opening), the bulk material flow is uniform, undisturbed and central.

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(a) Geometry

φr

hc

1 hh

2

Z

*

φdca

hb

β

hw ho

f

3

4ef

β

e*

α

eo

(b) Eccentricity Legend: 1 Junction

2 Equivalent bulk material surface

3 Surface contours in filled silo

4 central axis of silo

Figure 1: DIAGRAM OF SILO BINS WITH DESCRIPTION OF THE GEOMETRIC AND CHARACTERISTIC SIZES AND LOADS

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2r

UA =

4a

UA =

ph

Pw

Pv

Pf

Pn

φ

φdc a

(c) Loads

φdc

a

UA

( ) 443 Oda

UA ==

(d) Cross secti

d
c
2( )

bh

UA = 2

( ) 443 Oda ==

onal shape (for

r
( )a+1
φdc b

a

r φdc

4Od

UA =

m)

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6) The given load deposits on silo hoppers are applicable only for conical (generally

axial symmetric shape or pyramid shape with quadratic or rectangular cross-

sections) and cuneiform (generally with vertical walls at the front and the reverse

sides) hoppers. Hoppers that deviate from this or hoppers with inbuilt things

require specialized and greater attention.

7) Silos with symmetric axes of the geometrical horizontal projection type which

change along the vertical axis are not covered by this standard. For example, silos

with a hopper which blends from a cylindrical shape into a cuneiform shape fall in

this category.

8) The rules for calculation for tanks apply only for fluids under normal atmospheric

pressure.

9) Loads on the roofs of silos and tanks are subject to the relevant standards DIN

1055-3, DIN 1055-4, E DIN 1055-5, DIN 1055-9 and DIN 1055-10.

10) The calculations for silos with rotary operation are not within the scope of this

standard.

11) The calculations for silos against dynamic stresses, which can appear during

discharge, such as silo tremors, jolts, hooting and silo knocking, are not within the

scope of this standard.

NOTE These phenomena remain unexplained to date. Thus, in terms of the

applicability of this standard, one can neither rule out their occurrence nor ensure that the

silo structure is sufficiently dimensioned for the stresses they cause.

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2 REFERENCES TO OTHER STANDARDS

The documents mentioned below are required for using this standard. In case of dated

references, only the edition mentioned is applicable. In case of undated references the

latest edition of the document mentioned is applicable (inclusive of all revisions).

DIN 1045-1 Plain concrete, reinforced and prestressed concrete structures

- Part 1: design and construction

DIN 1055-1 Actions on structures – part 1: specific gravity and surface

loads of building materials, building components and storage

materials

DIN 1055-3 Actions on structures – part 3: self loads and superimposed

loads for high buildings

DIN 1055-4 Actions on structures – part 4: wind loads

DIN 1055-5 Actions on structures – part 5: snow and ice loads

DIN 1055-7 Actions on structures – part 7: temperature actions

DIN 1055-9 Actions on structures – part 9: unusual actions

DIN 1055-10 Actions on structures – part 10: actions due to cranes and

machines

DIN 1055-100 Actions on structures – part 100: bases of structural planning:

security concepts and rules for design calculations

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DIN EN 26184-1 Explosion protection systems – part 1: determination of

explosion indices of combustible dust in air

DIN EN 1127-1 Explosive atmospheres – explosion protection – part 1: basic

concepts and methodology

DIN EN 50014 Electrical equipment for areas with explosion hazard – general

specifications

ISO 3898:1997 Bases for design of structures – notations, general symbols

VDI 2263 Dust fires and dust explosions; dangers, evaluation and

protective measures

VDI 3673 Sheet 1 Pressure relief of dust explosions

3 DEFINITIONS AND SYMBOLS 3.1 Definitions The definitions given below as well as those given in DIN 1055-100 are applicable to this

standard.

3.1.1 Aerated silo bottom

A silo bottom in which grooves (aeration channels) have been provided, through which air

is injected in order to activate the bulk material flow in the area above the silo bottom

(see figure 6b).

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3.1.2 Internal diameter of a silo cross-section dc

The diameter of the largest inscribed circle of the inner cross-section of a silo bin (see

figure 1d).

3.1.3 Circular silo A silo whose ground plan or shaft cross-section shows a circular form (see figure 1 d)

3.1.4 Cohesion Shear strength of the bulk material when direct stress does not act in the plane of breach

3.1.5 Conical hopper A hopper in which the inclined side-surfaces converge at a point, which can – as a rule –

ensure an axially symmetric flow of bulk material

3.1.6 Eccentric discharge

A flow profile in the bulk material in which the distribution of the moving bulk material is

unsymmetrical with relation to the vertical central axis. This is usually due to an

eccentrically placed outlet opening (see figures 3c and 3d, 4b and 4c). It can, however,

also happen due to other phenomena which lead to non-symmetry (see figure 5d).

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3.1.7 Eccentric filling

A situation during or after the filling of the silo, in which the peak of the banked-up bulk

material surface (peak of the banked-up cone) is no longer centered in the vertical central

axis of the silo (see figure 1b).

3.1.8 Equivalent bulk material surface

Height of the envisaged leveled (horizontal) bulk material surface, which is the result of

the volume balance between the envisaged and the actual pattern of the surface shape

(see figure 1a)

3.1.9 Hopper for “expanded flow”

A hopper in which the side surfaces in the lower part of the hopper are steep enough to

create a mass flow, while the side surfaces in the upper part of the hopper have a more

gradual inclination so that a core flow can be expected there (see figure 6d). This

arrangement reduces the height of the hopper and at the same time ensures a reliable

discharge.

3.1.10 Horizontal (silo) bottom

The inner bottom surface of the silo with an inclination that is less than 5o

3.1.11 Flow profile The geometric form of the bulk material that is flowing out, when the flow is fully

developed (see figures 2 to 5). The silo is in this case is almost completely filled-up (state

of maximum fill).

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3.1.12 Fluidized bulk material That state of a stored powdery bulk material in which it contains a large proportion of air

pockets with a pressure gradient which acts against the weight of the particles and

counterbalances the same. The air can either be drawn in by means of specific

ventilation or be introduced through the filling process. A bulk material is designated as

fluidized even if only a part of the weight of the bulk material is counterbalanced by the air

pockets.

3.1.13 Free-flowing granular material Granular bulk material in which the flow pattern is not noticeably influenced by cohesion

3.1.14 Fully filled state

A silo is in the fully filled state when the surface of the bulk material has achieved the

highest position that it can possibly acquire within the service life of the structure while

the silo is in operation.

NOTE: This is taken as the ruling condition for design calculations of silos.

3.1.15 Core flow Flow profile, in which a flow channel develops in the bulk material above the outlet

opening, while the bulk material remains undisturbed in the area between the flow

channel and the silo wall (see figure 2)

NOTE: The flow channel can, in such case, come into contact with the vertical silo wall – one

would then term it “mixed flow” – or it can stretch right up to the surface without any point of contact

whatsoever with the silo wall, in which case the term “ funnel flow” or “shaft flow” is used to describe it.

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3.1.16 Granular material Material which is composed of separate and individual grains of specific particles, with

the particles having more or less equal dimensions and where the air between the

individual grains plays only a marginal role in the determination of the loads and has only

a marginal influence on the bulk material flow.

3.1.17 High fill speed That condition in a silo, in which the speed of the filling leads to an intake of air of such

an order that it would affect the pressure ratios at the wall.

3.1.18 Homogenizing silos Silos in which the bulk material is homogenized with the help of fluidization, i.e.

homogenized by means of mixing.

3.1.19 Hopper Silo bottom with inclined walls

3.1.20 Hopper load ratio value F

A value which specifies the relationship between the normal load pn on the inclined

hopper walls and the mean vertical load pv at this position in the bulk material.

3.1.21 Silo of medium slimness

A silo whose ratio of height to diameter lies between 1.0 < hc / dc < 2.0

NOTE: exceptions are defined in 5.3.

3.1.22

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Internal funnel flow Flow profile with funnel flow in which the flow channel limit stretches up to the surface of

the bulk material without the flow area coming into contact with the silo wall in the

process (see figures 2 and 3).

3.1.23 Horizontal load ratio K A value which specifies the relationship between the mean horizontal load pn acting on

the vertical silo walls, and the mean vertical load pv at this position in the bulk material.

3.1.24 Marginal cohesion

A bulk material sample shows a marginal cohesion when the cohesion c is smaller than

4% of the pre-consolidation stress σr

NOTE a process for the determination of cohesion is given in C.9

3.1.25 Mass flow

Flow profile in which all the bulk material particles in the silo are simultaneously in motion

during discharge (see figure 2a)

3.1.26 Mixed flow Core flow profile in which the flow channel, which is still beneath the bulk material

surface, comes into contact with the vertical silo walls (see figures 2c and 4)

3.1.27 Non-circular silo

A silo, wherein the cross-section is not a circle (see figure 1)

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3.1.28 Bulk material A term used to describe a granular material ranging from a dust-like to a large-grained

variety with and without cohesion, which contains pores in addition to and in-between the

individual solid material particles that may be filled with air or moisture.

3.1.29 Reference surface load Local load perpendicular to the vertical silo wall to be placed at any chosen height in a

specific portion of its surface.

3.1.30 Funnel flow Flow profile in which the bulk material is in motion above the outlet opening in a vertical

or almost vertical flow channel, but is in a state of rest next to the flow channel (see

figures 2 and 3).

NOTE If the outlet opening is placed eccentrically (see figures 3c and d) or if due to certain factors

the flow channel deviates from the vertical axis above the discharge (see figure 5), the flow of the bulk

material can appear against the wall.

3.1.31 Level flow

Flow profile in a silo with a rectangular or a quadratic cross-section and a slit-shaped

outlet opening. The discharge slit runs parallel to two silo walls. Its length corresponds to

the length of both these silo walls.

3.1.32 Powdery bulk material A bulk material whose mean particle size is smaller than 0.05 mm

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3.1.33 Silo with braced wall Silo with a horizontal bottom and and a height to diameter ratio of hc / dc < 0.4

3.1.34 Flat hopper A hopper in which the full amount of wall friction is not mobilized

3.1.35 Silo

A structure for storage of bulk material

3.1.36 Slim silo

A silo with a height-diameter ratio of hc / dc > 2.0, or one which fulfills the additional

conditions given in 5.3

3.1.37 Slimness

Ratio of the height to diameter hc / dc of the vertical portion of the silo

3.1.38 Low silo

A silo with a height-diameter ratio of 0.4 < hc / dc < 1.0 or one in which the additional

conditions as per 5.3 are fulfilled.

NOTE In case of a height-diameter ratio of hc / dc < 0.4, and if the silo contains a hopper, the silo

will fall into the category of a low silo. Otherwise – in case of a flat silo bottom – it falls into the braced-wall

silo category.

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3.1.39 Steep hopper A hopper in which the full wall friction is mobilized after the filling

3.1.40 Stress in the bulk material Force per unit area within the stored bulk material

3.1.41 Tank A structure for storage of fluids

3.1.42 A thick-walled silo

A silo with a diameter-to-wall thickness ratio which is less than dc /t = 200

3.1.43 A thin-walled silo

A silo with a diameter-to-wall thickness ratio which is greater than dc /t = 200

3.1.44 Wall friction

Force per unit area along the silo wall (vertical or inclined) on account of friction between

the bulk material and the silo wall.

3.1.45 Hopper junction

The section between the hopper and the vertical silo wall, i.e. the transition from the

vertical part of the silo into the hopper

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3.1.46 Vertical Silo shaft The part of the silo which comprises of the vertical walls

3.1.47 Wedge-shaped hopper A hopper in which the surfaces converge at a slit for ensuring an even flow of the bulk

material; the walls of each of the other two hoppers run vertically

3.2 Symbols 3.2.1 General A list of basic symbols (letter symbols) is given in DIN 1055-100. The additional letter

symbols for this part of the standard are given below. The symbols used are based on

the conventions of ISO 3898:1997.

3.2.2 Latin letters, capital

A cross-section of the vertical shaft

Ac cross-section of the flow channel in case of eccentric discharge (large

eccentricities)

B depth parameter in case of eccentrically filled low silos

C load augmentation factor

Co discharge factor (load augmentation factor during discharge) for the bulk material

Cop bulk material parameter for the reference surface load (load augmentation factor)

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Cb load augmentation factor for the bottom loads

Ch load augmentation factor for the horizontal discharge loads

Cpe load augmentation factor for the reference surface loads during discharge

Cpf load augmentation factor for the reference surface loads in case of fill loads

CS correction value for slimness in a silo with medium slimness

CT load augmentation factor for making allowance for temperature differences or

changes

Cw correction value for discharge for the wall friction loads (load augmentation factor)

E ratio of eccentricity (during fill and discharge) to silo radius

Es effective elasticity modulus of the stored bulk material at the relevant stress level

Ew elasticity modulus of the silo wall

F relationship between the vertical loads on the silo wall and the mean vertical load

in the bulk material at this point

Fe load ratio in the hopper during the discharge (relationship between loads

perpendicular to the silo wall and mean vertical loads in the bulk material)

Ff load ratio in the hopper after the filling (relationship between loads perpendicular

to the silo wall and mean vertical loads in the bulk material)

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Fpe integral of the horizontal reference surface load for thin walled circular silos in the

case of discharge loads

Fpf integral of the horizontal reference surface load for thin walled circular silos in the

case of filling loads

G ratio of the radius of the flow channel to the radius of the internal cross-section of a

circular silo

K characteristic value of the horizontal load ratio

Km mean value of the horizontal load ratio

Ko value of K when horizontal elongation as well as principal stresses that run or are

aligned horizontally and vertically are ruled out

Pwe characteristic value of the sum total of the wall friction loads for each running

meter in the circumferential direction of the vertical silo wall in the case of

discharge loads

Pwf characteristic value of the sum total of the wall friction loads for each running

meter in the circumferential direction of the vertical silo wall in the case of fill loads

PzSk characteristic value of the wall loads for each running meter in the circumferential

direction of the vertical silo wall for low silos and large filling eccentricities

S geometry factors for the hopper loads (= 2 in the case of cone shaped hoppers, =1

in the case of wedge shaped hoppers)

U inner circumference of the cross-section of the vertical silo shaft

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DIN 1055-6:2005-03

Usc (inner) circumferential length of the flow channel in the contact zone up till the non

flow zone of the bulk material during discharge with large eccentricities

Uwc (inner) circumferential length of the flow channel in the contact area with the silo

wall during discharge with large eccentricities

Y depth variation function: function for the description of the increase in load with

increasing depth in the silo

YJ depth variation function of the theory acc. to Janssen

YR depth variation function for small silos

3.2.3 Latin letters, small a side length of a silo with a rectangular or a hexagonal cross-section (see figure 1d)

ax divergence-coefficient (-factor) or conversion factor for calculating the upper and

lower characteristic bulk material parameters from the mean values

aK divergence-coefficient or conversion factor for the horizontal load ratio

aγ divergence-coefficient or conversion factor for the bulk material specific gravity

aφ divergence-coefficient or conversion factor for the angle of the internal friction

aµ divergence-coefficient (-factor) or conversion factor for the coefficients of wall

friction

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DIN 1055-6:2005-03

b width of a rectangular silo (see figure 1d)

b empirical coefficient for the hopper loads

c cohesion of the bulk material

dc characteristic dimensions for the inner cross-section of the silo (see diagram 1d)

e the larger value of the eccentricities ef and eo

ec eccentricities of the central axis of the flow channel during discharge with large

eccentricities (see figure 11)

ef largest eccentricity of the bulk cone at the bulk material surface during filling (see

figure 1b)

ef,cr largest fill eccentricity for which the simplified rules for the allowance for marginal

eccentricities can be used (ef,cr = 0.25dc )

eo eccentricities of the centre point of the outlet opening (see figure 1b)

eo,cr largest eccentricity of the outlet opening for which the simplified rules for the

allowance for eccentricities can be used (eo,cr = 0.25dc )

et eccentricities of the peak of the fill-up cone at the bulk material surface when the

silo is filled up (see figure 1b)

et,,cr largest eccentricity of the fill-up cone at the bulk material surface for which the

simplified rules for the allowance for eccentricities can be used (et,,cr = 0.25dc )

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DIN 1055-6:2005-03

hb overall height of a silo with hopper, measured from the envisaged hopper peak, up

to the equivalent bulk material surface (see figure 1a)

hc height of the vertical silo shaft, measured from the hopper junction up to the

equivalent bulk material surface (see figure 1a)

hh height of the hopper measured from the envisaged hopper top up to the hopper

junction

ho distance between the equivalent bulk material surface and the lowest point at the

base of the bulk material cone (at the lowermost point of the silo wall which is not

in contact with the stored bulk material when the latter has been filled to the

specified extent)(see fig 1, 13 and 17)

htp total height of the back-filled cone at the bulk material surface (vertical distance

from the lowest point of the silo wall up to the tip of filled-up cone when the bulk

material, which is filled to the specified extent, is not in contact with the silo

wall)(see figures 1a and 17)

n parameters in the conditional equations of the hopper loads

p load as force per unit area

ph horizontal load from the stored bulk material (see figure 1c)

phae horizontal load in the area where the bulk material is at rest next to the flow

channel, during a discharge with large eccentricities

phce horizontal load in the flow channel during a discharge with large eccentricities

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DIN 1055-6:2005-03

phco asymptomatic horizontal load at a great depth in the flow channel during a

discharge with large eccentricities

phe horizontal load during discharge

phe,u horizontal load during discharge and use of the simplified calculating method

phf horizontal load after the filling

phfb horizontal loads after the filling at the lower end of the vertical shaft

phf,u horizontal loads after the filling using the simplified calculating material

pho asymptomatic horizontal loads at a great depth from the stored bulk material

phse horizontal loads in the bulk material (which is in a state of rest) at a great distance

from the flow channel during a discharge with large eccentricities

phT increase of horizontal loads as a result of temperature differences or changes

pn loads from the stored bulk material, that are perpendicular to the hopper walls (see

figure 1c)

pne loads during discharge that are perpendicular l to the hopper walls

pnf loads after the fill that are perpendicular to the hopper walls

pp reference surface loads

ppe basic value of the reference surface loads during discharge

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DIN 1055-6:2005-03

ppei complementary reference surface loads during discharge

ppe.nc strip shaped reference surface load for silos with non-circular cross-sections

during discharge

ppf basic value of the reference surface loads after the filling

ppfi complementary reference surface loads after the filling

ppe,nc strip shaped reference surface load for silos with non-circular cross-sections after

the filling

ppes reference surface load at the cylinder ordinate θ for thin walled circular silos during

discharge

ppfs reference surface load at the cylinder ordinate θ for thin walled circular silos after

the filling

pt friction load in the hopper (see figure 1c)

pte friction load in the hopper during discharge

ptf friction load in the hopper after the fill

pv vertical load in the bulk material (see figure 1c)

pvb vertical load at the bottom of a low silo

pvf vertical load in the bulk material after the filling

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DIN 1055-6:2005-03

pvft vertical load at the hopper junction after the filling (foot of the vertical silo shaft)

pvho vertical load at the foot of the filled cone at the bulk material surface according to

equation (86) and with the bulk material depth being z = ho

pvsq vertical load on the horizontal bottom of a low silo or a silo of medium slimness

pvtp geostatic vertical load at the foot of the filled cone at the bulk material surface

pw wall friction load along the vertical wall (shear force per unit area due to friction)

(see figure 1c)

pwae wall friction loads in the bulk material which is in a state of rest right next to the

flow channel during the discharge with large eccentricities (at the transition from

stationary to flowing bulk material)

pwce wall friction loads in the flow channel during discharge with large eccentricities

pwe wall friction loads during discharge

pwe,u wall friction loads during discharge using the simplified calculation method

pwf wall friction loads after the filling

pwf,u wall friction loads after the filling using the simplified calculation method

pwse wall friction loads in the bulk material which is at rest at a large distance from the

flow channel during discharge with large eccentricities

r equivalent silo radius (r = 0.5dc)

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DIN 1055-6:2005-03

rc radius of the eccentric flow channel during discharge with large eccentricities

s dimensions of the area subject to the reference surface load (s = π dc /16 =

0.2dc)

t thickness of the silo wall

x vertical coordinate in the hopper with origin in the hopper peak (see figure 16)

z depth beneath the equivalent bulk material surface in the filled state (see figure

1a)

zo characteristic depth according to the theory of Janssen

zoc characteristic depth according to the theory of Janssen for the flow channel during

discharge with large eccentricities

zp depth of the mid-point of the reference surface load beneath the equivalent bulk

material surface in a thin-walled silo

zs depth beneath the highest point of contact between the bulk material and the silo

wall (see figures 13 and 14)

zV unit of measurement of the depth for determining the vertical loads in low silos

3.2.4 Greek letters, capital

∆ Horizontal displacement of the upper part of a shear bin

∆ Operator for incremental sizes (see symbols given below)

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DIN 1055-6:2005-03

∆T Temperature differences between the stored bulk material and the silo walls

∆v Incremental vertical displacements measured during the material examination

∆σ Incremental stress placed upon a specimen during material examination

3.2.5 Greek letters, small

α Mean angle of inclination of the hopper walls with reference to the horizontal

αw Coefficient of thermal elongation of the silo wall

β Angle of inclination of the hopper wall with ref. to the vertical (see figures 1a and

1b) or the angle of the steepest hopper walls in a quadratic or rectangular hopper

γ Characteristic value for the specific gravity of the stored fluid or the stored bulk

material

γl Specific gravity of the bulk material in fluidized state

γu Upper characteristic values of the specific gravity of the stored fluid or the stored

bulk material

δ Standard deviation of a parameter

θ Cylindrical coordinate: angle in direction of the circumference

θc Angle at circumference of the flow channel during discharge with large

eccentricities (see figure 11) with ref to the central axis of the silo shaft

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DIN 1055-6:2005-03

ψ Wall contact angle of the eccentric flow channel with reference to the central axis

of the flow channel

µ Characteristic value of the wall friction angle at the vertical silo wall

µheff Effective or mobilized wall friction coefficient in a flat hopper

µh Wall friction coefficient in the hopper

µm Mean value of the wall friction coefficients between bulk material and silo wall

ν Poissons number for the bulk material

φc Characteristic value of the angle of internal friction of a precompressed bulk

material in case of relief (i.e. inclusive of the portion from cohesion)

φi Characteristic value of the angle of internal friction of a bulk material in case of

equivalent load (i.e. without the portion from cohesion)

φim Mean value of the angle of internal friction

φr Angle of slope of a bulk material (conical bulk heap) (see figure 1a)

φw Wall friction angle (arc tan µ) between bulk material and hopper wall

φwh Wall friction angle in the hopper (arc tan µh) between bulk material and hopper wall

σr Reference stress for the tests for determination of the bulk material parameters

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DIN 1055-6:2005-03

4 DESCRIPTION AND CLASSIFICATION OF SILOS 4.1 Description of Actions in Silos

(1) The actions on silos are to be estimated with regard to the silo structure, the

properties of the stored bulk material and the flow profiles that arise during

emptying of the silo.

(2) Ambiguities related to the flow profiles, the influence of the fill and discharge

eccentricities on the fill and discharge processes, the influence of the silo

shape and size on the type of the flow profile and those that are related to the

time-dependant discharge and fill pressures are all to be taken into

consideration

NOTE 1 The magnitude and the distribution of the rated loads depend upon the silo structure, the

material parameters of the bulk materials and the flow profiles which build up during emptying. The

inherent differences in the properties of the different bulk materials that are stored and the

simplifications in the load models lead to variations between the silo loads that actually appear and the

design loads (calculated loads) according to sections 6 and 7. Thus, to quote an example, the

distribution of discharge pressures along the silo wall changes with time. An exact prediction of the

prevailing mean pressure, its divergence and its temporal variability is not possible, given the present

level of knowledge.

(3) Allowance should be made for loads on the vertical walls of the silo when it is

filled and while it is emptying, with fill- and discharge- eccentricities being

marginal; this is to be done using a symmetric load component and an

unsymmetric reference surface load. In case of large eccentricities the loads

are to be described using a pressure distribution curve.

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DIN 1055-6:2005-03

(4) Should the chosen form of the silo structure show a sensitive reaction to

changes of the estimated load-guidelines, allowance has to be made for this

through appropriate investigations

(5) The symmetric loads on the silo walls are to be estimated as follows: a) by

means of horizontal load components ph upon the inner surface of the vertical

silo wall; b) by means of loads pn that act perpendicular to inclined walls; c) by

means of frictional loads pw and pt that act in the tangential direction of the

wall; and d) by means of vertical load components pv in the stored bulk material

(see figure 1c)

(6) The unsymmetric loads on the vertical silo walls in case of marginal

eccentricities during fill and discharge have to be taken into account by using a

reference surface load. These reference surface loads consist of horizontal

pressures ph that act upon the inner surface of the silo wall locally.

(7) The unsymmetric loads on the vertical silo walls in case of large eccentricities

during fill and discharge are to be additionally registered using a unsymmetric

distribution of horizontal pressures ph and friction loads pw

(8) Unplanned and unaccounted load influences are to be registered using the

load augmentation factor C.

(9) The load augmentation factors C for silo cells in categories 2 and 3 (see 4.5)

register unaccounted additional load influences alone, which arise due to the

bulk material flow during emptying of the silo.

(10) The load augmentation factors C for silo bins in category 1 (see 4.5) register

additional influences during emptying that are caused by the bulk material

movement as well as the influences due to the deviation of the bulk material

parameters.

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DIN 1055-6:2005-03

NOTE 2 The load augmentation factors C are intended to cover the ambiguities related to the flow

profile, the influences of eccentricities during filling and emptying, the influence of the shape of the silo

on the manner of the flow profile and proximity influences which arise when allowance is not made for

the presence of fill and discharge pressures that are time dependant. For category 1 silos (see 4.5) the

load augmentation factor also takes into account the deviation of the material properties of the bulk

material. In silos of categories 2 and 3, allowance for the deviation of the material parameters

influenced by the loads is not made by a load augmentation factor C but by the formulation of the

appropriate characteristic calculation values for the bulk material parameters γ, µ, K and φi.

(11) In silos of category 1 (see 4.5) the allowance for unsymmetric loads is made by

means of an increase of the symmetric loads by applying a load augmentation

factor for the discharge loads C.

(12) In silos of categories 2 and 3 (see 4.5) allowance for the unsymmetric

reference surface loads can be made alternatively by a substitute

augmentation of the symmetric loads.

4.2 Description of Action on Tanks

(1) Allowance for loads on tanks as a consequence of filling them up is made

by hydrostatic load formulations

4.3 Classification of actions on silo bins

(1) Loads due to bulk materials stored in the silo bins are to be classified as

variable actions in accordance with DIN 1055-100.

(2) Symmetric loads on silos are to be classified as variable stationary actions in

accordance with DIN 1055-100.

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DIN 1055-6:2005-03

(3) Reference surface loads for making allowances for the filling and discharge

processes in silo bins are to be classified as variable free actions in


(4) Eccentric loads for making allowances for the eccentric filling and discharge

processes in silo bins are to be classified as variable stationary actions.

(5) Loads arising from air or gas pressures in connection with pneumatic conveyor

systems are to be regarded as variable stationary actions.

(6) Loads due to dust explosions are to be classified as extraordinary actions as

defined by DIN 1055-100.

4.4 CLASSIFICATION OF THE INFLUENCES ON TANKS

Loads on tanks that arise due to the filling up of the tanks can be classified as variable

stationary influences acc. to DIN 1055-100.

4.5 STANDARDISED CATEGORIES

(1) Based upon the design of the silo structure and its susceptibility to different types of

malfunctions, various accuracy standards are used in the process of determining the

influences on silo structures.

(2) The silo influences should be determined in accordance with one of the following

standardized categories specified in this standard (see Table 1).

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DIN 1055-6:2005-03

TABLE 1 – CLASSIFICATION OF THE DIMENSIONING CONDITIONS

STANDARDISED CATEGORIES

DESCRIPTION

standardized

category 3

Silos with a capacity of more than 10 000 tonnes

Silos with a capacity of more than 10 000 tonnes, in which one of the

foll. calculating conditions is present

a) eccentric discharge with 25.0>c

od

e (see fig 1b)

b) low silos with an eccentric filling of more than 25.0>t

od

e

standardized

category 2

all silos which are covered by this load standard and do not fall in the

other two categories

standardized

category 1 silos with a capacity of less than 100 tonnes

NOTE The differences amongst the categories listed in Table 1 have been determined

taking into account the shortfalls of an exact estimation of the influences. The rules for small silos

are simple and conservative on the safer side, as they have a robustness of their own and high

costs of an estimation of bulk material parameters for example, are not justified.

(3) A higher category for a silo than that which is required as per Table 1 can always be

chosen. For any part of the procedures (computation of loads) described in this standard,

a higher category than that in Table 1 can be taken as a basis, if required.

(4) In case several silos are connected to one another, the suitable category for each

bin should be individually determined, and not for the set of silos as a whole.

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DIN 1055-6:2005-03

5. CALCULATING CONDITIONS 5.1 GENERAL

(1) The influences on silos and tanks, for each of the relevant calculating conditions,

are to be determined in compliance with the general specifications contained in DIN

1055-100.

(2) It is important that the relevant calculating conditions be observed and the critical

load types are determined.

(3) The combination rules depend on each of the verifications and are to be chosen in


NOTE The relevant combination rules are given in Annex A.

(4) Influences on account of the adjacent building structures are to be taken into

account.

(5) Influences of transporting equipment and pouring equipment are to be taken into

account. Special care is requested in case of permanently installed transporting

equipment. They can transmit loads to the silo structure across the stored bulk materials.

(6) Depending on the circumstances, the following extraordinary influences and

situations are to be taken into account:

- Influences caused by explosions

- Influences caused by vehicular impact

- Influences caused by earthquakes

- Influences caused by fire-load

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DIN 1055-6:2005-03

5.2 CALCULATING CONDITIONS CAUSED BY “BULK MATERIAL” STORED IN SILOS

(1) Loads on silos caused by stored bulk materials are to be ascertained for the

maximum possible state of fullness.

(2) The loads estimates for filling and for discharge can be used as evidence for

supporting safety as well as performance capability.

(3) The dimensioning for filling and for discharge of bulk materials has to comply with

the principal load-types which can lead to differing boundary states for the structure:

- Max loads perpendicular to the vertical silo wall (horizontal loads)

- Max vertical wall friction loads on the vertical silo wall

- Max vertical loads on the silo bottom

- Max loads on the silo hoppers

(4) For determination of loads, the upper characteristic values of the bulk material

specific gravity γ are to be used always.

(5) The determination of the loads of a load type should always be made for a specific

combination of matching parameters µ , K and iϕ , so that every boundary state is

assigned a specific defined condition of the bulk material.

(6) For each of these load types its extreme value is attained when each of the bulk

material characteristic values µ , K and iϕ acquires differing extreme values within the

variance range of their characteristic bulk material parameters. In order to ensure

adequate safety for all boundary states during dimensioning, differing combinations of the

extreme values of these parameters have to be examined. Table 2 gives the extreme

values of the bulk material parameters which are to be used for each load types that are

to be examined.

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DIN 1055-6:2005-03

TABLE 2 - VITAL PARAMETERS FOR THE DIFFERENT LOAD CALCULATIONS

CHARACTERISITC VALUE TO BE CALCULATED

TYPE OF LOAD EXAMINED COEFFICIENT OF

WALL FRICTION µ

HORIZONTAL LOAD

RATIO

K

ANGLE OF INTERNAL

FRICTION

iϕ

SECTION OF VERTICAL WALL Max. horizontal load ratio

perpendicular to the vertical wall Lower limit value Upper limit value Lower limit value

Max. wall friction loads on the

vertical walls Upper limit value Upper limit value Lower limit value

Max. vertical loads on the hopper

or the silo bottom Lower limit value Lower limit value Upper limit value

Type of load examined Coefficient of wall friction µ

Load ratio in the hopper

F Angle of internal friction iϕ

HOPPER WALLS Maximum hopper loads in the

filled state

Lower limit value for the

hopper Lower limit value Lower limit value

Maximum hopper loads during

discharge Lower limit value for the

hopper upper limit value upper limit value

NOTE 1 It is to be noted that the wall friction angle is always smaller or same as the angle of internal friction of the

stored bulk material ( )iwhei ϕϕ ≤.. . Otherwise, when transverse stresses recorded at the wall contact surface are larger

than those due to the internal friction of the bulk material itself, a slide surface develops within the bulk material. This means

that in all cases the coefficient of wall friction should not be taken as larger than tan iϕ ( )iw ϕϕµ tantan ≤=

NOTE 2 The loads that are perpendicular to the hopper walls are as a rule largest when the wall friction in the

hopper is small, because thereby a smaller portion of the loads in the hopper are take away are removed through friction. It

is to be observed which maximum parameters become decisive for the individual dimensioning exercises (i.e. it is the

malfunctioning that is being examined, which determines whether the wall friction loads or loads that are perpendicular to

the hopper wall are to be calculated as maximum)

np

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DIN 1055-6:2005-03

(7) The above table notwithstanding, silos of category 1 can be dimensioned using the

mean values of the bulk material parameters, namely the mean value of the coefficient of

wall friction mµ , the mean value of the horizontal load ratio and the mean value of the

angle of internal friction

mK

imϕ .

(8) The fundamental equations for calculating the silo loads are given in sections 7

and 8. These are to be taken as the basis for the calculation of the following

characteristic loads:

- Filling loads on vertical wall sections (see section 7)

- Discharge loads on vertical wall sections (see section 7)

- fill and discharge loads on horizontal bottoms (see section 8)

- Fill loads on hoppers (see section 8)

- Discharge loads on hoppers (see section 8)

5.3 CALCULATING CONDITIONS CAUSED BY DIFFERING GEOMETRIC DESIGNS OF THE SILO GEOMETRY (1) Differences in slimness of silos (ratio of height to diameter), hopper geometries

and arrangements of vents lead to differences in calculating conditions and these

have to be observed.

(2) In a silo that has been filled-up, the trajectory of the filling stream of the filled up

bulk material may at times cause the build-up of an eccentric back-fill cone at the

bulk material surface (see fig 1b) and when this happens different storage

densities can arise in different parts of the silo which lead to un-symmetric loads.

While calculating the size of these loads, the largest possible eccentricity of the

filling stream is to be taken as a basis (see 7.2.1.2 and 7.3.1.2)

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DIN 1055-6:2005-03

(3) While dimensioning, the effects of the flow profiles are to be observed which can

be divided into the following Categories (see fig. 2):

-- Mass flow

-- funnel flow

-- mixed flow

1

2

3

4 4

3

5

4 4

2 a) MASS FLOW b) CORE FLOW C)CORE FLOW

(FUNNEL FLOW) (MIXED FLOW) Legend 1 Entire bulk material in motion 4 Bulk material at rest

2 flow 5 Effective passages

3 Limits of flow channel 6 Effective hopper

Figure 2 – BASIC FLOW PROFILES

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DIN 1055-6:2005-03

(4) If it can be additionally ensured during funnel flow that the flow channel is always

located within the bulk material without coming into contact with the silo wall (see figures

3a and 3b), the emptying pressures can be ignored. Low silos with concentric discharge

aided by gravity and silos with a mechanical discharge system located at the bulk

material surface which ensures a build-up of funnel flow (see fig. 5a, 5b and 6a) fulfill

these conditions (see fig. 7.1 (9) and 7.3.2.1(2) and (4)).

NOTE A suitably designed central tube with lateral vents (“anti dynamic tube”) can

also ensure that this condition - i.e. building up an internal funnel flow - is fulfilled.

(5) In case of symmetric mass flow or a mixed flow (see fig. 2), the un-symmetric

loads that usually occur are to be taken into account during the dimensioning (see

7.2.2.2 and 7.3.2.2).

(6) In case of flow profiles with core flow (see fig 2) and partial contact of the moving

bulk material mass with the silo wall, other un-symmetric load components – which

may arise specifically in this case – are to be taken into account during

dimensioning (see fig 3c and 3d as well as fig 4b and 4c) (see 7.2.4).

(7) For silos with several vents and presuming a state of maximum fullness, one has

to take into account that during operation either all the vents may be opened

simultaneously or a single vent alone may be open.

(8) For silos with several vents, provisions of the combination of active vents for the

operation are to be regarded as normal calculating conditions. Other openings

which are not part of the planned operation are to be regarded as extraordinary

calculating conditions.

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DIN 1055-6:2005-03

(9) In case of an eccentrically filled very slim silo ⎟⎠⎞⎜

⎝⎛ > 4..

c

cd

hei , the effects of mixed

flow in different areas could lead to either differing packing densities or cohesion of

the bulk material. In such cases the asymmetric alignment of the bulk material

particles can set off a unsymmetric core flow (see fig. 5d). This creates zones in

the silo where the bulk material flows along the silo wall and thereby gives rise to

un-symmetric loads. For such cases special load computations are to be used

(see 7.2.4.1 (2)).

1

2

3

1

2

3

2

3 4

1

4

1

2

3

INTERNAL CONVERGENTINTERNAL PARALLEL ECCENTRIC CONVERGENT ECCENTRIC PARALLEL Funnel flow funnel flow funnel flow funnel flow Legend 1 flow

2 flow channel limits

3 flowing funnel

4 bulk material at rest

Figure 3 – FLOW PROFILES WITH FUNNEL FLOW

49

DIN 1055-6:2005-03

1 3

6

31

6

2

1

3

4

5 5

(A) (B) (C) a) Concentric mixed flow b) Fully eccentric mixed flow c) Partially eccentric mixed flow Legend

1 At rest

2 Effective hopper

3 Limits of flow channel

4 Effective passage

5 Flow zone

6 Effective passage varies in the silo’s circumferential direction

Figure 4 – FLOW PROFILE WITH MIXED FLOW OF BULK MATERIAL

50

DIN 1055-6:2005-03

]

2

1

2

1

5

4

5

3

1

4 5

1

2

a) Braced wall silo b) Low silo c) Slim silo d) Very slim silo Legend 1 Bulk material at rest

2 Flow channel limits

3 Effective hopper

4 Effective passage

5 Flow

Figure 5 – EFFECTS OF THE SLIMNESS (RATIO OF HEIGHT TO DIAMETER) ON THE MIXED FLOW OF THE BULK MATERIAL AND THE FUNNEL FLOW

51

DIN 1055-6:2005-03

(10) For silos with pneumatically conveyed powdery bulk materials two calculating

conditions, both at maximum fullness, are to be considered:

- The bulk material filled in can develop a cone, as is the case with other bulk

materials.

- It is to be taken into account that the bulk material surface, independent of the

gradient of slope and the filling eccentricities, could possibly also be of even shape

(see fig 6c). In this case the eccentricities and can be fixed at zero. fe te

(11) In case of silos for storage of powdery bulk material where air-injection is used as

a discharge aid in the bottom area, (see fig 6b), the entire bulk material zone near

the bottom can become fluidized, which can generate an effective mass flow even

in low silos. Such silos are to be computed in accordance with the procedure for

slim silos, regardless of their actual slimnessc

cd

h .

(12) In case of silos for storage of powdery bulk material where air-injection is used as

a discharge aid in the bottom area, (see fig 6b), just a part of the bulk material

zone near the bottom can become fluidized. This can generate an eccentric mass

flow (see fig 4b), which is to be taken into account while dimensioning. The

eccentricity of the resultant flow channel and the resultant value of the eccentricity

that is to be computed are to be derived keeping in mind the fluidized zone, in

addition to the position of the vent.

0e

(13) The vertical silo walls with a discharge hopper which causes an expanded flow

(see fig 6d), can form the basis of the conditions for a mixed bulk material flow.

This can lead to un-symmetric discharge loads. In this type of silo the ratio

c

bd

h can be fixed for slimness instead of c

cd

h (see fig 1a).

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DIN 1055-6:2005-03

(14) A silo with a slimness of c

cd

h smaller than 0.4 and with a funnel hopper is to be

graded as a low silo. In case of a horizontal silo bottom this silo is to be graded as

a braced wall silo.

a) Mechanically aided discharge e.g. with a rotating space arm b) Air injection and air vents generate mass flow c) Pneumatic filling of powdery bulk material generally results in a level bulk

material surface d) “Expanded flow” hoppers lead to mass flow at least in the lower hopper Figure 6 - SPECIAL FILLING AND SICHARGE ARRANGEMENTS

53

DIN 1055-6:2005-03

5.4 CALCULATING CONDITIONS CAUSED BY SPECIFIC STRUCTURAL SHAPES OF SILOS

(1) In case of dimensioning of silos fro usability, the size of fissures is to be limited to

suitable dimensions. The inspection of fissure size has to comply with the fissure

size limitation specified in DIN 1045-1 subject to the exposition categories based

on the ambient conditions of the silo.

(2) For metal silos which mainly consist of nuts and bolts, the specifications for un-

symmetric load values (reference surface loads) are to be complied with.

(3) For metal silos with rectangular cross-sections that contain beam ties within the

silo shaft for reducing the wall’s bending moment, the specifications in 7.7 are to

be followed.

(4) The effects of fatigue in silos and tanks are to be taken into account if they are

exposed to a load cycle more than once a day on an average. A load cycle is

equivalent to a complete filling and emptying cycle of a silo or, in the case of a air-

injection silo, a complete process conclusion (rotation) of the sectors subjected to

air-injection. Fatigue effects are also to be taken into consideration in silos which

are exposed to the influence of vibrating machines/equipment components.

(5) Prefabricated silos are to be dimensioned for the influences related to

manufacture, transport and assembly.

(6) In case of slip openings or observation holes in the silo or hopper walls, the loads

on the stopper covers are to be taken into account using double the value of the

maximum load-values upon the adjacent wall sections. These loads are to be

computed only for the dimensioning of the stopper cover and its support or

attachment structures.

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DIN 1055-6:2005-03

(7) If the silo roof has to bear loads imposed by dust filtering equipment, cyclones or

mechanical transporting equipment, then these loads are to be treated as live

loads.

(8) If pneumatic transport systems are used for filling and emptying of silos, then

loads resulting from differences in air-pressure are to be taken into account.

NOTE These loads normally amount to <10kPa as a rule, but higher sub

pressures (generally 40kpa ≈ 0.4 bar) may also arise as a result of defective

dimensioning of specific transporting equipment or in case of an operational fault. Silos

must therefore be equipped with suitable pressure-relief devices for unforeseen

occurrences, if the designing engineer cannot otherwise rule out the same.

(9) If vibrating equipment, air guns or rotary extraction arms on the silo bottom have

been used, the load changes caused by these have to be examined with respect

to the boundary state of fatigue, vibrations due to pneumatic transporting

equipment are likewise to be taken into consideration.

(10) In case of reconditioning of existing silos by putting a lining on the silo walls, the

effects of modified wall friction on silo dimensioning are to be considered,

including the possible effects of a flow profile that may have undergone a change.

5.5 DIMENSIONING CONDITIONS CAUSED BUY FLUIDS STORED IN TANKS Loads on tanks caused by the fluids stored therein are to be calculated for the state of

maximum fullness.

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5.6 PRINCIPLES OF DIMENSIONING FOR EXPLOSIONS

(1) As the liquids or bulk material stored in tanks or silos respectively may have a

tendency to explode, the potential damage could be limited or avoided by means

of the following measures:

-- Arrangement of adequate pressure relief areas

-- Arrangement of adequate explosion suppression systems

-- designing/dimensioning the structure for absorbing the explosive pressures

(2) A few bulk materials which are prone to explosions are listed in Annex I.

(3) The instructions given in Annex I for the explosion loads are to be followed.

Further instructions including rules for dimensioning for dust explosions can be

taken from DIN-Fachbericht 140.

(4) The effects of silo structure dust explosions upon the surrounding structures or

structural parts are to be taken into account.

6 BULK MATERIAL PARAMETERS 6.1 General

(1) For the estimation of silo loads the following influences have to be taken into

account:

the divergences from the bulk material parameters

the fluctuations of the wall friction at the silo wall

the silo geometry

the filling and emptying processes

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(2) Influences which have a favourable impact upon the bulk material stiffness may

not be taken into account while determining the loads and examining the

stability of the wall. A positive impact of a wall deformation upon the pressures

which develop in the bulk material may not be estimated, except if a

reasonable and verified method of calculation can be proved.

(3) If required, the manner of the flow profile (mass or core flow) is to be

determined from figure 7. Figure 7 may be used on the grounds of simplifying

hypotheses that have been taken as a basis - for example, the influence of

internal friction is ignored – but may not be used for technical layout of silos.

NOTE The layout of the silo geometry for a mass flow is beyond the scope of this standard. The

methods and procedures specific to bulk material technology have to be used for this purpose.

(a) conical hopper

0

0.2

0.4

0.6

0.8

1

1.2

0° 20° 24° 40° 60°

Series1

1

2

Co-

effic

ient

of w

all f

rictio

n in

the

hopp

er µ

h

Angle of inclination of hopper β

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(b) cuneiform hopper

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 8

0

Series1

Co-

effic

ient

of w

all f

rictio

n in

the

hopp

er µ

h

1

2

Angle of inclination of hopper β

Legend 1 area with core flow

2 areas with the possibility of mass flow

Figure 7 – CONDITIONS UNDER WHICH PRESSURES CAUSED BY MASS FLOW ARISE

6.2 Bulk Material Parameters 6.2.1 General

(1) The material properties of the bulk material stored in the silos, which are to be

quantified for calculating the loads, are to be derived or obtained either as test results or

as data in any other suitable form.

(2) While using values from test results and other sources of data, the same are to be

evaluated in a suitable manner keeping in mind the type of load in question in each case.

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(3) It should be kept in mind that there may be significant differences between the

material parameters measured in tests and the parameters that are determined by the

actual behaviour of the bulk material in the silo.

(4) While evaluating the differences in bulk material parameters mentioned in (3), the

following are some of the factors that must be kept in mind:

a lot of parameters are not constant, and may be dependant upon the

stress level and the background of load application

Influences on account of particle shape, sizes and distribution of grain size

can have a strong impact on the test and the silo in a variety of ways.

temporal influences

fluctuations of the moisture content

influences of dynamic actions

brittleness or ductility of the tested bulk material

the manner of putting-in the bulk material in the silo and in the testing

apparatus

(5) While evaluating the differences in bulk material parameters mentioned in (3) with

ref. to the coefficients of wall friction, the following factors must be kept in mind:

corrosion and chemical reaction of the bulk material particles, dampness

and the wall

abrasion and wear which can roughen or smoothen the wall of the silo

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polishing of the wall surface

accumulation of fat deposits on the wall

particles which get impressed in the wall surface (usually an influence

which leads to the roughening of the wall surface)

(6) While determining the values for the material parameters the following is to be

kept in mind:

the facts regarding the application of the relevant tests should be well-

publicised and common knowledge

a comparison of the values of the individual parameters which have been

measured in the tests with the corresponding published parameters, taking

into account the experimental values

the deviation of the parameters relevant to the calculations

the results obtained from the large scale measurements on silos of similar

styles

correlation of results from different types of tests

perceptible changes in the material parameters during the period when the

silo is in use

(7) The choice of the characteristic material parameters has to be made on the basis

of values the have been determined through laboratory tests, with due regard for

know-how acquired through experience.

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(8) The characteristic value of a material is to be chosen after a careful evaluation of

the value which has influenced the occurrence of the load.

CATEGORY DESCRIPTION OF WALL-

SURFACE TYPES OF MATERIAL

D1 Polished

Cold-rolled stainless steel

Scarred stainless steel

Polished stainless steel

Galvanized carbon steel

Aluminium

Extruded high-density polyethylene

D2 Smooth

Carbon steel with slight surface corrosion

Coated carbon steel

Cast high-density polyethylene

Smooth ceramic plates

Concrete surface manufactured with steel shell

D3 Rough

Rough shell concrete

Scarred carbon steel

Steel silos with bolts on the inside surface of the

wall

Roughly polished ceramic plates

D4 Corrugated

Horizontal corrugated wall

Contoured sheet metal with horizontal notches

Non-standardised walls with large deviations

The effect of wrinkling in these surfaces has to be very carefully examined by means of the

particles embedded in the wall surface.

NOTE The classification and description given in Table 3 refers to the friction

rather than the roughness. The main reason for this is that there is only a small

correlation between the degree of roughness and the measured amount of wall friction

caused by the bulk material that slides along the wall surface.

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6.2.2 Determination of the Bulk Material Parameter (1) The material parameters to be used for the design calculation may have deviations

due to the changes in the structure, the production procedure, the grain size

distribution, moisture content, age and electrical charging during handling; these

need to be taken into account.

(2) The bulk material parameters are to be determined either according to the

simplified procedure laid down in 6.2.3 or by means of test measurements in

accordance with 6.3.

(3) Bulk materials parameters which are not contained in Table E.1 are to be obtained

by means of test measurements in accordance with 6.3.

(4) The calculated correction values for the coefficient of wall friction µ of the bulk

materials should take into account the roughness of the wall surface along which

they glide. In Table 3 the different classes of wall surfaces are defined for use in

this standard.

(5) For silos with wall surfaces belonging to the class (category) D4 according to

Table 3, the effective wall friction coefficients should be determined according to

the procedure described in D.2.

(6) The bulk material correction value Cop for the reference surface loads is to be

taken from Table E.1 or calculated according to the equation (8).

6.2.3 Simplified Procedure

(1) The parameters of commonly known bulk materials are to be taken from the Table

E.1. The values given there for the specific gravity γ correspond to the upper

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characteristic value, while the parameters for the wall friction µm, for the horizontal

load ratio Km and for the angle of the internal friction φim represent mean values of

these characteristic quantities.

(2) If individual bulk materials cannot be clearly classified under the bulk material

categories listed in Table E.1, then their parameters are to be determined

experimentally in accordance with the procedure described under 6.3

(3) For determining the characteristic parameters of µ, K and φi, the listed values of

µm, Km and φim are to be multiplied or divided by the so called conversion factor.

The conversion factors ax are given in the table E.1 for the bulk materials listed

therein. For calculating the maximum loads, the following combinations are to be

used:

Upper characteristic value of mk KaK = (1)

Lower characteristic value of k

ma

KK = (2)

Upper characteristic value of ma µµ µ= (3)

Lower characteristic value of µ

µµ am= (4)

Upper characteristic value of imi a ϕϕ ϕ= (5)

Lower characteristic value of ϕ

ϕϕ aim

i = (6)

(4) For determining the effect of action on silos of the requirement category 1, the

mean values µm, Km and φim may be used instead of the upper and lower characteristic

values.

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6.3 Measurement of Bulk Material Parameters in Tests 6.3.1 Experimental Determination (Measuring System)

(1) The experimental determination of the parameters is to be executed with

representative bulk material specimens. For every bulk material property a mean value of

the relevant parameter is to be determined keeping in mind the deviation of its relevant

so-called secondary influence parameter such as bulk material structure, filtering curve,

moisture content, temperature, age and the possibility of electrical charging during

operation or manufacture.

(2) The characteristic values are derived from the experimentally determined mean

values with the aid of equations (1) to (6) and the corresponding conversion factors ax.

(3) Each conversion factor ax is to be carefully determined. While determining the

same one should take into account the fact that the bulk material parameters can

undergo a change during the service life of the silo. Likewise, the possible consequences

of the sedimentation phenomena in the silo and the inaccuracies during processing of the

material specimens are to be taken into account.

(4) If the test data is there, the conversion factors ax are to be ascertained acc. to

C.11 in order to determine the standard deviation of the parameters.

(5) The span between the mean value and the characteristic value of the bulk material

parameter is expressed by the conversion factor ax. If a secondary influence parameter is

by itself responsible for more than 75% of the conversion factor ax, it has to be raised by

a factor of 1.10.

NOTE The above-mentioned specifications serve to ensure that the values of xx adequately

represent the probability of occurrence for the derived loads.

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6.3.2 Specific Gravity γ of the Bulk Material

(1) The specific gravity of the bulk material is to be determined for such a packing

density of the bulk material particles and at such a pressure-level, which corresponds to

the packing density or the pressure level that is present in the zone of maximum vertical

fill-pressure bzw in the silo. The vertical pressure Pvft can be determined from the

equations (11) or (86) for the depth of the bulk material at the lower end of the silo shaft.

(2) For measuring the specific gravity γ the test procedures acc. to C.6 should be

used.

(3) The conversion factor for deriving the characteristic value from the measured

value is to be determined in accordance with the procedure described in C.11. The

conversion factor aγ may not be less than aγ = 1.10, except when a smaller value can be

separately established through tests or a suitable estimation (see C.11).

6.3.3 Coefficient of Wall Friction µ

(1) The experimental determination of the coefficients of wall friction µ for the

estimation of loads is to be determined for such a packing density of the bulk material

particles and at such a pressure-level, which corresponds to the packing density or the

pressure level that is present in the zone of maximum horizontal fill-pressure Phfb in the

silo. The pressure level Phfb can be determined from the equations (9) or (78) for the

depth of the bulk material at the lower end of the zone with vertical walls. (2) For measuring the coefficients of wall friction µ the test procedures acc. to C.7

should be used.

(3) The mean value µm of the coefficients of wall friction and its standard deviation are

to be determined and derived through tests. If only one mean value can be ascertained

from the data material, the standard deviation is to be estimated in accordance with the

method described in C.11.

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conversion factor may not be less than aµ = 1.10, except when a smaller value can be


6.3.4 Angle of Internal Friction ϕi

(1) The angle of internal friction ϕi for the calculation of loads is to be determined – as

arc tangents from the ratio of the shear force to the normal force at the break under

equivalent load - for such a packing density of the bulk material particles and at such a

pressure-level, which corresponds to the packing density or the pressure level that is

present in the zone of maximum vertical fill-pressure Pvf. The pressure level Pvf can be

determined from the equations (11) or (86) for the depth of the bulk material at the lower

end of the zone with vertical walls.

(2) For measuring the angle of internal friction ϕi the test procedures acc. to C.9

should be used.

(3) The mean value ϕim of the angle of internal friction and its standard deviation δ are

to be determined and derived through tests. If only one mean value can be ascertained

from the data material, the standard deviation is to be estimated in accordance with the




conversion factor aϕ may not be less than aϕ = 1.10, except when a smaller value can be


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6.3.5 Horizontal Load Ratio K

(1) The horizontal load ratio K for the estimation of loads (the ratio of mean horizontal

pressure to mean vertical pressure) is to be determined for such a packing density of the

bulk material particles and at such a pressure-level, which corresponds to the packing

density or the pressure level that is present in the zone of maximum vertical fill-pressure.

The pressure level pvft can be determined from the equations (11) or (86) for the depth of

the bulk material at the lower end of the zone with vertical walls.

(2) For measuring the horizontal load ratio K the test procedures acc. to C.8 should be

used.

(3) The mean value Km of the horizontal load ratio and its standard deviation are to be

determined and derived through tests. If only one mean value can be ascertained from

the data material, the standard deviation is to be estimated in accordance with the


(4) An approximate value for Km can be alternatively calculated according to the foll.

Equation (7) from the mean value of the angle of internal friction for first load application

imϕ determined through tests (see 6.3.4)

Km = 1.1 (1- sin ϕim) (7)

NOTE The factor 1.1 in equation (7) is used in order to ensure an appropriate derivative

unit of measure for making allowance for the difference between a value of K (= Ko ) that was

measured under virtually absent wall-friction influences and a value of K that was measured in

the presence of wall friction influences (see also 6.2.2 (5)).

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conversion factor aK may not be less than aK = 1.10, except when a smaller value can be


6.3.6 Cohesion c

(1) The cohesion of bulk material varies with the consolidation stress to which the

specimen is subjected. It is to be determined for such a packing density of the bulk

material particles and at such a pressure-level, which corresponds to the packing density

or the pressure level that is present in the zone of maximum vertical fill-pressure Pvf. The

pressure level Pvf can be determined from the equations (11) or (86) for the bulk material

depth at the lower end of the zone with vertical walls.

(2) For measuring the cohesion c the test procedures acc. to C.9 should be used.

NOTE Alternatively the cohesion can be estimated by means of results of tests in the shear cells

of Janike. A method for calculating the cohesion from test results is to be taken from C.9.

6.3.7 Bulk material Correction Value for the Reference Surface Load Cop

(1) The bulk material correction value for the reference surface load Cop is to be

estimated on the basis of suitable test data.

NOTE 1 The discharge factors C make allowances for a host of phenomena which arise during the

emptying of silos. The symmetric increase of pressures is relatively independent of the stored bulk material,

yet the unsymmetric components are greatly dependant upon the material. The material-dependency of the

unsymmetric components is represented by the bulk material correction value Cop . This parameter is not

easy to determine with the help of experimental test procedures.

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NOTE 2 A suitable experimental test procedure for the parameter Cop has not so far been

developed. This factor is therefore based on evaluations of tests on silos and on experimental values of

silos with conventional filling and discharge systems, which were established within the usual structural

tolerances.

(2) Values for the bulk material correction values for the reference surface load Cop of

commonly known bulk materials are to be taken from Table E.1.

(3) For materials which are not listed in Table E.1, the bulk material correction value

for the reference surface load can be estimated from the divergence factors for the

horizontal load ratio aK and the wall friction correction value aµ acc. to equation (8):

Cop = 3.5 aµ = 2.5 aK – 6.2

Where

aµ divergence factor for the coefficients of wall friction µ;

aK divergence factor for the horizontal load ratio K of the bulk

Material.

(4) For special silos or special bulk materials (in the individual case) the suitable bulk

material correction value for the reference surface load Cop can be estimated by means of

large scale experimental investigations in silos with designs that are comparable.

7 LOADS ON VERTICAL SILO WALLS 7.1 General (1) For the filling and the emptying types of loads, the characteristic values of the

loads described in this section have to be fixed. For this purpose the loads are

differentiated as follows:

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DIN 1055-6:2005-03

slim silos

silos of medium slimness

low silos

braced walls silos (silos consisting of braced walls)

silos for the storage of bulk materials air pockets between the bulk material

particles (for example, due to pneumatic discharge aids and homogenizing

silos)

silo hoppers and silo bottoms

(2) The loads on the vertical silo walls are to be determined in accordance with the

following criteria pertaining to the slimness of the silos:

slim silos, with 2.0 < hc / dc (with exceptions acc. to 5.3)

silos with medium slimness, with 1.0 < hc / dc < 2.0 (with exceptions acc. to

5.3)

low silos, with, 0.4 < hc / dc < 1.0 (with exceptions acc. to 5.3)

braced wall silos (silos consisting of braced walls) with horizontal bottoms

and hc / dc < 0.4

silos for bulk materials with air pockets between the bulk material particles

(3) A silo with an aerated bottom is to be handled – independent of its actual slimness

hc/ dc -- like a slim silo.

(4) The loads on the vertical walls are made up of a stationary load component, the

symmetrical loads and a free load component, the reference surface loads. Both the

components are to be assessed as acting simultaneously.

(5) Special types of loads are to be taken into account for large fill and discharge

eccentricities. These are not to be placed simultaneously with the symmetrical and

reference surface loads; each represents a separate and clearly defined load category.

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(6) Detailed guidelines for the calculation of fill and discharge loads are given within

the context of silo slimness in sections 7.2, 7.3 and 7.4.

(7) Rules for the additional types of loads for special types of silos and special design

conditions are given in 7.5 till 7.7:

see 7.5 for silos with air injection equipment for complete or partial

fluidization of bulk material

see 7.6 for loads due to hot-filled bulk materials

see 7.7 for loads in rectangular silos

(8) For circular silos with large fill and discharge eccentricities, load estimates are

given in 7.2.4. For non-circular silo bins corresponding load estimates should be derived

from these load estimates, if they are found to be suitable for design calculations.

(9) If funnel flow can be ensured within the bulk material without contact points

between the flow zone and the silo walls (see 5.3 (4)), the calculations can be limited to

the estimates of the filling loads, in which case the reference surface loads are to be

taken into account along with these, if required.

7.2 Slim Silos 7.2.1 Fill Loads on Vertical Walls 7.2.1.1 Symmetric Fill Loads

(1) The symmetric fill loads (see figure 8) are to be calculated acc. to the equations

(9) to (14).

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(2) After the filling is done and during the storage of the bulk material, the horizontal loads

Phf, the wall friction loads Pwf and the vertical loads Pvf are to be estimated as follows:

(9) ( ) ( )zYPzP jhohf =

( ) ( )zYPzP jhowf µ= (10)

( ) ( )zYKP

zP jho

vf = (11)

With

oho KzP γ= (12)

UA

Kzo µ

1= (13)

( ) ozz

j ezY−

−=1 (14)

Where

γ The characteristic value of the bulk material specific gravity

µ The characteristic value for the coefficients of wall friction for the bulk

material at the vertical silo walls

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K The characteristic value of the horizontal load ratio

z The depth of the silo material beneath the equivalent surface of the bulk

material

A The inner cross-sectional area of the silo

U The circumference of the inner cross-sectional area of the silo

(3) For the status after the filling is done, the resultant characteristic value of the wall

friction loads Pwf that have been added-up up till depth z – with the force per unit of length

in the direction of the circumference e.g. [kN/M] – is calculated using:

(15) ( ) ( )[ ]zYzzPdzzPP joho

z

wfwf −==∫ µ0

(4) For determining the characteristic values for the required bulk material parameters

(specific gravity (γ), correction value for wall friction µ and horizontal load ratio K), the

values given in 6.2 and 6.3 are to be used.

7.2.1.2 Reference Surface Load for Filling Loads: General Requirements

(1) For making an allowance for unplanned unsymmetrical loads due to eccentricities

and imperfections during the filling of the silos, reference surface loads or other suitable

load arrangements are to be placed.

(2) For silos of category 1 the reference surface load can be ignored for the filling

loads.

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Legend

1 equivalent bulk material surface

1

vfPwfP

wfP

z

hchfP

z1

hfP

Figure 8 – SYMMETRIC FILLING LOADS NEAR THE VERTICAL SILO WALLS

3) For silos in which powdery bulk material is stored and which are filled with the help

of air injection equipment, the placing of reference surface loads for the filling loads can,

as a rule, be done away with.

(4) The amount of reference surface load to be placed for the filling loads Ppf is to be

estimated on the basis of the maximum possible eccentricity ef the filled cone that

appears at the surface of the bulk material (see fig. 1b).

(5) The fundamental value of the reference surface load for the filling load Ppf is to be

fixed with:

hfpfpf PCP = (16)

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With:

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−+=

⎟⎠⎞

⎜⎝⎛ −⎥⎦

⎤⎢⎣⎡

⎟⎠⎞⎜

⎝⎛− 15.1

2 12121.0 cc

dh

oppf eECC (17)

c

f

de

E2

= (18)

But pfC > 0 (19)

Where

fe Is the maximum eccentricity of the filled cone which appears at the

Bulk material surface during filling;

hfP Is the local value of the horizontal fill pressure acc. to equation (9) at

the position at which the reference surface load is placed

opC Is the correction value of the bulk material for the reference surface

load (see table E.1).

(6) The height of the zone at which the reference surface load is to be placed (see

figures 9 and 10) amounts to:

cc dds 2.0

16≈=

π (20)

(7) The reference surface load consists of only a horizontally acting load component.

There are no frictional forces to be taken into account as a result of these

horizontal load components.

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(8) The form of the reference surface load for the filling loads depends upon the

structural design of the silo. The following structural designs of silos can be

distinguished with respect to the reference surface load to be placed:

-- Thick walled silos with circular cross-section see figure7.2.1.3 (e.g.

reinforced concrete silos);

-- thin walled silos with circular cross sections, see figure 7.2.14 (e.g. metal

silos without braces);

-- Silos with non-circular cross-sections, see 7.2.1.5

a) Thin walled circular silo b) ot

S

Ppf1

Ppf

Ppf

Ppf

S S

S

z php

a

hc

Ppfs

Ppf

θ

h

Ppf

Figure 9 - Longitudinal Section and Transverse SectionDiagrams of the Reference Surface Loads

her circular silo

b

s

Showing the Load

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Ppe,ncPpf,nc

P pe,

nc

P pf,n

c

P pe,

nc

] p

pf,n

c

S

a

h c

S a

h c

Legend

a smaller value of zo and hc/2

b as per choice

Figure 10 – LONGITUDNAL SECTION AND TRANSVERSE SECTION SHOWING THE LOAD DIAGRAMS OF THE REFERENCE SURFACE LOADS FOR NON-CIRCULAR SILOS

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7.2.1.3 Reference Surface Load for Filling Loads: Thick-Walled Circular Silos

(1) For thick-walled circular silos of the categories 2 and 3, the fundamental value of

The reference surface load for the filling load is to be estimated as it acts outwards pfP

Along the opposite sides of a quadratic reference surface with the side length s (see

equation (20)). The unit of measurement for the side length s should be applied to

the curved surface in a suitable manner.

2) In addition to the reference surface load that acts outwards, a complementary pfP

Reference surface load that is directed inwards is to be placed in the remaining

portion of the silo circumference above the same wall-height (see fig. 9b):

pfiP

pfiP = 7pfP (21)

Where

pfP is the fundamental value of the reference surface load acting outwards

for the filling loads acc. to equation (16)

NOTE The amount and the impact area of the load which is directed inwards are chosen

such that the resultants of both the load components counterbalance each other in the

middle at the position at which these are to be placed.

pfiP

(3) The reference surface load for the filling loads is to be placed at any

position on the silo wall. However it may be placed in accordance with the manner

described in 7.2.1.3(4).

(4) In thick-walled circular silos of category 2, a simplified proof may be furnished.

Half the height of the vertical bin shaft may be regarded as the most unfavourable

Position for placing the reference surface load. The largest percentage increase of the

dimensioning sections which result from the placing of reference surface loads at this

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position can be carried over to the other areas of the wall by multiplying over there the

design sectional sizes with the value of the ratio between the horizontal fill pressure at

the observed position and the horizontal fill pressure at the position where the reference

surface load was placed.

7.2.1.4 Reference Surface Load for the Filling loads: Thin-Walled Circular Silos

(1) For thin-walled circular silos (dc/t > 200) of the categories 2 and 3 the reference

surface load for the filling loads has to be placed above the height s acc. to equation (20).

It changes from a maximum pressure with the quantity ppf that acts outwards at a

particular point, into a maximum inwards-acting pressure with the same quantity ppf at the

opposite side (see figure 9a). The progression in the circumferential direction is to be

estimated with:

θcospfpfs PP = (22)

Where

is the reference surface load acting outwards acc. to equation (16) pfP

θ is the angle coordinate in the circumferential direction (see fig. 9a).

(2) The horizontal load that results from the reference surface load of the filling

loads is to be calculated for circular silos acc. to equation (23):

pfF

pfcpf PsdF2π

= (23)

(3) For welded silos of category 2, the reference surface load can be placed as active

load in a depth zp beneath the bulk material surface. For zp the smaller of the following

values is decisive:

zp = zo and zp = 0.5 hc (24)

Where, hc is taken as the height of the vertical silo shaft (see fig. 1a).

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(4) For silos with screw and bolt connections of category 2, the reference surface

loads the reference surface load is to be placed at any position as active load.

7.2.1.5 Reference Surface Load for Filling Loads: Non-Circular Silos (1) For non-circular silos of categories 2 and 3, one can make allowance for

the reference surface loads of the fill type by an increase of the symmetrical loads acc. to

(2) and (3).

(2) The reference surface load in the outward direction is to be positioned at each

point and depth in the silo as a stripe-shaped band with the band width s (acc. to

equation (20)) (see fig. 10a)

(3) The quantity of the uniform reference surface load is to be estimated using: ncpfP ,

(25) pfncpf PP 36.0, =

Where represents the fundamental value of the reference surface load of the fill type

acc. to equation (16). A suitable estimate for dc is to be derived from fig. 1d.

pfP

NOTE The value and the extent of the uniform load are so chosen that the resultant

bending moments for a silo with rectangular cross-section and without internal braces will take on

approximately the same order of magnitude as would result in the case of placing a local

reference surface load in the middle of the wall.

nhfP ,

pfP

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7.2.2 Discharge Loads on Vertical Walls 7.2.2.1 Symmetric Discharge Loads

(1) To make allowance for possible short-term load-increases during the discharge

process, an increase of the symmetric load components in the discharge loads is to be

made.

(2) For silos of all categories the symmetric discharge loads xx and xx are to be

determined from:

(26) hfhhe PCP =

(27) wfwwe PCP =

Where

is the discharge factor for horizontal loads; hC

is the discharge factor for wall friction loads; wC

The emptying factors and are to be estimated for each case present from the

equations (28) up till (32).

hC wC

(3) For silos of all categories which are emptied at the surface of the bulk material

(and therefore do not show any flow within the stored bulk material), the values from xx

and xx can be taken as

= = 1.0 (28) hC wC

(4) For slim silos of categories 2 and 3, the discharge factors are to be estimated

using:

(29) 15.1=hC

10.1=wC (30)

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(5) For slim silos of category 1, for which the mean values of the bulk material

parameters K and µ are used for load determination, the following values are to be taken

as discharge factors:

opc

h CdeC ⎟

⎠⎞⎜

⎝⎛ ++= 4.015.115.1 (31)

⎟⎠⎞⎜

⎝⎛ +=

cw d

eC 4.014.1 (32)

( )of eee ,max= (33)

Where

fe is the maximum eccentricity of the filled cone which appears during

filling at the bulk material surface (see fig 1b);

oe is the eccentricity of the midpoint of the discharge outlet;

opC is the bulk material correction value for the reference surface load

(see Table E.1)

(6) For the discharge type load the resultant characteristic value of the wall friction

loads which have been added-up up to the depth z – with the force per unit length for

the circumferential direction of the wall, e.g. [kN/m] – is derived from:

weP

(34) ( ) ( )[∫ −==z

johowwewe zYzzPCdzzpp0

µ ]

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7.2.2.2 Reference Surface Load for Discharge Loads: General Requirements (1) Reference surface loads for the discharge loads are to be estimated in order to

make allowances for the unplanned unsymmetric loads during emptying of the silo on the

one hand and the eccentricities during filling and emptying on the other (see fig. 1b).

(2) For silos of category 1, the reference surface load of the discharge type may be

ignored.

(3) For silos of categories 2 and 3 the procedures described in this section are to be

used for estimating the discharge loads.

(4) For silos of categories 2 and 3 the load estimates for slim silos (7.2.4) with large

discharge eccentricities (see 7.1 (5)) are to be used as a separate load-type, in addition

to the procedures described in this section, if the following conditions apply:

the eccentricity of the discharge outlet is larger than the critical value

(see fig. 4c);

oe

ccro de 25.0, =

The maximum eccentricity during filling is larger than the critical value

and the silo slimness is greater than the limit value

fe

ccrf de 25.0, =lim

⎟⎟⎠

⎞⎜⎜⎝

⎛

c

c

dh

=4.0 (see fig. 5d).

(5) The fundamental value of the outwardly-directed reference surface load for the

discharge type load is to be fixed with: peP

(35) hepepe PCp =

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With

( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−+=

⎟⎠⎞

⎜⎝⎛

⎥⎦⎤

⎢⎣⎡ −⎟

⎠⎞⎜

⎝⎛− 15.1

2 12142.0 cc

dh

oppe eECC (36)

cd

eE 2= (37)

But 2.101272.0 ≤⎟⎟⎠

⎞⎜⎜⎝

⎛≥⎥

⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−≥

c

c

c

coppe d

hforEdhCC (38)


Where

fe Is the maximum eccentricity of the filled cone which appears at the

bulk material surface during filling (see fig 1b);

oe Is the eccentricity of the midpoint of the outlet opening;

heP Is the local value of the horizontal discharge pressure acc. to

equation (26) at the position at which the reference surface load is

placed

opC is the correction value of the bulk material for the reference surface

load (see Table E.1)

(6) The reference surface load for the discharge type load consists of only one

horizontally acting load component. Additional frictional forces due to this horizontal load

are to be disregarded.

(7) The form of the reference surface load for the discharge type load depends upon

the structural style of the silo. This standard refers to the following structural styles of the

silos with respect to the reference surface loads to be assessed:

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Thick-walled silos with circular cross-sections see. 7.2.2.3 (reinforced

concrete silos);

thin-walled silos with circular cross-sections, see 7.2.2.4 (metal silos);

Silos with non-circular cross-sections, see 7.2.2.5.

7.2.2.3 Reference Surface Load for Discharge Loads: Thick-Walled Circular Silos

(1) For thick-walled circular silos, the fundamental value of

The reference surface load for the discharge type load (see equation (20)) is to be peP

Assessed as it acts outwards along the opposing sides on a quadratic reference

Surface with the side length s, in accordance with the illustration in fig. 11b

(2) In addition to the reference surface load that acts outwards, a complementary peP

Reference surface load that is directed inwards is to be placed in the remaining

portion of the silo circumference above the same wall-height (see fig. 11b):

peiP

7pe

pei

PP = (40)

Where

peP is the fundamental value of the reference surface load acting outwards

acc. to equation (35)

NOTE The amount and the impact area of the load which is directed inwards are chosen

such that the resultants of both the load components counterbalance each other in the

middle at the position at which these are to be placed.

peiP

(3) The reference surface load for the discharge type load is to be placed at any

position on the silo wall. However this is to be laid out in the manner described in

7.2.2.3(4).

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(4) In thick-walled circular silos of category 2 a simplified proof may be furnished.

Half the height of the vertical bin shaft may be regarded as the most unfavourable

position for placing the reference surface load. The percentage increase of the

dimensioning sectional sizes due to the placing of reference surface loads at this position

can be carried over to the other areas of the wall by multiplying over there the sectional

sizes with the value of the ratio between the horizontal fill pressure at the observed

position and the horizontal fill pressure at the position where the reference surface load

was placed.

S S

Ppe

Ppe1

Ppe

Ppes

Ppe

θ

Ppe

Ppe

a

h pz p

S h S

b

h c

a) Thin walled circular silo b) other circular silo Legend

a smaller value of Zp and ho /2

b any

Figure 11: Longitudinal Section and Transverse Section Showing the Load Diagrams of the Reference Surface Loads during Discharge

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7.2.2.4 Reference Surface Load for Discharge Loads: Thin-Walled Circular

Silos

(1) For thin-walled circular silos ( 200>t

dc ) of the categories 2 and 3 the reference

surface load for the filling loads has to be placed above the height s acc. to equation (20).

It changes from a maximum pressure with the quantity that acts outwards at a

particular point, into a maximum inwards-acting pressure with the same quantity at the

opposite side (see figure 11a). The progression in the circumferential direction is to be

estimated with:

peP

peP

θcospepes PP = (41)

Where

Is the reference surface load acting outwards acc. to equation (35) peP

θ Is the angle co-ordinate in the circumferential direction (see fig. 11a).

(2) The horizontal load that results from the reference surface load of the filling

loads is to be calculated for circular silos acc. to equation (42):

peF

pecpe PsdF2π

= (42)

(3) For welded silos of category 2, the reference surface loads can be placed as

active load in a depth beneath the bulk material surface. For the smaller of the

following values is to be fixed:

pZ pZ

op ZZ = and cp hZ 5.0= (43)

Where the height of the vertical silo shaft is to be put for (see fig. 1a) ch

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(4) For silos with screw and bolt connections of category 2, the reference surface

loads the reference surface load is to be placed at any position as active load.

Alternatively, the procedure in 7.2.3 can be used.

7.2.2.5 Reference Surface Load for Discharge Loads: Non-Circular Silos (1) For non-circular silos of categories 2 and 3, one can make allowance for

The reference surface loads of the fill type by an increase of the symmetrical loads acc.

to (2) and (3)

(2) The reference surface load in the outward direction is to be positioned at each

point and depth in the silo above a height s (acc. to equation (20)) (see fig. 10b)

(3) The amount of the uniform reference surface load is to be assessed using: ncpeP ,

(44) pencpe PP 36.0, =

Where represents the fundamental value of the reference surface load of the

discharge type acc. to equation (35). A suitable estimate for is to be derived from fig.

1d.

peP

cd

NOTE The value and the extent of the uniform load are so chosen that the resultant bending

moments for a silo with rectangular cross-section and without beam ties will take on approximately the

same order of magnitude as would result in the case of placing a local reference surface load in the

middle of the wall.

nheP ,

peP

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7.2.3 UNIFORM INCREASE OF LOADS AS REPLACEMENT FOR THE REFERENCE

SURFACE LOADS – FILL LOAD AND DISCHARGE LOADS – FOR CIRCULAR SILOS

(1) In circular silos of category 2 the procedure, using reference surface loads given in

7.2.1 and 7.2.2, for taking into account the unsymmetries in case of filling and

discharge can be approximately replaced by increasing the loads.

(2) In circular silos the following processes can be used only if the vertical silos are

designed such that they have adequate stiffness at their upper and lower ends to

withstand horizontal deformations and an adequate lateral distribution is ensured.

The upper end and the foot of the silo cylinder shell must be supported along its

circumference against the roof or a ring brace with a structural joint.

(3) For thick-walled circular silos the resulting horizontal loads in case of filling

and in case of emptying are to be calculated using uhfp , uhep ,

( )pfhfuhf Cpp ς+= 1, (45)

( )peheuhe Cpp ς+= 1, (46)

With

( tdc01.05.0 += )ς (47)

And

0.1≥ς (48)

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Where

hfp is the symmetrical horizontal load after filling acc to equation (9)

is the symmetrical horizontal load during emptying acc to equation (26) hep

is the correction value for the reference surface load in case of filling acc to pfC

equation (17)

peC is the correction value for the reference surface load in case of emptying acc

to equation (36)

(4) For thin -walled circular silos the resulting horizontal loads in case of filling

and in case of emptying and the wall friction loads and which result

from these loads are to be calculated using

uhfp ,

uhep , uwfp , uwep ,

( )pfhfuhf Cpp 5.01, += (49)

( )pfwfuwf Cpp 5.01, += (50)

( )pfheuhe Cpp 5.01, += (51)

( )pfweuwe Cpp 5.01, += (52)

Where

wfp is the symmetrical horizontal load in case of filling acc to equation (10)

is the symmetrical horizontal load in case of emptying acc to equation (27) wep

The parameters , , and are to be calculated using the procedure given in

(3).

hfp hep pfC peC

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7.2.4. DISCHARGE LOADS FOR CIRCULAR SILOS WITH LARGE ECCENTRICITIES DURING DISCHARGE

7.2.4.1 General

(1) For silos of categories 2 and 3, if the eccentricity of the outflow opening is

larger than the critical value

oe

ccro de 25.0, = , then the following procedures are to be

adopted for determination of the load distribution in order that allowance can be

made for an eccentric discharge in the form of a funnel flow above the outflow

opening (see fig 12a)

(2) For silos of categories 2 and 3, if the maximum eccentricity during filling is

larger than the critical value

fe

ccrf de 25.0, = , and the silo slimness larger

than 0.4=c

cd

h , then the following procedures are to be adopted for determination

of the distribution of pressure in the silo. This pressure distribution can arise as a

consequence of the build-up of an external funnel flow (see figures 5d and 12 a).

(3) In case it is necessary to use the procedure given in 7.2.4.2 and 7.4.2.3, these are

to be treated as separate load-types in addition to the filling and discharge loads

and the estimates of the reference surface loads in 7.2.2 and 7.2.3.

(4) The estimation of these loads is to be made using the lower characteristic value of

the wall friction µ and the upper characteristic value of the angle of internal

friction iϕ .

(5) For silos of category 2 a simplified procedure is allowed acc to 7.2.4.2. For silos of

category 3, the procedures in 7.2.4.3 are to be adopted.

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7.2.4.2 Procedure for Silos of Category 2 7.2.4.2.1 Geometry of the Flow Canal

(1) For silos of category 2 the calculations must be made only for that volume of the

flow canal which is in contact with the silo wall. The volume of the flow zone in

such case is to be determined through the value of the angle

(53) 035=Cθ

7.2.4.2.2 Wall Pressures during Eccentric Discharge (1) In the flow zone the horizontal loads on the vertical wall (see fig 12c) are to be

taken as

(54) 0=hceP

(2) In that area in which the bulk material is at rest, the horizontal loads on the vertical

silo walls at depth z (see fig 12c) are to be estimated using

(55) hfhse PP =

(56) hfhae PP 2=

and the wall friction load at the wall at depth z:

(57) wfwse PP =

(58) wfwae PP 2=

Where

hfP is the horizontal load ratio in case of filling acc to equation (9)

wfP is the wall friction load in case of filling acc to equation (10)

NOTE This simplified procedure corresponds to an ‘empty’ funnel and is very

conservative.

(3) Alternatively the procedures in 7.2.4.3.2 can also be used.

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7.2.4.3 Procedure for Silos of Category 3 7.2.4.3.1 Geometry of the Flow Canal (1) The geometry and the position of the flow channel are to be chosen such that

adequate allowance is made for the geometry of the silo, the discharge-conditions

and the bulk material properties.

(2) If the conditions for discharge lead to the build-up of a flow channel with a clearly

defined geometry and position, then the parameters which can be derived from

this flow channel should be adopted for further use.

(3) If the geometry of the flow channel cannot be directly derived from the

arrangement of the outflow openings and the silo geometry, calculations must be

made with at least three different flow channel radii , in order to make allowance

for the any chance that the volume of the flow channel may change with the

passage of time. The following three values should be considered:

cr

(59) rrc 5.0=

(60) rrc 75.0=

(61) rrc 9.0=

Where

r is the radius 2cd= of the circular silo

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4

2

1

3

5

1

2

a) Front view b) cross-section a) Flow channel and reverse distribution

1phae

5

phceθ

θc

θc

6

θc

ec

rc

r ψ

ph

3

b) Geometry of the flow channel loads varying with the depth of the silo Legend 1 bulk material at rest

2 flow channel

3 loads in the static zone

4 local high loads

5 loads in the flow zone

6 flow channel-margin loads

Figure 12 – FLOW CHANNEL AND PRESSURE DISTRIBUTION IN CASE OF DISCHARGE WITH LARGE ECCENTRICITIES

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(4) The eccentricity of the flow channel can be worked out by:

( ) ( ){ }GGrec −−+−= 111 ηη (62)

With rrG c= (63)

And iϕ

µη tan= (64)

Where

µ is the lower characteristic value of the coefficient of wall friction for the vertical silo

wall

iϕ is the upper characteristic value of the angle of internal friction of the stored bulk

material

cr is the dimensioning value of the flow channel radius acc to equations (59) to (61)

NOTE 1 It must be emphasized that iw ϕϕ ≤ is always given, because

otherwise a sliding surface would build up within the bulk material. This means that

in equation (64) 1≤η always.

NOTE 2 As indicated in fig 5d the eccentricity of the flow channel can vary. It is

not solely and exclusively dependant upon the eccentricity of the outflow opening.

The given procedure intends to make allowance for all those situations which

could lead to the most unfavourable ratios possible in each silo geometry and in

each structural arrangement. The eccentricity of the flow channel can, in effect,

therefore be smaller than the critical filling eccentricity and the critical

discharge eccentricity .

ce

crcfe ,

crcoe ,

NOTE 3 This estimate of the position and volume of the flow channel is based upon

the principle of minimizing the frictional resistance of the bulk material at the

peripheral surface of the flow channel based on the simplistic assumption that the

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circumference of the flow channel is a circular curve. Other suitable procedures for

the determination of the circumference of the flow channel may also be used.

(5) Apart from the flow channel geometries mentioned in (3), in case of a hopper for

“expanded flow” (see fig 6d) one has to consider the additional possibility of a flow

channel with a radius equivalent to the radius of the silo cross-section at the upper end of

the hopper for “expanded flow”.

(6) The limitation of the contact surface between the flow channel and the silo wall is

defined in terms of the angle at circumference cθθ ±= , where:

( )c

ccc re

rer2cos

222 −+=θ (65)

(7) The curve-length of the contact surface between the flow channel and the wall is:

rU cwc θ2= (66)

And the curve-length of the contact surface between the flow channel and the bulk

material which is in a state of rest is:

( )ψπ −= csc rU 2 (67)

Where

ccrr θψ sinsin = (68)

And the two angles cθ and ψ are to be put in radian measure.

(8) The cross-section of the flow channel is to be calculated as follows:

( ) ( )ccccc rrrrA θψθψπ −−+−= sin22 (69)

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7.2.4.3.2 Wall Loads during Discharge with Large Eccentricities (1) The horizontal loads on the vertical walls in the flow channel zone (see fig 12c) are

dependant upon the depth z beneath the equivalent bulk material surface and can be

calculated in acc with:

⎟⎠⎞

⎜⎝⎛ −=

−ocz

z

hcohce epp 1µ (70)

The wall friction loads acting upon the walls at depth z can be determined by:

⎟⎠⎞

⎜⎝⎛ −==

−ocz

z

hcohcewce eppp 1µµ (71)

With

ochco Kzp γ= (72)

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=iscwc

coc UU

AK

zϕµ tan

1 (73)

Where

µ is the coefficient of wall friction in the area of the vertical wall

K is the horizontal ratio of the bulk material.

(2) The horizontal loads on the silo walls at depth z in the area outside the flow zone

where the bulk material is in a state of rest are to be calculated using

(74) hfhse pp =

And the wall friction loads upon at depth z:

(75) wfwse pp =

Where

hfp is the horizontal loads in case of filling loads in acc with equation (9)

wfp is the wall friction loads in case of filling loads in acc with equation (10)

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(3) Higher loads act directly upon the vertical silo walls (see fig 12c) in the passage

leading from the flow zone to the area where the bulk material is in a state of rest. These

outward-acting horizontal loads next to the flow channel at depth z beneath the

equivalent surface of the bulk material are to be estimated using:

(76) hcehfhae ppp −= 2

And the accompanying wall friction loads corresponding to these, upon the wall at depth

z are to be estimated using:

haewae pp µ= (77)

7.3 Low Silos and Silos with Medium Slimness 7.3.1 Fill Loads on the Vertical Walls 7.3.1.1 Symmetric Fill Loads

(1) The symmetric fill loads (see figure 13) are to be calculated acc. to the equations

(78) to (87).

(2) The values for the horizontal loads and the wall friction loads for the fill type

loads are to be fixed at each position as follows:

hfP wfP

(78) ( )zYPP Rhohf =

hfwf PP µ= (79)

With:

UAKzP oho µ

γγ 1== = (80)

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

+⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=n

oo

or hz

hzzY 11 (81)

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UA

Kzo µ

1= (82)

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−+−=

o

or z

hn 1tan1 ϕ (83)

Where

oh is the vertical distance between the equivalent bulk material surface

and the highest contact point of the stored bulk material with the wall

(see fig. 1a and 13)

The quantity is to be measured as: oh

rorh ϕtan3

= for a symmetrically filled circular silo (84)

And as

ϕtan3

co

dh = for a symmetrically filled rectangular silo (85)

Where

γ Characteristic value of the bulk material specific gravity

µ Characteristic value for the coefficients of wall friction between the bulk

material and the vertical silo walls

K is the characteristic value of the horizontal load ratio of the stored bulk

material

z is the depth beneath the equivalent surface of the bulk material

A is the inner cross-sectional area of the vertical silo

U is the inner circumference of the cross-section of the vertical silo

rϕ Is the gradient of slope of the bulk material (see Table E.1)

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(3) The amount of the vertical load at a depth of is to be fixed for the fill type load

using:

vfP vz

vvf zP γ= (86)

Where

( )( )

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−−−

−−+

−=+

noo

noo

ooov hzhzzhz

nhz

121

1 (87)

3

2 ho

G 1

z

Legend 1 equivalent bulk material surface

2 silo loads as per the rules for slim silos

3 loads for low silos

Figure 13 – LOADS IN A LOW SILO OR SILO OF MEDIUM SLIMNESS AFTER FILLING (FILL LOADS)

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(4) For the fill load the resultant characteristic value of the wall friction loads which

have been added up to a bulk material depth z – with the force per unit length in the

circumferential direction of the wall, e.g. [kN/m] – is calculated using:

wfP

( ) ( )vho

z

wfwf zzPdzzPP −== ∫ µ0

(88)

With acc. to equation (87) vz

7.3.1.2 Reference Surface Load for Fill Loads

(1) The fill type of reference surface loads are to be fixed at each point in the

vertical projection of the silo as allowance for unplanned loads and small filling

eccentricities (see figure 1b)

pfP

(2) Details for determining the form, the position and the amount of the reference

surface load for fill loads are to be taken from the regulations in 7.2.1

(3) The reference surface load consists of only one horizontally acting load component.

There are no additional friction loads to be taken into account as a consequence of this

horizontal component.

(4) For low silos 0.1≤c

c

dh of all categories, the fill type of reference surface loads need

not be taken into account 0=pfC

(5) For silos with medium slimness 0.20.1 <<c

c

dh of category 1, the fill type of reference

surface loads need not be taken into account 0=pfC

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(6) For silos with medium slimness 0.20.1 <<c

c

dh of categories 2 and 3 the reference

surface loads of the fill type are to be used acc. to 7.2.1 by way of allowance for the

incidental unsymmetric loads and small eccentricities during filling up (see fig. 1b).

fe

pfP

7.3.2 Discharge Loads on the Vertical Silo Walls 7.3.2.1 Symmetrical Discharge Loads

(1) In the case of discharge loads an increase of the symmetric load components is to

be fixed for making allowance for the possible short term load increases during the

discharge processes.

(2) For low silos ⎟⎟⎠

⎞⎜⎜⎝

⎛≤ 0.1

c

c

dh

the symmetric discharge loads can be equalized with the

fill loads acc. to 7.3.1.

(3) For silos of medium slimness ⎟⎟⎠

⎞⎜⎜⎝

⎛<< 0.20.1

c

c

dh the symmetrical discharge loads and

are to be calculated as follows:

heP

weP

(89) hfhhe PCP =

(90) wfwwe PCP =

Where

hC And are the discharge factors for the horizontal loads and wall

friction loads acc. to the equations (91) to (96).

wC

(4) For silos of all categories which are emptied from the surface (whereby no friction

takes place within the stored bulk material) the values and can be taken as hC uwzC

wC = = 1.0 (91) hC

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(5) For silos with medium slimness of the categories 2 and 3, the discharge factors

are to be fixed such that

Sh CC 15.00.1 += (92)

Sw CC 10.00.1 += (93)

With as the correction value for slimness SC

0.1−=c

cS d

hC (94)

(6) For silos with medium slimness of category 1, the discharge factors are to be

calculated as follows if the mean values of the material parameters K and µ have been

used in fixing the load:

sopc

h CCdeC

⎭⎬⎫

⎩⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+++= 4.015.115.00.1 (95)

Sc

h CdeC ⎟⎟

⎠

⎞⎜⎜⎝

⎛++= 4.114.00.1 (96)


Where

fe Maximum eccentricity of the banked-up cone during the filling

Eccentricity of the midpoint of the outlet opening oe

opC Bulk material correction value for the reference surface load acc. to Table

E.1

Slimness correction value acc. to equation (94) sC

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(7) For discharge load the resultant characteristic value of the wall friction loads

added up to depth z - with the force per unit length in the circumferential direction of

the wall, e.g. [kN/m] to be derived from:

weP

(97a) ( ) ( )vhow

z

wewe zzPCdzzPP −== ∫ µ0

With acc. to equation (87) vz

7.3.2.2 Reference Surface Load for Discharge Loads

(1) The reference surface loads in case of discharge are to be fixed taking into

account unplanned loads and small filling eccentricities (see fig. 1b).

peP

(2) Details of the form, positioning and quantity of the discharge type reference

surface load are to be taken from the regulations in 7.2.2.


⎞⎜⎜⎝

⎛≤ 0.1

c

c

dh of all categories, the formulation of a reference surface

load of the discharge type can be ignored (i.e. 0=peC ) in case of an eccentricity during

emptying which is smaller than the critical value of oe ccro de 1.0, =

(4) For low silos and silos of medium slimness ⎟⎟⎠

⎞⎜⎜⎝

⎛< 0.2

c

c

dh of category 1, the

formulation of a reference surface load of the discharge type can be ignored (i.e 0=peC ).


⎞⎜⎜⎝

⎛≤ 0.1

c

c

dh of category 2 and an eccentricity during emptying which

is greater than the critical value of

oe

ccro de 1.0, = , the formulations in 7.3.2.3 can be used.

(6) For silos with medium slimness ⎟⎟⎠

⎞⎜⎜⎝

⎛<< 0.20.1

c

c

dh of category 2, the formulations in

7.3.2.3 can be used.

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⎞⎜⎜⎝

⎛≤ 0.1

c

c

dh of category 3 and an eccentricity during emptying xx which

is greater than the critical value of ccro de 1.0, = , the formulations in 7.2.2.2 up to 7.2.2.5

are be used.

(8) For silos with medium slimness ⎟⎟⎠

⎞⎜⎜⎝

⎛<< 0.20.1

c

c

dh of category 3, the procedures in

7.2.2.2 up to 7.2.2.5 are to be used.

7.3.2.3 Uniform Increase of the Horizontal Loads as Replacement for the Reference Surface Loads of the Fill Type and the Discharge Type

(1) For silos of category 2, the procedure for reference surface loads in 7.3.1.2 and

7.3.2.2 can, by and large, be replaced by a uniform increase of the horizontal loads in

order to make allowance for the non-symmetries during fill and discharge.

(2) The procedures under 7.2.3 can be applied to the values of the reference surface

loads from 7.3.1.2 and 7.3.2.2 by using the equations (45) to (52), depending on the case

at hand.

7.3.3 LARGE FILLING ECCENTRICITIES IN CIRCULAR SILOS

(1) In circular low silos and circular silos of medium slimness ⎟⎠⎞⎜

⎝⎛ < 0.2

c

cd

h that belong

to category 3 and in which the eccentricity of the cone formed during filling is greater than

the critical value of (see fig. 14) the effect of the unsymmetric load

distribution on the vertical silo walls has to be examined.

ccrt de 25.0, =

(2) A conventional manual calculation, in which the vertical wall loads as per

equation (98) are added to the symmetric fill loads and discharge loads, can be used to

zSkP

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meet the requirements of 7.3.3 (1). The symmetric loads are to be determined for a state

of fullness with equivalent bulk material surface presuming a symmetric filling in

accordance with 7.3.1.1.

Zs

ef

1

φdc=2r

Legend

1 highest contact point of the bulk material with the silo

Figure 14 – FILLING PRESSURES IN CASE OF ECCENTRICALLY FILLED LOW SILOS OR SILOS WITH MEDIUM SLIMNESS

(3) The effect of the unsymmetric loads can be taken into account by increasing the

vertical forces near that wall where the filling height is the maximum.

NOTE The increase of the vertical forces arises from the global bending of

the silo. The bending occurs because the height of the material heaped along the wall

opposite to side from where the material is being fed is comparatively smaller and thus

the relevant horizontal loads – which maintain equilibrium – are absent. The increase of

the vertical load is to be added with the wall friction loads, which are calculated using the

symmetric loads (see above).

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(4) The upper characteristic value of the bulk material parameters K and µ is to be

used for the calculations.

(5) The characteristic value of the resultant additional vertical wall load ( )szSk zP is to

be determined at a depth z beneath the highest lying contact point of the bulk material

and the wall, using:

( )276tan04.0 ZZrezpP t

rshozSk −+⎟⎠⎞⎜

⎝⎛= ϕ (98)

And the force per unit of length in the circumferential direction with:

µ

γµγ

2r

UApho == (99)

BZ

Z s= (100)

ohK

rB −=µ2

(101)

3

1tan2

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞⎜

⎝⎛−

=r

erh

tr

o

ϕ (102)

Where

sz is the depth beneath the highest lying contact point of the bulk material and the

wall

rϕ is the gradient of slope of the bulk material

r is the radius of the circular silo wall

te is the eccentricity of the peak of the fill cone (see fig 1b and 14).

(6) The load component from equation (98) is to be added with the load component

fsrom the sum total of the wall friction loads acc to equation (88).

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7.3.4 LARGE DISCHARGE ECCENTRICITIES IN CIRCULAR LOW SILOS AND CIRCULAR SILOS WITH MEDIUM SLIMNESS

(1) For a discharge eccentricity , which is greater than the critical value oe ccro de 25.0, =

the procedure as per 7.2.4 is to be used in case of low silos and silos with medium

slimness ⎟⎠⎞⎜

⎝⎛ < 0.2

c

cd

h of categories 2 and 3. The loads described therein are to

be regarded as additional loads that have to be treated as a separate category

different from the symmetric loads and the reference surface loads (given in 7.3.2).

7.4 Braced Wall Silos 7.4.1 Fill Loads on Vertical Walls (1) The effect of the geometry of the filling angle and – if required – the buckling of the

braced wall is to be taken into account for the determination of the fill loads.

(2) While determining the horizontal load ratio K, the resistance of the wall to radial

elongation should be taken into account. In case mathematical calculations show a

sizeable (elastic) deformation of the braced wall (e.g. a positive displacement of the limit

value acc. to DIN 4085 or DIN V 4085-100) a lower horizontal load ratio K may be taken.

(3) A characteristic value for the horizontal load upon the vertical walls (see fig. 16)

is to be worked out.

hP

NOTE 1 The characteristic value of the horizontal load xx upon the vertical walls can be

approximately determined in the following manner:

( Srh zKP )ϕγ sin1+= (103)

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Where

Sz Is the depth beneath the highest contact point of the bulk material with the wall

(see fig 16);

γ Is the upper characteristic value of the bulk material’s specific gravity

Κ Is the upper characteristic value of the horizontal load ratio of the bulk material

rϕ is the slope gradient of the stored bulk material

NOTE 2 Equation (103) provides recognized realistic load estimates for a straight vertical wall with

fully developed wall friction contacts, subject to the condition that the angle of slope and the angle of

internal friction are identical.

(4) The characteristic value of the resultant additional vertical wall load (pressure)

– the force per unit of length in the circumferential direction – at any depth

beneath the highest contact point of the bulk material and the wall, is to be determined in

accordance with the load estimate under (3) taking into account the wall friction angle

( )Szsk zP Sz

uzµ .

NOTE 3 The characteristic value of the resultant additional vertical wall load (pressure) ( )Szsk zP

can be approximately determined as follows:

( ) Srzsk zKP 2sin12

ϕµγ += (104)

Where µ is the upper characteristic value of the coefficients of wall friction of the bulk material

(5) The other regulations within this standard notwithstanding, the deviation of the

bulk material parameters in case of braced wall silos has to be accepted by making

adequate allowance for it using the upper characteristic value of the specific gravity γ

and the horizontal correction value of the bulk material K .

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Zs

φr

1

Legend 1 load computation in a braced wall silo

Figure 15 – FILL PRESSURES IN A BRACED WALL SILO 7.4.2 Discharge Loads on Vertical Walls

(1) It can be presumed that the discharge loads on the vertical walls here are smaller

than the fill loads in 7.4.1.

(2) With reference to 7.4.2 (1) it must be taken into account that uneven distribution of

loads can occur as a result of an uneven intake of bulk material into the silo.

7.5 SILOS WITH FLUIDISED BULK MATERIAL

7.5.1 GENERAL

(1) Additional loads arising from fluidization and from air pressures caused by the

injection of air are to be taken into account while dimensioning.

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(2) Homogenising silos with fluidized bulk material and silos into which bulk material is

poured at high speed (see 3.1.16 and 3.1.17) are to be dimensioned for both the

situations:

-- fluidized bulk material

-- Non-fluidized bulk material

(3) In the situation where the bulk material is not fluidized, the loads are to be treated

in accordance with the procedure in 7.2 or 7.3.

7.5.2 LOADS IN SILOS FOR STORAGE OF FLUIDISED BULK MATERIAL

(1) In silos for storage of powdery bulk material (see 3.1.31) it is to be presumed that

the stored bulk material can become fluidized in case the speed of the increasing

bulk material surface exceeds 10m/h.

NOTE The conditions under which the bulk material can fluidise depend on several

factors that are not easy to define. The above-mentioned criterion is a simple

means of assessing whether this type of load can have a bearing on dimensioning.

If doubts still persist about a possible fluidization of the bulk material, then a

specialised opinion (e.g. bulk material mechanics) is called for.

(2) In homogenizing silos for storage of powdery bulk material (see 3.1.16) which are

in continual operation, one has to take into account the fact that the bulk material

could fluidise.

(3) The horizontal loads on the silo walls on account of the fluidized bulk material

can be computed acc to equation (105):

hp

zph 1γ= (105)

Where

1γ is the specific gravity of a bulk material (fluidized specific gravity)

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(4) The specific gravity 1γ of a bulk material in the fluidized state can be estimated

using the relationship

γγ 8.01 = (106)

Where γ is the specific gravity of the powdery bulk material acc to section 6

7.6 Temperature Differences between Bulk Material and Silo Construction 7.6.1 General (1) Design calculations for a silo structure should take into account the effects of

temperature differences between the bulk material and the silo structure and/or between

the surroundings and the silo structure.

(2) In case of a possibility of temperature differences between the stored bulk material

and parts of the silo wall or the entire silo wall, the silo is to be rated for the additional

loads due to differing thermal elongations subject to acceptance of a stiff bulk material.

(3) The temperature conditions are to be fixed acc. to the regulations in DIN 1055-7.

(4) Differing temperature deformations of the silo and the components associated with

the silo are to be taken into account.

(5) The following situations are to be watched while making calculations:

decrease of the surrounding temperature relative to the temperatures of the

silo structure and the stored bulk material

filling of the silo with bulk material which is hot

differences in the heating-up and cooling-down speeds between the

unprotected and uncovered components of steel and reinforced concrete

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retardation of wall deformation by the silo structure

NOTE Differences in warming-up of unprotected components made of steel and reinforced

concrete is typical of roof structures in which the roof trusses just run upon the silo walls on slide bearings

(without structural connections).

7.6.2 Loads due to a Decrease in the Surrounding Atmospheric Temperature (1) If there is a possibility of a decrease in the surrounding atmospheric temperature

within a short span of time, then the additional loads due to differences between the

temperature deformations of the outer structure and the mass of the bulk material that

has been filled (the latter being relatively less affected by thermal influences) are to be

taken into account.

(2) For silos with a circular ground plan, additional horizontal loads are to be fixed,

which act upon the vertical silo walls when the container cools down to a greater degree

than the bulk material stored. The additional loads at each point of the contact surface

between the silo walls and the bulk material are to be computed by:

hTP

( ) ⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛

∆=

sU

w

wwThT

EE

tr

ETCPν

α1

(107)

Where

TC Load augmentation factor due to temperature

wα Coefficient of thermal elongation of the silo wall

T∆ Is the temperature difference

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r Is the silo radius ( 2dc= )

t Is the wall thickness

wE is the elasticity modulus of the silo wall

ν is the Poisson number of the bulk material (approximately fixed with v = 0.3)

sUE is the effective elasticity modulus of the bulk material during pressure relief at a

depth z in the bulk material.

(3) The computation of the effective elasticity modulus of the bulk material during

pressure relief in the bulk material depth z, has to take into account the size of the

vertical fill load in the bulk material at this position.

sUE

vfP

(4) The effective elasticity modulus of the bulk material during pressure relief is to

be determined acc. to the procedure described in C.10.

sUE

(5) If the effective elasticity modulus of the bulk material is determined by tests, a

temperature-related load augmentation factor of

sUE

2.1=TC is to be fixed. Should an

effective elasticity modulus be derived by approximation from the bulk material

thickness, a temperature-related load augmentation factor of is to be fixed. 3=TC

7.6.3 Loads due to Filling of Hot Bulk material

(1) Should bulk materials with high temperatures be stored in a silo, an allowance has

to be made for the difference in the temperatures between that part of the material

which has been in the silo for a longer time and cooled down, and that part of the

material which is being added on above the bulk material surface where the air

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temperatures are higher. The effects of these temperature differences upon the

expansion pattern of the silo wall has to be observed.

(2) These effects do not need to be taken into account for silos of category 1.

7.7 Loads in Rectangular Silos 7.7.1 Rectangular Silos

(1) The wall loads caused by the bulk materials stored in silos of rectangular cross

section are to be fixed, depending upon the case, acc. to 7.2, 7.3 and 7.4.

(2) The loads determined at a specific bulk material depth in accordance with 7.2 can

be taken as mean values. The localized loads at this position can deviate from this mean

value.

(3) The general requirements of 6.1 (2) notwithstanding, for design calculations for

silos of categories 1 and 2 the favourable effect of the interaction between the bulk

material and the silo wall which takes the form of a transpositioning of the horizontal

loads from the centre of the wall (decrease) to the corners (increase) can be taken into

account if the silo wall is so designed that its stiffness is comparable with the stiffness of

the stored bulk material.

(4) In case the load transpositioning is being estimated in accordance with 7.7.1 (3),

the relevant load estimates should be used.

7.7.2 Silos with Internal Braces (1) In rectangular silo bins with beam ties running within the silo’s cross-section, the

bulk material loads upon the walls are to be fixed acc. to the methods in 7.2, 7.3 or 7.4

depending on the case.

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(2) The loads which are imposed by the braces upon the silo walls are to be

determined taking after making allowances for the following influences:

loads on the respective internal braces

position and securing of braces

slack of the braces

Influence of the structure’s rigidity on the increase of the slack caused by

the bulk material loads upon the beam tie.

(3) For silos of category 1 and 2, the calculation methods given in DIN V ENV 1993-4-

1:2002-05 Section 9 are to be used for making allowances for the loads upon the silo

structures caused by the internal beam ties.

8 LOADS ON SILO HOPPERS AND SILO BOTTOMS 8.1 General 8.1.1 Physical Parameters

(1) This section gives the applicable characteristic values of the fill and discharge

Loads for silo bottoms with the following types of layout:

flat bottoms

steep hoppers

flat inclined hoppers

(2) The loads on the walls of the silo hoppers are to be determined as per the foll.

Classification relating to the inclination of the hopper walls:

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if the angle of inclination of the bottom vis-à-vis the horizontal α is less than

5o then the bottom is presumed to be level

if the other two cases mentioned do not apply, then the hopper is presumed

to have a gentle inclination

A hopper is said to be steep if the foll. criteria are met (see figures 17 and

18):

⎟⎟⎠

⎞⎜⎜⎝

⎛ −<

h

Kµ

β2

1tan (108)

Where

K Lower characteristic value of the ratio of horizontal load acting upon

the vertical walls

β Angle of inclination of the hopper measured with reference to

The vertical axis (half of the vertical and opposite angle)

hµ Lower characteristic value of the coefficients of wall friction in the

hopper

NOTE A hopper is said to be steep if the bulk material slides along the inclined walls subject to the

condition that the silo is filled-up and the bulk material is in a thickened (consolidated) state caused by the

bulk material stored in the silo. The resistance to friction on the hopper walls may then be defined in terms

of the normal pressures on the hopper wall and the coefficients of wall friction. It may be referred to as “fully

mobilized wall friction” in this case. A hopper is said to be gently inclined if the bulk material does not flow

along the inclined walls of the hopper when the silo is full (the angle of inclination with reference to the

horizontal is too small or the wall friction is too high). The wall friction then does not have a direct

relationship with the normal pressures acting on the hopper walls and the coefficients of wall friction, but is

somewhat lower and depends upon the hopper’s angle of inclination and the level of stress in the hopper

(wall friction is not fully mobilized). Here the compressibility of the bulk material does play a role, yet it may

be ignored. In case of a transition from a steep hopper to a flat hopper the pressure estimates of both types

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of hoppers show an identical distribution pattern and identical values in both cases. The transition from a

steep to a flat hopper therefore takes place in uniform manner (angle of inclination for which the wall friction

is fully mobilized

0

0.1

0.20.3

0.4

0.5

0.6

0.7

0.80.9

1

1.1

0 10 20 30 40 50 60

K=0.7K=0.6K=0.5K=0.4K=0.3

Co-

effic

ient

of w

all f

rictio

n in

the

hopp

er µ

h

A

Figure 16 – BO

hh

x

P

Figure 17 – DIS

ngle of inclination of hopper with ref. to the vertical β

UNDARIES BETWEEN STEEP AND FLAT HOPPER

Phf

steil flach

Phf

Phf

Phf

z

Phf Phfβ

vft

TRIBUTION OF FILLING PRESSURES IN A STEEP AND FLAT SILO

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8.1.2 General Rules

(1) The mean vertical loads at the hopper transition and on a horizontal bottom may

be calculated with:

vfbvft PCP = (109)

Where

vfP is the vertical fill load acc. to the relevant equations (11) or (86)

depending upon the slimness of the silo. For coordinate z here, one

has to take the height of the silo walls h (i.e. at the hopper transition

shown in fig. 1a) and the bulk material parameters which lead to the

maximum hopper loads given in Table 2;

c

bC is the bottom load augmentation factor to make allowance for the

possibility that vertical loads larger than given in equations (11) and

(86) may be imposed upon the hopper and the silo bottom, if the bulk

material in the vertical shaft heaps-up over hopper.

(2) For silos of categories 2 and 3 the bottom load augmentation factor is to be

estimated in accordance with equation (110):

bC = 1.0 except under the conditions described in paragraph (4) (110)

(3) For silos of category 1, if the mean values and the material parameters Κ and

µ are used for determination of the load, then the bottom load augmentation factor is to

be fixed acc. To equation (111):

bC = 1.3 except under the conditions described in paragraph (4) (111)

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(4) There could be a pre-disposition for dynamic behaviour (conditions in paragraph

4), particularly under following conditions:

-- In a silo with a slim vertical silo shaft, when used for storage of bulk materials

which cannot be classified as bulk materials with marginal cohesion (see 3.1.23),

-- If the stored bulk material shows a tendency for interlocking amongst the bulk

material particles and for bridging (e.g. cement clinker),

-- Or, due to reasons other than the ones mentioned, there is a tendency for

sporadic loads during emptying (such as pulsating or knocking).

NOTE 1 The determination of the cohesion c of a bulk material is described in C.9. The cohesion c

is rated as marginal, if it does not exceed the value c/σΓ = 0.04, when the bulk material consolidates on

being subjected to a stress level of σΓ (see 3.1.23).

(5) If the stored bulk material shows a significant tendency to behave dynamically

during emptying of the silo (see paragraph (4)), then larger loads have to be placed for

the hoppers and the silo bottoms. The bottom load increase factor is then to be estimated

by:

= 1.2 for the categories 2 and 3 (112) bC

= 1.6 for category 1 (113) bC

NOTE 2 The loads on the hopper walls can alternatively be fixed acc. to the procedure described

in Annex H.

NOTE 3 The increased values for xx acc. to equation (113) must be used only when the

simplified procedures for load determination with the mean values of the characteristic bulk material

parameters have been used in category 1.

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(6) In each of the cases, the mean vertical load in the hopper is to be determined at a

height x above the (theoretical) apex of the hopper (see fig. 18) as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛+

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎥⎦⎤

⎢⎣⎡

−=

hft

n

hh

hv h

xPvhx

hx

nhP

1γ (114)

Where

( ) 2cot −+= FFSn heff βµ (115)

and

S = 2 for conical and quadratic pyramid-shaped hoppers (116)

S = 1 for wedge-shaped hoppers (117)

S = (1+b/a) for hoppers with rectangular plan (118)

Where

γ Upper characteristic value of the bulk material’s specific gravity

Is the vertical distance (height) between the apex of the hopper and the

transition into the vertical shaft (see fig. 18)

hh

x The vertical coordinate going outwards from the apex of the hopper (see fig.

18)

heffµ Is the effective or the mobilized characteristic coefficient of wall friction for

the hoppers (in each case acc. to the equation (122) or (132)

S is the coefficient for making allowance for the shape of the hopper

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F is the characteristic value of the load ratio in the hoppers (in each case acc.

to the equations (123), (127) or (133)

β Is the angle of inclination of the hopper with respect to the vertical (= 90o –

α) or the steepest angle with respect to the vertical in the case of a

quadratic or rectangular pyramid type of hopper

ftPv Is the mean vertical load in the bulk material at the transition of the hopper

for the filling loads (equation (109))

a is the length of the long side of a rectangular cross-section of the hopper

b is the length of the short side of a rectangular cross-section of the hopper

(7) While determining the load ratio F in the hopper, one has to consider whether the

hopper has to be rated as steep or as flat and whether the load in question is fill-type or

discharge-type of load. Suitable values for F are to be determined acc. to 8.3 or 8.4.

(8) The determination of a suitable value for the effective or mobilized coefficients wall

friction heffµ in the hopper has to take into consideration the question whether the hopper

has to be classified as steep or as flat or whether the load in question is of fill-type or

discharge-type. Suitable values are to be determined acc. to 8.3 or 8.4.

8.2 Horizontal Silo Bottoms

8.2.1 Vertical Loads on Horizontal Silo Bottoms

(1) The vertical loads on horizontal silo bottoms (inclination α ≤ 5o) can approximately

be taken as constant, except if the silo is classified as low and medium-slim. In such

cases the specification in 8.2.2 are to be used.

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(2) The vertical loads on horizontal bottoms are to be calculated using:

pv = pvft (118)

Where

pvft is to be calculated using equation (109)

(3) The vertical loads on horizontal silo bottoms for discharge loads are to be

equalized with the loads of the fill type.

8.2.2 Vertical Loads on Level Silo Bottoms in Low Silos and Silos with Medium Slimness

(1) For low silos and silos with medium slimness one has to keep in mind that in case

of horizontal silo bottoms, local bottom loads larger than the ones in 8.1.2 (equation

(109)) can occur.

(2) The vertical loads pvsq on the horizontal silo bottom of a low silo and a silo with

medium slimness are to be determined with

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

−∆+=

c

tp

c

c

sqvbvsq

dhdh

PPP0.2

0.2 (119)

Where

(120) vhovtpsq PPP −=∆

tpvtp hP γ= (121)

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hc

ho

htp

2

1

Legend

1 equivalent bulk material surface

2 lowest point of the wall without any contact with the bulk material

Figure 18 – BOTTOM LOADS IN LOW SILOS AND SILOS OF MEDIUM SLIMNESS

(3) The bottom loads acc to equation (119) can be computed for both fill loads

and discharge loads.

vsqp

(4) The value of acc to equation (119) reproduces the vertical loads in the vicinity

of the midpoint of the silo bottom. If support cannot be ensured for the bottom plate, then

a functional distribution of loads is required.

vsqp

8.3 STEEP HOPPER

8.3.1 MOBILISED FRICTION (1) For filling as well as for emptying loads the following value has to be computed for

the effective or mobilized coefficient of wall friction in equation (115):

hheff µµ = (122)

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Where

hµ is the lower characteristic value of the angle of wall friction in the hopper.

8.3.2 FILL LOADS

(1) For fill loads the mean vertical stress at any given position x in a steep hopper is to

be calculated acc to equations (114) and (115) as well as the parameter acc to

equation (123):

fF

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

h

fbF

µβtan1

1 (123)

In this case the parameter n in equation (114) is:

( ) βµ cot1 hbSn −= (124)

Where

b . Represents an empirical coefficient, which is to be taken as 2.0=b

The other parameters are defined in 8.1.2 (6).

(2) The loads perpendicular to the hopper walls and the wall friction loads at

any given position x of the wall of a steep hopper are to be calculated for the fill type of

loads (see fig 17) acc to the equations (125) and (126):

nfp tfp

(125) vfnf pFp =

vfhtf pFp µ= (126)

Where

fF is to be calculated using the equation (123)

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8.3.3 DISCHARGE LOADS

(1) For discharge loads the mean vertical stress at any given position x in a steep

hopper is to be calculated acc to equations (114) and (115) using the parameter : eF

( )εβϕεϕ+−

+=

2cossin1cossin1

i

ieF (127)

With

⎭⎬⎫

⎩⎨⎧

+=i

whwh ϕ

ϕϕε

sinsin

arcsin (128)

hwh µϕ arctan= (129)

Where

hµ is the lower characteristic value of the coefficient of wall friction for the hopper

iϕ is the upper characteristic value of the angle of internal friction of the bulk material

stored in the hopper

NOTE 1 It is to be noted that the angle of internal friction of the hopper wall is always

smaller than or equal to the angle of internal friction of the bulk material stored in the

hopper ( iwhei )ϕϕ ≤.. , because otherwise a sliding surface will develop within the bulk

material when transverse stresses that can act upon the wall are larger than the internal

friction of the bulk material.

NOTE 2 The above equation (127) for is based upon the simple theory of Walker

for discharge pressures in hoppers. It is also possible to use the alternative expression

for by Enstad which is given in H.11.

eF

eF


any position x of the wall of a steep hopper are to be calculated for the discharge type of


nep tep

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(130) vene pFp =

vehte pFp µ= (131)

Where

eF is to be calculated using the equation (127)

Figure 19 – DISCHARGE PRESSURES IN A STEEP HOPPER AND A GENTLY

Pne

PhfZf

Phe

Pne

Phf

Pne

steep flat

z

hh Phe

Pne

β x

Pvft

SLOPING HOPPER

8.4 FLAT HOPPERS

8.4.1 MOBILISED FRICTION

In a gently sloping hopper the wall friction is not fully mobilized. The partially mobilized or

effective coefficient of wall friction is to be calculated as follows:

( )β

µtan2

1 Kheff

−= (132)

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Where

K is the lower characteristic value of the horizontal load ratio in the vertical

silo shaft, which leads to the maximum hopper loads (see table 2)

β is the angle of inclination of the hopper with reference to the vertical axis

(see fig 18)

8.4.2 FILL LOADS

(1) In fill loads the mean vertical stress at each depth of the bulk material in the

hopper is to be calculated as per equations (114) and (115), using the parameter , as

follows:

fF

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎠⎞

⎜⎝⎛ +

−=

heff

fbF

µβtan1

1 (133)

The parameter n in equation (114) amounts in this case to:

( ) βµ cot1 heffbSn −= (134)

Where

heffµ is the mobilized or effective coefficient of wall friction in a flat hopper acc to

equation (132)

b is an empirical coefficient, which is to be taken as 2.0=b

The other parameters are defined in 8.1.


any position x of the wall of a flat hopper are to be calculated for the discharge type of


nfp tep

(135) vene pFp =

vehte pFp µ= (136)

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Where

fF is to be calculated using the equation (132)

8.4.3 DISCHARGE LOADS

In flat hoppers the discharge loads can be calculated - like the discharge loads (see fig

8.4.2) - perpendicular to the hopper walls and the wall friction loads (see fig 20). nep tep

8.5 Hopper Loads in Silos with Air-Injection Equipment

(1) For hoppers in which fluidization of the bulk material in the entire silo or certain

parts thereof due to use of air-injection equipment cannot be ruled out, allowance has to

be made for the additional loads due to fluidization and the air pressures.

(2) These loads should be determined without an estimation of the wall friction loads

as described in 7.5.2.

9 LOADS ON TANKS

9.1 GENERAL

The following rules are applicable for the determination of the characteristic loads caused

by fluids stored in tanks.

NOTE 1 These rules are applicable for all types of tanks under static conditions.

Tanks in which dynamic processes are at play, are not included.

NOTE 2 A lists of relevant influences, component safety factors and combination of

influences on tanks can be obtained from Annex B.

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9.2 LOADS CAUSED BY STORED FLUIDS

(1) Loads from stored bulk materials are to be calculated keeping in mind the

following factors:

-- The defined range of fluids which may be stored in the tanks

-- The geometry of the tank

-- The maximum possible filling height in the tank

(2) The characteristic value of the load is to be calculated acc to the equation: p

( ) zzp *γ= (137)

Where

is the depth beneath the fluid surface z

γ is the specific gravity of the stored fluid

9.3 CHARACTERISIC VALUES OF FLUIDS The specific gravities given in DIN 1055-1 are applicable.

9.4 SUCTION LAODS CAUSED BY INADEQUATE VENTILATION If the ventilation system of the tank is susceptible to interferences, a suitable calculating

method should be adopted in order to determine the sub pressures which arise during

discharge under extreme conditions. The calculation has to take into account the possible

adiabatic properties of the processes described.

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ANNEX A

(INFORMATIVE)

THE BASES FOR STRUCTURAL PLANNING – RULES SUPPLEMENTING DIN 1055-100 FOR SILOS AND TANKS

A.1 General

(1) The format given in DIN 1055-100 is the basis for design calculations. However

there is a fundamental difference between silos and tanks vis-à-vis other structures – for

the most part of their service life they are exposed to full loads arising from the bulk

material and fluids stored therein and these , as a rule, constitute a large proportion of

the fixed loads which result from the structure’s inherent weight.

(2) This Annex lays down additional rules for the partial safety factors relating to the

influences ( Fγ -correction values) and the combination of influences as well as for the

relevant combined correction values (ψ -correction values) for silos and tanks.

(3) The possible temperature-influences include the effects of climatic temperature

and the effects of hot bulk materials. The following calculating-conditions must be taken

into account:

-- Hot bulk materials that are poured into partially filled silos or tanks. In such cases

the repercussions of an increase of the air-temperature above the bulk material is to be

monitored.

-- Deformation of the silo wall structure caused by the bulk material as it cools down.

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(4) For determining the consequences of differing subsidence’s in the silo groups or

groupings of silo bins or tanks, the most unfavorable combination possible of filled and

empty bins are to be used.

A.2 Boundary State of the Loading Capacity

A.2.1 Correction Value γ of the Partial Safety Factor

(1) For the design calculations of silos and tanks, the values given in DIN 1055-

100:2001-03 Table 6 are used.

(2) If the maximum filling height and the highest specific gravity to be computed in

case of the fluids provided for storage is not exceeded, then the safety factor correction

value Qγ may be reduced from 1.50 to 1.35.

A.2.2 Combined Correction Value ψ

The combined correction values ψ for silo loads and loads in tanks and the combined

correction values for other influences are given in Table A.1

A.3 Combination of Influences

While furnishing proof of the loading capacity of a silo the following influences are to be

considered:

filling and storage of bulk materials

emptying of bulk materials

own loads and live loads (DIN 1055-3)

snow loads and ice loads (DIN 1055-5)

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wind actions, in filled as well as empty silos (DIN 1055-4)

temperature influences (DIN 1055-7)

forced deformations (impressed deformations): subsidence’s in the foundation

zone

earthquakes (DIN 4149)

dust explosions (see DIN-special report on dust explosions1)

A.4 Calculating-Conditions and Combined-Influences for Categories 2 and 3

(1) The predominant (dominant) and permanent influences are to be computed at

their full values whereas the secondary influences may be reduced using the

correction values ψ , in order to take into account the remote possibility of a

simultaneous occurrence in compliance with DIN 1055-100. The combinations

in Table A.1 can be used as reference values.

(2) In case the dominant influences in question are earthquakes or extraordinary

influences of loads, the secondary influences for the bulk material loads can be

calculated using the mean values of the coefficients of wall friction mµ , of the

horizontal load ratio , and of the hopper load ratio value , subject to the

condition that the suitable procedures given in 7.1, 7.3 and 8.1 are used.

mK mF

------- 1) under preparation

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TABLE A.1 – COMBINED CORRECTION VALUES XX

Influence oψ 1ψ 2ψ

filling / emptying of bulk-material 1.0 0.9 0.8

live loads, impressed deformations 0.7 0.5 0.3

snow loads and ice loads

places up to NN + 1 000 m

places over NN + 1 000 m

0.5

0.7

0.2

0.5

0

0.2

wind loads 0.6 0.5 0

temperature influences (not fire)* 0.6 0.5 0

building site subsidence’s 1.0 1.0 1.0

other influences ** 0.8 0.7 0.5

* see DIN 1055-7

** correction-values ψ for fluid pressure are to be determined based on the location

A.5 Combined Correction Values for category 1

For silos of category 1 the following simplified calculating situations can be used:

-- Filling

-- Emptying

-- Wind in case of empty silo

-- Silo filled completely and wind

-- Snow (for the roof)

-- Dust explosion

In case of wind loads the use of the simplified rules given in DIN 1055-4 are allowed.

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ANNEX B (NORMATIVE)

INFLUENCES, PARTIAL SAFETY FACTORS AND COMBINED CORRECTION VALUES FOR THE INFLUENCES ON TANKS B.1 General (1) The design calculations have to take into account the characteristic values of the

influences listed in section B.2.1 up to B.2.14.

(2) For these characteristic values the partial safety factors of the influences given in

B.3 and the combination rules given in B.4 are to be used.

B.2 Influences B.2.1 Loads from Stored Fluids

(1) During operation, the inherent-weight loads of the products that are filled in are to

be computed (beginning from the state of maximum fullness till the state of complete

emptying out) as loads resulting from filling.

(2) During a test filling, the inherent-weight loads of the test-filling substances that are

filled in are to be computed (beginning from the state of maximum fullness till the state of

complete emptying out) as loads resulting from filling.

B.2.2 Loads from Internal Pressures

(1) During operation, loads at the specified minimum and maximum values of the

internal pressures are to be regarded as “loads resulting from internal pressure”.

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(2) During a test filling, loads at the specified minimum and maximum values of the

internal pressures during the test filling are to be regarded as “loads resulting from

internal pressure”.

B.2.3 Loads from Temperature (-Changes)

Stresses due to forces caused by temperature expansions can be ignored if the number

of load cycles of temperature expansions does not lead to a risk of a fatigue or a cyclic

plastic failure.

B.2.4 Inherent Loads

(1) The resultant of the inherent weights of all individual components of the container

and the components attached to the latter are to be computed as inherent load.

B.2.5 Loads from Insulation (1) The inherent weights of the insulation are to be computed as loads arising due to

insulation.

(2) The computational values are to be taken from DIN 1055-1.

B.2.6 Distributed Live Loads

The distributed loads from usage (traffic/operation) that are to be computed should be

taken from DIN 1053-3, unless they are specified by the customer.

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B.2.7 Concentrated Live Loads

Concentrated individual loads from usage (traffic/operation) that are to be computed

should be taken from DIN 1053-3, unless they are specified by the customer.

B.2.8 Snow Loads

The snow loads are to be taken from DIN 1055-3.

B.2.9 Wind (1) The wind loads are to be taken from DIN 1055-4.

(2) Additionally one can take the following coefficients of pressure for circular

cylindrical tanks (see fig. B.1):

a) Internal pressure in case of top-open tanks and top-open collecting tanks:

6.0−=pc

b) Internal pressure in case of aerated tanks with small openings: 4.0−=pc

c) If there is a collecting tank then the pressure acting externally on the tank can be

computed as it decreases with height in a linear direction from top to bottom.

(3) In keeping with their temporary character, the wind loads – reduced during the

building phase – can be computed in accordance with DIN 1055-4 and

DIN 1055-8

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a) TANK WITH COLLECTING TROUGH

Cp a

Cp b

Cp a

φDT

φDc

∇ 0 00m

Cp=0.6

Cpa

Cpb

φDT

Cpa

b) TANK WITHOUT COLLECTING TROUGH Legend

a) acc. To DIN 1055-4 b) pc 4.0−=pc in case of ventilation

Figure B.1 – COEFFICIENTS OF PRESSURE FOR WIND LOADS IN CASE OF CIRCULAR CYLINDRICAL TANKS

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B.2.10 Low Pressure through Inadequate Ventilation Loads which arise due to inadequate ventilation are to be computed acc. to 9.4.

B.2.11 Seismic Loads

Seismic loads are to be computed acc to DIN 4149.

B.2.12 Loads from Connected Structures

Loads from pipelines, shutters or other objects and loads which result from the

subsidence of building foundations which are independent relative to the foundation of

the tank are all to be taken into account. Piping equipment should be designed such that

loads affecting the tanks are as small as possible. B.2.13 Loads from Irregular Subsidence

Loads from subsidence are to be taken into account if the occurrence of irregular

subsidences is to be expected during the designated service life.

B.2.14 Loads from Catastrophies

This includes blast wave, shock stress, fire damage, explosion, leakage inside the tank,

spillage and overfilling of internal tank.

B.3 Partial Safety Factors for the Influences (1) The safety factors given in DIN 1055-100 are to be used for influences listed under

B.2.2 till B.2.14

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(2) It is recommended that the safety factor for loads from fluids be computed for

operation (B.2.1 (1)) with 20.1=Fγ

(3) It is recommended that the safety factor for loads from fluids be computed during

the test filling (B.2.1 (2)) with 00.1=Fγ .

(4) In case of calculating conditions for extraordinary influences it is recommended

that the safety factor be computed using 00.1=Fγ for variable influences.

B.4 Combinations of Influences (1) The general stipulations in DIN 1055-100:2001-03 9.4 are to be followed.

(2) Live loads and snow loads must not be computed as simultaneous forces.

(3) Seismic influences must not be taken into consideration during the test filling.

(4) Catastrophic influences must not be taken into consideration during the test filling.

The combination regulations for extraordinary loads in DIN 1055-100:2001-03 10.4 are

however to be taken into consideration.

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ANNEX C (Normative)

Measurement of Bulk Material Parameters for the Determination of Silo Loads

C.1 General

(1) This annex describes test procedures which are introduced in this

standard exclusively for the purpose of determining bulk material parameters

which are used in the determination of the loads in silos. These procedures

are not applicable for designing of silos in the context of ensuring a reliable

bulk material flow. The level of pressure taken as the basis for the

determination of the bulk material parameters is far higher in the case of the

determination of bulk material loads than it would be in the case of a study of

the bulk material mechanism in the context of bulk material flow -- the reason

being that high pressures are required for the bulk material specimen being

tested to satisfy the relevant conditions pertaining to bulk materials. The

process of preparation of the specimens therefore differs in some respects

from what is considered standard procedure in terms of bulk material

mechanics.

(2) Compactness of a high order is required while preparing the specimen in

order to obtain a representative bulk material packing. All parameters which

influence the silo loads are to be determined subject to this condition,

because this condition of high compactness describes the reference status

for the upper characteristic values of the actions on the silo structure.

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C.2 Application

(1) The test procedures described in this annex are to be used for the

calculation of loads of silos in category 3 and for bulk materials which are not

contained in Table E.1. They can also be used as an alternative to the values

given in Table E.1 for the determination of the bulk material parameters. The

reference stresses in the tests act either in the vertical or the horizontal

direction. They have to reproduce stress levels, which are representative of

those that exist in the stored bulk material e.g. in the hopper passage during

the fill-load.

(2) The test procedures could also be used for the measurement of generally

applicable bulk material parameters for determining the loads of silos, but not

for specific silo geometry. Tests which are supposed to provide generally

applicable parameters for the designing of different silos can be conducted

subject to the foll. Level of reference load:

(a) for making allowance for vertical loads (C.6, C.8 and C.9):

reference stress rσ = 100 kPa;

(b) for making allowance for horizontal loads (C.7.2): reference stress

rσ = 50 kPa;

C.3 Symbols

The foll. Symbols have been used in this annex:

xa Conversion factor for the bulk material parameters for making

allowance for deviation

c Cohesion (see fig. C.4)

D Internal diameter of the test bin

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rF Residual shear-resistance (-force) at the end of the wall friction test

(see fig. C.2b)

moK Mean value of the horizontal load ratio for smooth walls

∆ Displacement of the upper part of the shear bin during shear test

iϕ Angle of internal friction while subjecting the specimen to stress (angle

of the overall shear strength)

cϕ Angle of internal friction during relief of the specimen (“effective

internal angle of friction”)

µ Coefficient of friction between the bulk material specimen and the wall

specimen (coefficient of wall friction)

rσ Reference stress

aτ The residual shear strength measured in a shear test after increasing

the normal pressure (see fig. C.4) (during relief)

• The shear pressure measured in a shear test

τb The maximum shear strength measured after reduction of the normal

stress in a shear test (refer fig. C.4) (stress relief)

C.4 Definitions

The following definitions are applicable to this annex.

C.4.1 Secondary Parameters

Each parameter which can influence the characteristic values of the stored

bulk material, but is not listed amongst the main factors that lead to variance

of the characteristic values. The composition, the grain grading (grain-size

distribution), the moisture content, the temperature, the age, the electrical

charging during operation and the production methods are a few examples of

the secondary parameters. The variances in the reference stresses defined in

C.2 may be regarded as secondary parameters.

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C.4.2 Specimen Selection Choosing specimen that represent the bulk material, that is provided for

storage or the material of the silo wall, while taking into account that the

properties of the material are subject to change with the passage of time.

C.4.3 Reference stress The state of stress that is prevalent at the time of measuring the

characteristic values of the bulk material. The reference stress is generally

chosen such that it corresponds to the level of stress prevalent in the bulk

material after the filling of the silo. At times it may be necessary to define the

reference stress in terms wider than just the principal stress.

C.5 Selection and Preparation of Specimen

(1) The tests are to be conducted with specimens that are representative of

the bulk material that has been provided for storage in the silo.

(2) The choice of the specimen has to be made keeping in mind that there

may be possible changes in the bulk material parameters during the course

of the silos usage, apart from the changes that occur on account of the

changing environmental conditions, the effects of the silos operational

processes and the effects of the sedimentation of the bulk material in the silo.

(3) The mean value of each of the bulk material parameters has to be

determined after making adequate allowance for variances of the relevant

secondary parameters.

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(4) For each test the reference stress rσ is to be determined as a function of

the pressure prevailing in the stored bulk material. The value for the

reference stress however should not to be very precisely defined.

NOTE 1 A precise determination of the reference stress would imply

that the test result was known before the test was conducted. The allowance

for an approximate value for the reference stress is not critical to the

interpretation of the test results. The tests however are to be conducted at a

stress level which is appropriate for the serving the purpose of conducting the

test.

(5) For tests in accordance with C.6, C.7.2, C.8.1 and C.9 the procedure

given below for specimen preparation has to be followed.

(6) The specimen is to be introduced into the test bin without vibrations or

other measures that may lead to its compression and is to be subjected to

the reference stress. In order to consolidate the specimen, a cover plate is to

be rotated (“twisted”) back and forth several times around its vertical axis,

both in the clockwise and the anticlockwise directions, at an angle of 10°.

NOTE 2 The number of rotations (“twists”) required depend on the bulk

material being tested.

(7) The mean values obtained from the tests are to be multiplied with a

conversion factor in order to derive extreme values. The conversion factors

are to be chosen such that allowance is made for the influence of secondary

parameters, for the changes of the bulk material parameters in the course of

use, and for inaccuracies while taking the specimens.

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(8) The conversion factor must be suitably adjusted in case the variance of

any of the secondary parameters amounts to more than 75% of the variance

range that is covered by the conversion factor.

C.6 Determination of Bulk Material Specific Gravity γ

C.6.1 Short Description

The bulk material density γ is to be determined using a consolidated (super

critically compressed) specimen of the bulk material.

NOTE The purpose/meaning of this test is to obtain a good estimate of the

maximum bulk material density that arises in the silo. This aim is fulfilled by the

determination of that density, which reaches its peak when the bulk material specimen is

subjected to that level of pressure which is prevalent in the silo after filling has taken

place. In order to achieve this it is necessary to pour the bulk material into the test bin in

such a manner that a suitable density is developed in the bulk material packing before

the specimen is subjected to a consolidating pressure. This can be achieved either by

using the “rain filling procedure” to pour the bulk material into the shear bin or by means

of preconditioning the specimen using the above-mentioned “twisting” of the cover plate.

This will lead to such density of the bulk material which is representative for the

conditions with respect to the determination of the silo loads. This procedure deviates

substantially from the procedure specified in ASTM D6883-01 because that mainly deals

with powdery bulk materials where the lowest possible density has to be achieved.

C.6.2 Test Apparatus The shear bin shown in fig. C.1 has to be used for the determination of the

weight and volume of a bulk material specimen. The bin diameter D must be

at least 5 times the maximum diameter of the bulk material grain and may not

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be lesser than 10 times the mean grain size. The height H of the compressed

specimen must lie between 0.3D and 0.4 D.

NOTE These restrictions relating to the grain size of the bulk material are

chosen due to the following reasons: the restriction on the maximum grain

size of the bulk material would ensure that the arrangement and orientation of

the bulk material grains are not unduly disturbed due to the influence of the

enclosing wall. Moreover it is known that this influence is greater in the

situation where all the particles have the same size, than in the situation

where the smaller particles can take up the space between the larger

particles. It is due to this reason that in case of uniform size of the particles a

restriction of 10 times the size of the particle and in case of a wider range of

particle-sizes a restriction of 5 times the maximum particle diameter is

prescribed.

4

3DN rπσ=

1

Dφ

a

b

H Legend

1 standardized rotation

a smooth surface

b rough surface

Figure C.1 – ARRANGEMENT FOR DETERMINATION OF γ

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DIN 1055-6:2005-03

C.6.3 Procedure/Process

(1) The reference stress rσ has to correspond to the vertical pressure level

of the bulk material that is stored in the silo. vp

(2) The preparation of the specimen has to comply with the procedure given

in C.5. The density of the specimen has to be determined using the quotient

from the measured weight of the consolidated specimen and from the volume

of the bulk material that has been taken. The height of the specimen H has to

be in the form of the mean value of three measurements which are to be

taken at the same radial distance from the midpoint of the bin and within

three 120° sectoral sections which are to be chosen in the direction of the

circumference.

NOTE The densities determined acc. to the procedure given in ASTM D6683

can turn out to be lower. The deviation is generally low for powdery bulk

material, but for coarse-grained bulk material it can assume significant

proportions.

C.7 Wall Friction

C.7.1 General

(1) The two parameters below are distinct from each other:

-- Coefficient of the wall friction mµ for the determination of loads (wall friction

Coefficient);

-- Wall friction angle whϕ for the evaluation of the flow behaviour.

(2) For bulk materials with a wide range of grain sizes, which tend to separate out during

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The filling process, due allowance has to be made for possible mixing of materials while

choosing the material specimens for determination of the coefficients of wall friction mµ .

(3) The tests relating to wall friction are to be conducted using units of wall specimens

which are representative of the material used in the wall surfaces of the silo structure.

NOTE 1 Although the test laboratories are equipped with a wide range of

construction and surfacing materials, the individual units of wall specimens can show a

transformation of the surface that makes it different from the surface condition at the time

of the silo manufacture. Units of wall specimens with nominally identical designation can

have angles of wall friction that vary from each other by several degrees. In such cases

the wall specimens need to be procured from the prospective manufacturer of the

construction material (e.g. the rolling mill or the tank manufacturer). Coated steel

surfaces are to be coated with the same brand of coating. For large-scale projects it is

recommended that the wall specimen units be retained for a subsequent comparison with

the actual manufactured surface. It is presently not possible to characterize the wall

surfaces in a manner such that the wall friction ratios can be reliably predicted.

(4) If there is the possibility of subsequent exposure of the silo wall to corrosion or

abrasion, then the wall friction tests should be conducted with wall specimens which

make due allowance for the actual conditions that are present immediately after

manufacture and those that arise after usage and wear and tear.

NOTE 2 The constitution of the silo wall surface can change with time. Corrosion

can lead to roughening of the surface; subjection to abrasion can cause roughening as

well as smoothening of the surface. Surfaces of materials such as polyethylene can

become hollow and coated surfaces can get scratched. Silo walls can however also

become smooth when fine particles from the bulk material such as fat or fine grains

accumulate in the pores of the wall surface. These changes can lead to changes in the

flow pattern, sometimes to such an extent that, for example, a core flow may arise in a

silo designed originally for mass flow or vice versa. The horizontal or vertical loads can

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increase in silos with polished wall surfaces and the wall friction loads can increase in the

case of silos with roughened surfaces.

C.7.2 Coefficient of Wall Friction mµ for the Determination of Loads

C.7.2.1 Short Description A bulk material specimen is sheared-off along an area that represents the wall surface -

and in the case of a corrugated sheet silo along a corrugated specimen. While doing this

the shearing force is measured along the area that is sheared-off.

NOTE While interpreting the data from the shear tests, proper care should be

exercised to see whether the load calculations and inspection of the flow behaviour have

been duly executed.

C.7.2.2 Test Apparatus The apparatus for the test is shown in fig. C.2. The diameter of the bin must be at least

20 times the value of the diameter of the largest grain of the bulk material and may not be

less than 40 times the value of the mean particle size. The height H of the compressed

specimen must lie between 0.15 D and 0.2 D. In the case of wall specimens with

discontinuities, e.g. in the case of a corrugated wall, the bin size has to be adjusted

accordingly.

NOTE These restrictions relating to the grain size of the bulk material

are chosen due to the following reasons: the restriction on the maximum

grain size of the bulk material would ensure that the arrangement and

orientation of the bulk material grains are not unduly disturbed due to the

influence of the enclosing wall. Moreover it is known that this influence is

greater in the situation where all the particles have the same size, than in the

situation where the smaller particles can take up the space between the

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larger particles. It is due to this reason that in case of uniform size of the

particles a restriction of 40 times the size of the particle and in case of a

wider range of particle-sizes a restriction of 20 times the maximum particle

diameter is prescribed.

C.7.2.3. Procedure/Process

(1) The largest horizontal load that arises in the silo is to be taken as the basis for the

reference stress

hp

rσ .

(2) The preparation of the specimen has to be in accordance with the procedure laid

down in C.5.

(3) The shearing of the specimen has to be executed in such a manner that a constant

feed velocity of about 0.04 mm/s is ensured.

(4) For the determination of the coefficients of wall friction the residual value of the

frictional force is to be used in the case of large deformations (see Fig. C.2) rF

(5) The coefficient of wall friction for determination of loads are to be determined from

the tests in the form of

NFr=µ (C.1)

Where

rF Is the end or residual value of the shear force (see fig C.2b);

N Is the vertical load placed upon the cover of the shear bin.

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C.7.3 Angle of Wall Friction whϕ for Analysis of Flow Behaviour

(1) The angle of wall friction whϕ for the analysis of flow behaviour can be determined in

accordance with the details given in fig. C.2.

(2) The angle of wall friction for the analysis of flow behaviour of the bulk material is to be

determined in case of low pressure levels.

NFr=µ

Fr

Shear force F

4

2DN rπσ=

F

1

φD

H

a) Shear bin for measurement of wall friction b) typical shearing-force

deformation relationships Legend

1 wall sample

Figure C.2 - TEST PROCEDURE FOR THE DETERMINATION OF COEFFICIENTS OF WALL FRICTION

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C.8 Horizontal Load Ratio K

C.8.1 Direct Measurement C.8.1.1 Test Principle

Taking care to obstruct horizontal deformations, a vertical stress 1σ has to be imposed

upon a specimen and the horizontal stress 2σ resulting from this strain has to be

measured. The secant value of the horizontal load ratio has to be determined from

this.

0K

NOTE 1 The size of the coefficient is dependant on the directions in which the

principal stresses build up in the specimen. For evaluation of the tests the horizontal and

vertical stresses are to be regarded as an approximation of principal stresses in the

specimen. As a rule this does not happen in the silo.

0K

NOTE 2 For specimens where horizontal deformations are obstructed, it must be

understood that horizontal elongations within the bulk material are restricted to such an

extent that their influence on the stresses in the bulk material specimen are negligible.

These elongations are, nevertheless, large enough to assume measurable proportions in

the thin wall of the shear bin or in specific portions of the wall which are to be measured

for concentrated elongations. Generally this criterion of restricted elongation in the bulk

material specimen and the simultaneous measurability of the deformations in the

apparatus wall is fulfilled by an average peripheral elongation of magnitude 1/10 per mil.

C.8.1.2 Apparatus

The geometry of the test apparatus can be seen in fig. C.3. the horizontal stresses are to

be derived from the elongations that are measured at the periphery of the vertical ring.

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For this purpose the wall of the measuring bin must be thin enough and so designed that

the stress level in the wall can be interpreted correctly and clearly.

NOTE Generally, a base plate which is separated from the ring of the bin wall is

required here so that both horizontal as well as vertical measurements are possible

without any mutual interference. It is moreover necessary to position the points for

measuring the elongations at adequate distance from the edges of the specimen. In

addition, care should be taken to ensure that the elongations measured are linked with

the internal horizontal stresses using a conversion factor, and that the bending of the

walls of the test apparatus can be ignored in the relationship thus established.

( )112

4σσπ

∆+= DN

a

b H

Dφ

1

( )22 σσ ∆+

σ2

σ1

Kmo

a) Test equipment b) Typical progression of 2σ

with increasing 1σ

Legend a smooth surface

b rough surface

Figure C.3 - TEST PROCEDURE FOR DETERMINATION OF KO

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C.8.1.3 Procedure/Process

(1) The reference stress rσ has to be equivalent to the greatest level of vertical pressure

that is expected to build up in the bulk material stored in the silo. VP

(2) The preparation of the specimen should comply with the procedure given in C.5

(3) The horizontal stress 1σ in the specimen that arises due to the imposition of the

vertical strain rσ - which corresponds to the reference stress 2σ - is to be observed.

The value of KO is to be calculated from these stress components (see fig. C.3) in the

form:

1

2

σσ

=OK (C.2)

(4) The value of K is to be taken as:

(C.3) OKK 1.1=

NOTE Using the factor 1.1 in equation (C.3), one should make allowance for the

difference between the horizontal load ratio (=KO ) in the shear bin which is measured in

the (almost total) absence of wall friction influences and the value K under the influence

of wall friction in the silo.

C.8.2 Indirect Measurement An approximate value of K can be derived from the angle of internal friction for the strain

imposed iϕ ; this can be determined either by the procedure laid down in C.9 or by a

triaxial test. If the value K is being derived from iϕ , the calculation in equation (7) is to be

used.

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C.9 Stability Parameters: Cohesion c and Angle of Internal Friction iϕ

C.9.1 Direct Measurement C.9.1.1 Test Principle The stability of a bulk material specimen can be determined using shearing bin tests. The

two parameters and c iϕ are to be used for describing the implications of the stability of

the bulk material stored in the silo bins.

C.9.1.2 Apparatus The equipment used for the test is a cylindrical shear bin in accordance with fig. C.4. The

bin diameter must amount to at least 20 times the value of the largest grain diameter of

the bulk material and must not be lesser than 40 times the value of the mean particle

size. The height H of the compressed specimen must lie between 0.3D and 0.4D.

NOTE These restrictions relating to the grain size of the bulk material are chosen

due to the following reasons: the restriction on the maximum grain size of the bulk

material would ensure that the arrangement and orientation of the bulk material grains

are not unduly disturbed due to the influence of the enclosing wall. Moreover it is known

that this influence is greater in the situation where all the particles have the same size,

than in the situation where the smaller particles can take up the space between the

larger particles. It is due to this reason that in case of uniform size of the particles a

restriction of 40 times the size of the particle and in case of a wider range of particle-

sizes a restriction of 20 times the maximum particle diameter is prescribed.

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(1) The reference stress rσ must be approximately equivalent to the greatest level of

vertical pressure that is expected to build up, acc. to C.2, in the bulk material stored in

the silo. The preparation of the specimen must be carried out in accordance with the

procedure given in C.5.

vp

(2) The shearing of the specimen must be done at a constant feed velocity of about

0.04 mm/s.

(3) The determination of the stability parameters has to be based upon the shear

stress τ determined during or before a horizontal displacement of , with D

being the internal bin diameter (see fig. C.4)

D06.0=∆

a) Shear bin

4

2DN rπσ=

4

2DF τπ=

a

φD

H

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τaτb

τ

Tran

sver

se st

ress

whi

ch is

mea

sure

d

σb σa

φi

φc

tra

nsve

rse

stre

ssτ

τb

τa

2

1

Shear bin displacement Normal stress σ (b) (C) b) Typical curve depicting shear stress and displacement c) Typical relationship between shear stress and normal stress as measured in a shear test Legend

1) Curve a

2) Curve b

Figure C.4 - TEST PROCEDURE FOR THE DETERMINATION OF THE ANGLES OF

INTERNAL FRICTION iϕ AND cϕ AND THE COHESION c BASED ON THE STRESS rσ

IMPOSED DURING THE PRECOMPRESSION

(4) There are at least two tests to be conducted acc. to the conditions defined under

(5) and (6) (table C.1 and fig. C.4)

(5) For determination of the transverse stress aτ one material specimen is to be

subjected to a normal load equivalent to the reference stress rσ

(6) Then a second specimen is to be initially subjected, like the first specimen, to a

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normal load that is equivalent to the reference stress rσ - but only until the shearing.

There after the normal load is to be reduced to about half the value of the reference

stress (2

rb

σσ ≈ ). Subsequently it is to be further sheared at this stress level in order to

get the maximum transverse stress bτ (see fig. C.4b). the stresses determined in these

two tests are listed in the Table C.1.

TABLE C.1 - TEST PARAMETERS `

TEST

AMOUNT OF PRELIMINARY STRAIN

NORMAL STRESS IN THE TEST

MAX TRANSVERSE STRESS MEASURED

No.1

rσ rσ

aτ

No.2

rσ 2

rb

σσ ≈

bτ

C.9.1.4 Evaluation (1) The angle of internal friction when the stored bulk material is subject to strain is to

be determined using

⎟⎟⎠

⎞⎜⎜⎝

⎛=

r

ai σ

τϕ arctan (C.4)

(2) The cohesion c activated in the bulk material under reference stress rσ is to be

calculated using

crac ϕστ tan−= (C.5)

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With

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=br

bac σσ

ττϕ arctan (C.6)

Where

cϕ The angle of internal friction in case of strain relief of a super

critically consolidated specimen

NOTE 1 The value of the cohesion c is largely dependant upon the

consolidating stress rσ and as such it cannot be regarded as a full-fledged material

parameter.

(3) For a bulk material without cohesion (i.e. c = 0), the shear resistance should only

be described in terms of the angle of internal friction iϕ - which then corresponds to cϕ .

C.9.2 Indirect Measurement (1) The cohesion of a bulk material can also be determined approximately from the

results of shear tests with a shear bin of Jenike.

(2) The cohesion should be determined within the pressure ratios corresponding to

the maximum vertical pressure vftσ n the silo after filling (see designs in C.2).

(3) The maximum vertical pressure in the silo after the filling vftσ is to be fixed as the

maximum consolidating stress cσ .

(4) The uni-axial yield stress uσ which corresponds to this consolidating stress is to

be determined from the flow function. In addition the angle of the effective internal friction

δ under the corresponding conditions of stress is to be determined.

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(5) The foll. Approximate values for cohesion can be determined:

( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

δϕϕδ

σsin1cos

sinsin

c

ccc (C.7)

With

⎟⎠⎞

⎜⎝⎛

−−

=K

Kc 2

sin2arcsin δϕ (C.8)

( δσσ

sin1+⎟⎟⎠

⎞⎜⎜⎝

⎛=

u

cK ) (C.9)

Where

cσ The maximum consolidating stress in the Jenike shear bin test

uσ The uni-axial yield stress obtained from the Jenike shear bin test

δ The effective angle of the internal friction obtained from the Jenike shear

bin test

cϕ Angle of internal friction during the stress relief (see fig. C.4c)

NOTE 1 The magnitude of cohesion c depends greatly on the consolidating stress

and as such does not represent an independent material parameter of the bulk material.

(6) An approximate value for the angle of internal friction during stress relief iϕ can be

obtained from the Jenike shear bin test (C.10)

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=δϕ

ϕδϕ

sinsin1cossin

arctanc

ci (C.10)

NOTE 2 The two parameters and c iϕ are used in this norm only for assessing the

effects of the bulk material stability on the silo pressures.

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C.10 Effective Modulus of Elasticity ES

C.10.1 Direct Measurement C.10.1.1 Test Principle

A vertical load 1σ is imposed upon a specimen placed laterally. For each increment of the

load 1σ∆ (vertical) the resulting horizontal stress 2σ∆ and the change in the vertical

displacement are to be measured. The effective elasticity modulus for the imposed

strain (modulus of strain) is to be derived from these measurements using the

horizontal load ratio

1V∆

sLE

K . The vertical load is to be thereafter reduced by the amount 1σ∆

and the horizontal stress 2σ∆ and vertical displacement 2V∆ to be measured. From

these measurements the effective elasticity modulus for stress relief (relief modulus) is to

be derived.

NOTE 1 The magnitude of and depends upon the direction of the principal

stresses in the specimen. The horizontal and the vertical stresses in the specimen are

approximately equivalent to the principal stresses; as a rule this does not happen in a

silo.

sE suE

NOTE 2 For specimens where horizontal deformations are obstructed, it must be

understood that horizontal elongations within the bulk material are restricted to such an

extent that their influence on the stresses in the bulk material specimen are negligible.

These elongations are, nevertheless, large enough to assume measurable proportions in

the thin wall of the test apparatus. Generally an average peripheral elongation of

magnitude 1/10 per mil fulfills this criterion.

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C.10.1.2 Apparatus

(1) The geometry of the test apparatus can be seen in fig. C.5. It is similar to the

apparatus described in C.8 for measuring the horizontal load ratio K.

(2)The horizontal stresses are to be derived from the elongations that are measured at

the periphery of the vertical ring. For this purpose the wall of the measuring bin must be

thin enough and so designed that the stress level in the wall can be interpreted correctly

and clearly.

NOTE Generally, a base plate that is separated from the bin walls is required here

so that both horizontal as well as vertical measurements are possible without any mutual

interference. It is moreover necessary that the elongations are measured at an adequate

distance from the edges of the specimen. In addition, care should be taken to ensure that

the elongations measured are proportional to the internal horizontal stresses and that the

bending of the walls of the test apparatus can be ignored in this relationship.

(2) It must also be ensured that vertical deformations of the specimen in suitably small

amounts will occur.

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( )12

4σπ

∆= DN

Dφ

a

bH

∆V1

( )2σ∆

Ver

tical

dis

plac

emen

t inc

rem

ent ∆

V

∆σ1

∆Vu

∆VL

Vertical stress increment ∆σ

a) Test equipment b) typical vertical displacement

for vertical increments of stress 1σ∆

Legend

a smooth surface

b rough surface

Figure C.5 – TEST PROCEDURE FOR THE DETERMINATION OF THE ELASTICITY MODULI DURING STRAIN IMPOSITION AND STRAIN RELIEF


(1) The highest level of vertical pressure that can be expected in the bulk material

stored in the silo is to be taken as the reference stress

Vp

rσ

(2) The specimen is to be prepared in accordance with the procedure given in C.5.

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(3) After the imposition of a vertical load 1σ which corresponds to the reference

stress rσ , the readings for horizontal stresses and vertical deformations are to be taken.

The height of the material specimen H is to be measured carefully (see C.6.3).

(4) After a small increment of the vertical stress 1σ∆ , the horizontal stresses and the

vertical deformations have to be measured again. The increment of the vertical stresses

may be chosen as approximately 10% of the reference stress 1σ .

(5) The change in the horizontal stress 2σ∆ as a consequence of the vertical load

increments 1σ∆ is to be determined and the changes in the vertical displacements V∆

(both negative) are to be measured. The incremental value of K under subjection to strain

is then to be determined in the form of KL :

⎟⎟⎠

⎞⎜⎜⎝

⎛∆∆

=1

2

σσ

LK (C.11)

(6) The effective elasticity modulus under subjection to strain may then be derived

as follows

sLE

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

∆∆

=l

LsL K

Kv

HE12

12

1σ (C.12)

(7) Subsequently a minor incremental reduction of the vertical strain 1σ∆ has to be

made (to be treated as a quantity with a negative sign) and the resultant changes in the

horizontal stresses and the vertical deformations are to be measured. The increment of

the vertical strain 1σ∆ should amount to approx. 10% of the reference stress 1σ .

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(8) The change in the horizontal stress 2σ∆ as a consequence of the vertical load

increments 1σ∆ is to be determined and the changes in the vertical displacements V∆

(both negative) are to be measured. The incremental value of K in case of strain relief is

then to be determined in the form of KU :

⎟⎟⎠

⎞⎜⎜⎝

⎛∆∆

=1

2

σσ

UK (C.13)

(9) The effective elasticity modulus in case of strain relief may then be derived as

follows

sUE

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

∆∆

=U

UsU K

Kv

HE12

12

1σ (C.14)

NOTE The effective elasticity modulus in case of strain relief is usually far greater

than the elasticity modulus in case of subjection to strain. In a case where a greater

elasticity modulus is harmful for the supporting framework (e.g. in case of temperature

changes) the strain-relief elasticity modulus is to be used. Should the elasticity modulus

of the bulk material be favourable for the structure (e.g. in case of thin-walled rectangular

silos), the elasticity modulus for strain-imposition (strain-imposition modulus) is to be

used.

C.10.2 Indirect Measurement

(1) For the purpose of assisting the specific inspection of the adjustment of the test,

an approximate value EsU may be determined as follows:

vftsU PE χ= (C.15)

Where

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vftP The vertical stress at the lower end of the vertical wall section (equation

(11) or (86));

χ The contiguity coefficient

NOTE The effective elasticity modulus for stress-relief and the vertical stress

have the same unit in equation (C.15)

sUE

vftP

(2) In case of missing experimental test data in accordance with the procedure in

C.10.1 the contiguity coefficient χ can be calculated as follows:

23

7γχ = (C.16)

Where for γ the specific gravity of the bulk material expressed in kN/m3 is to be

substituted.

(3) Alternatively the value of χ can be fixed at 70 for dry agricultural cereal products,

at 100 for small-sized mineral grains and at 150 for large-sized mineral grains.

C.11 Determination of the Upper and Lower Characteristic Values of the Bulk Material Parameters and Calculation of the Conversion Factor a

C.11.1 Test Principle

(1) The silo is to be designed for the most unfavourable conditions of strain which it

can be exposed to during its course of its use. This section deals with the assessment of

variances in the bulk material parameters which can occur at the time of the design

calculations.

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NOTE 1 it is possible that the parameters of the stored bulk material can undergo

changes during the service life. These changes that occur over a period of time cannot

be easily assessed.

(2) The extreme values of the calculated loads are described in terms of their

characteristic values. These are values – normally 5% and 95% fractile values - which

are not exceeded during the designated service life or the course of the assessment

period given the recognized predicted probabilities.

(3) The extreme values of the parameters which are necessary for the achievement of

this extreme load level are the characteristic values of the bulk material parameters.

(4) For the determination of the decisive load ratios both the upper as well as the

lower characteristic values are to be used.

(5) The simplified procedure described here is to be used while viewing the

characteristic value on the basis of 1.28 times the standard deviation from the mean

value.

NOTE 2 The corresponding material parameters for a specific probability of

exceeding the load level depends on the geometry, the absolute size of the tank, the type

of load and whether the loads are to be viewed in the vertical silo shaft or the hopper. In

addition these values are influenced by the moisture content, the temperature, and the

tendency of sedimentation and the age of these values.

NOTE 3 as shown in the above passage, there are several bulk material properties,

each distinct from the other, which contribute to the characteristic loads. Therefore a 10

or 90 percentage value of each of the characteristic values is regarded as a suitable and

reasonable estimate for the value which represents an adequate occurrence-possibility

for the design load.

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(6) For calculation of the relevant load conditions the upper as well as the lower

characteristic values of the relevant parameters are to be used.

(7) In case adequate experimental data is available, the characteristic values are to

be calculated using statistical methods.

NOTE 4 Although test data is helpful for the determination of characteristic values, it

has its limitations such as limitations on account of specimen size, on account of the

process of specimen preparation etc. This may lead to a situation where the data for all

the properties relevant to the operation life may be unrepresentative.

NOTE 5 the values in Table E.1 are worked backwards from the assessments which

are based upon a combination of experience and actual data from experiments.

(8) In case the designer or the customer has at his disposal data or experimental

values for a specific design calculation, he can derive the characteristic bulk material

parameters from this data if it represents the range of parameters of the bulk materials

used during the service life.

C.11.2 Methods for Assessment

(1) For calculating the characteristic values of each parameter the following

procedures can be used. The variable Χ represents the characteristic values observed

in each case.

(2) The mean value of the characteristic value Χ is to be calculated from the test

data.

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(3) Wherever possible, the coefficient of variation δ is to be determined from the

available test data.

(4) If the test data is not suitable for determining a coefficient of variation, a suitable

value is to be estimated for the bulk material. Table C.2 can be used as a guide here.

(5) The upper characteristic value of a parameter ( )90,0XXU = is to be determined

using

( δ28.1190,0 += XX ) (C.17)

(6) The lower characteristic value of a parameter ( )90,0XXU = is to be determined

using

( δ28.1110,0 −= XX ) (C.18)

(7) The conversion factor of a parameter is to be determined using Xa

228.1128.1128.11 δδ

δδ

++≈−+

=Xa (C.19)

(8) When estimating the value of the conversion factors, the coefficients of variation δ

for the bulk material specific gravity have to be fixed at 0.10. In case of other bulk

material parameters the values are to be estimated using the specifications for the bulk

materials with similar properties listed in the Table C.2.

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TABLE C.2 --- TYPICAL VALUES OF THE COEFFICIENTS OF VARIATION FOR THE BULK MATERIAL PARAMETERS

COEFFICIENT OF VARAITION δ

COEFFICIENT OF WALL FRICTION µ

category of wall-roughness

BULK MATERIAL

HORI- ZONTAL

LOAD RATIO

K

ANGLE OF INTERNAL FRICTION

iϕ

in degrees D1 D2 D3

Gravel for Concrete 0.11 0.11 0.09 0.09 0.09

Aluminum 0.14 0.16 0.05 0.05 0.05

Fodder concentrate mix 0.08 0.06 0.16 0.19 0.19

Fodder concentrate pellets 0.05 0.05 0.14 0.14 0.14

Barley 0.08 0.10 0.11 0.11 0.11

Cement 0.14 0.16 0.05 0.05 0.05

Cement Clinker 0.21 0.14 0.05 0.05 0.05

Coal 0.11 0.11 0.09 0.09 0.09

Coal dust 0.14 0.18 0.05 0.05 0.05

Coke 0.11 0.11 0.09 0.09 0.09

Fly Ash 0.14 0.12 0.05 0.05 0.05

Flour 0.08 0.05 0.11 0.11 0.11

Iron Pellets 0.11 0.11 0.09 0.09 0.09

Calcium Hydrate 0.14 0.18 0.05 0.05 0.05

Limestone Powder 0.14 0.16 0.05 0.05 0.05

Maize 0.10 0.10 0.17 0.17 0.17

Phosphate 0.11 0.13 0.09 0.09 0.09

Potatoes 0.08 0.09 0.11 0.11 0.11

Sand 0.08 0.07 0.11 0.11 0.11

Slag Clinker 0.08 0.07 0.11 0.11 0.11

Soya Beans 0.08 0.12 0.11 0.11 0.11

Sugar 0.14 0.14 0.05 0.05 0.05

Sugar Beet Pellets 0.11 0.11 0.09 0.09 0.09

Wheat 0.08 0.09 0.11 0.11 0.11

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ANNEX D (NORMATIVE)

ASSESSMENT OF THE BULK MATERIAL PARAMETERS FOR THE DETERMINATION OF SILO LOADS D.1 Aim

This annex describes methods for the assessment of the characteristic values of bulk

materials which are required in this standard for the purpose of calculating silo loads and

cannot be determined experimentally by means of tests.

D.2 Assessment of the coefficients of wall friction for a corrugated wall

(1) The effective wall friction coefficient for D4 type of wall (corrugated or contoured-

metal sheet or metal sheet with horizontal slits) is to be determined from

( ) wwiweff aa µϕµ +−= tan1 (D.1)

Where

effµ Effective coefficient of wall friction

iϕ Angle of internal friction

wµ Coefficient of wall friction (against a level wall surface)

Wall contact factor wa

NOTE 1 The effective wall friction depends on the angle of internal friction of the

bulk material, the coefficient of wall friction against the level wall and on the profile of the

wall surface.

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(2) The parameter in equation (D.1), which represents the portion of the sliding

surface against the wall surface, is to be determined from the geometry of the profile of

the wall surface, with allowance being made for a suitable estimate of the contact zones

that have been activated between the bulk material and the wall surface (see fig. D.1)

wa

(3) For corresponding depths of the folds and the waves a simple estimate can be made

with equation (D.2):

iw

ww bb

ba

+=

NOTE 2 The interface between sliding surfaces and stationary zones is in contact

partially with the wall and partially with the broken surface within the bulk material. The

portion which slides along wall surface is expressed using the factor . This portion

cannot be easily determined and its estimation depends on the profile of the wall surface.

wa

1

3

b

bi

1

3

bi

b

22

a) Trapezoidal folded profile b) Sinusoidal wavy profile

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Legend

1 bulk material

2 bulk material flow

3 sliding surface

Figure D.1 – DIMENSIONS OF THE CONTOURING OF THE WALL SURFACE

NOTE 3 For wall surface contouring which resemble the one in fig. D.1b, the factor

can be taken as approximately 0.20. wa

D.3 Internal Friction and the Wall Friction of a Coarse Bulk Material without Fines

The coefficient of wall friction µ and the angle of the internal friction iϕ cannot be

easily determined in case of coarse bulk materials without fines (e.g. lupin, peas, beans

and potatoes). In such cases, in place of the angle of internal friction one has to take the

gradient of slope rϕ of a bulk material heap (debris cone) which is loosely fed on to a

level base plate.

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ANNEX E

(Normative)

Details of Bulk Material Parameters

This annex specifies parameters for a few bulk materials commonly stored in silos,

which are to be used as characteristic values for design calculations.

Table E.1 – Bulk Material Parametersa

Coefficient of wall frictionb

µ

( wϕµ tan= )

(Mean value)

Paramet

er for

referenc

e

surface

load

opC

Density

γ

kN/m3

Angle of

internal

friction

iϕ degree

imϕ qa

Horizontal load

ratio

K

Type of

bulk

material

Lower

value

γ1

Upper

value

γ2

Gradi

ent of

slope

rϕ

degre

e

Mea

n

valu

e

Conv

ersion

factor

Mean

value

Km

Conver

sion

factor

ka

Wall

type

D1

Wall

type

D2

Wall

type

D3

Conver

sion

factor

µa

general

bulk

material

6.0 22.0 40 35 1.3 0.50 1.5 0.32 0.39 0.50 1.40 1.0

Concrete

gravel 17 18 36 31 1.16 0.52 1.15 0.39 0.49 0.59 1.12 0.4

Aluminium 10 12 36 30 1.22 0.54 1.2 0.41 0.46 0.51 1.07 0.5

Concentrat

ed feed

mixture

5 6 39 36 1.08 0.45 1.1 0.22 0.30 0.43 1.28 1

Concentrat

ed feed

pellets

6.5 8 37 35 1.06 0.47 1.07 0.23 0.28 0.37 1.20 0.7

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Barley 7 8 31 28 1.14 0.59 1.11 0.24 0.33 0.48 1.16 0.5

Cement 13 16 36 30 1.22 0.54 1.2 0.41 0.46 0.51 1.07 0.5

Cement

clinkerc 15 18 47 40 1.20 0.38 1.31 0.46 0.56 0.62 1.07 0.7

Coal 7 10 36 31 1.16 0.52 1.15 0.44 0.49 0.59 1.12 0.6

Coal dust 6 8 34 27 1.26 0.58 1.2 0.41 0.51 0.56 1.07 0.5

Coke 6.5 8 36 31 1.16 0.52 1.15 0.49 0.54 0.59 1.12 0.6

Fly ash 8 15 41 35 1.16 0.46 1.20 0.51 0.62 0.72 1.07 0.5

Flour 6.5 7 45 42 1.06 0.36 1.11 0.24 0.33 0.48 1.16 0.6

Iron pellets 19 22 36 31 1.16 0.52 1.15 0.49 0.54 0.59 1.12 0.5

Lime

hydrate 6 8 34 27 1.26 0.58 1.20 0.36 0.41 0.51 1.07 0.6

Limestone

powder 11 13 36 30 1.22 0.54 1.20 0.41 0.51 0.56 1.07 0.5

Maize 7 8 35 31 1.14 0.53 1.14 0.22 0.36 0.53 1.24 0.9

Phosphate 16 22 34 29 1.18 0.56 1.15 0.39 0.49 0.54 1.12 0.5

Potatoes 6 8 34 30 1.12 0.54 1.11 0.33 0.38 0.48 1.16 0.5

Sand 14 16 39 39 1.09 0.45 1.11 0.38 0.48 0.57 1.16 0.4

Slag clinker 10.5 12 39 36 1.09 0.45 1.11 0.48 0.57 0.67 1.16 0.6

Soya beans 7 8 29 25 1.16 0.63 1.11 0.24 0.38 0.48 1.16 0.5

Sugar 8 9.5 38 32 1.19 0.50 1.2 0.46 0.51 0.56 1.07 0.4

Sugar beet

pellets 6.5 7 36 31 1.16 0.52 1.15 0.35 0.44 0.54 1.12 0.5

Wheat 7.5 9.0 34 30 1.12 0.54 1.11 .24 0.38 0.57 1.16 0.5

NOTE The upper characteristic value xx of the bulk material density uγ is to be always used when determining the silo loads. The

lower characteristic value θγ in table E.1 is meant to support calculations for storage capacities when, for example, a certain specified

storage capacity has to be ensured. A When a bulk material that is not in the list has to be stored, then tests should to be conducted.

If the expense incurred on the tests is not justified, esp. if an assessment of the expense shows that the wide spectrum of values used for

calculations would have only marginal

Effect on the overall effort, then the values given in the so-called ‘general bulk material’ category may be used. These values can be particularly

appropriate for small silo loads. For

Large silo loads, however, these values generally result in unviable calculations. As a rule, in such cases tests are preferable. b The effective wall friction coefficient for wall type D4 (corrugated wall) can be assessed according to D.2 C The bulk material shows a tendency to mechanically interlock leading to arching or discharge disturbances.

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ANNEX F (NORMATIVE)

DETERMINATION OF THE FLOW-PROFILE, MASS-FLOW AND CORE-FLOW The dimensioning of silos - with respect to their flow profiles - in terms of functional

process technology is not included within the scope of this standard. The following

information has been provided in order to enable a safe estimate about whether specific

load ratios for mass flow conditions are present in a prospective silo design. This

information is moreover necessary when alternate procedures for determination of

hopper loads as given in Annex H are used.

a) Conical hopper

Conical hopper

00.20.40.60.8

11.21.41.61.8

2

0 20 40 60 80

Series1

Series2

Coe

ffic

ient

of w

all f

rictio

n in

the

hopp

er, µ

h

H

alf-angle β at the hopper apex, in degrees

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b) Cuneiform hoppe

00.20.40.60.8

11.21.41.61.8

2

0 20 40 60 80

Series1Series2

Legend 1 core flow

2 mass flow

3 mass flow

Figure F.1 – BOUNDARIECONICAL AND CUNEIFO

NOTE In th

the flow profile that aris

standard.

H

Coe

ffic

ient

of w

all f

rictio

n in

the

hopp

er, µ

h

or core flow can occur between the two lines

S FOR MASS FLOW AND CORE FLOW CONDITIONS IN CASE OF RM HOPPERS

e zone between the boundary lines of mass flow and core flow

es depends on other parameters which are not included in this

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alf-angle β at the hopper apex

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ANNEX G (Normative)

Seismic Actions G.1 General

(1) This annex lays down general guidelines for calculations of silos under seismic

actions. These rules for calculations complement the general rules in DIN 4149 for

design calculations under seismic conditions.

(2) The value for the acceleration due to earthquakes for the silo structure has to be

fixed according to EN 1998.

G.2 Symbols

α horizontal acceleration due to earthquakes

∆ph.so additional horizontal loads due to seismic actions

G.3 Conditions during Calculations

--- Horizontal acceleration and the resultant horizontal and vertical loads on

the silo structures (or the silo substructure) and the foundation (G.4.1);

--- Additional loads on the silo walls (G.4.2);

--- Rearrangement of bulk material at the material surface in the filled-up silo.

The seismic actions can lead to a situation where a slide surface develops

in the filled up bulk material cone in the vicinity of the bulk-material’s

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surface. This can pose a threat to the silo roof and the upper regions of the

silo walls due to additional horizontal loads (see diagram G.1)

1 2

`Legend

1 slide surface during seismic actions

2 bulk material surface after the seismic action

Figure G.1 POSSIBLE REARRANGEMENT OF BULK MATERIAL SURFACE DUE TO SEISMIC ACTIONS G.4 Seismic Actions

Directions for calculating the seismic actions are given in G.4.1 for the silo substructure

and in G.4.2 for the silo walls.

G.4.1 Silo Substructures and Foundations

Seismic actions due to the accelerated mass of the silo structure and the stored bulk

material can be regarded as individual loads, which place a strain at the centre of gravity

of the mass of the silo structure and the stored bulk material (see diagram G.2).

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Fs

Figure G.2 Seismic actions for the substructure (e.g. the supports)

G.4.2 Silo Walls

(1) The influence of seismic actions on the silo walls has to be taken into account

using an additional horizontal load portion. This has to be superimposed with the

loads from the stored bulk material according to sections 7 and 8. The overall load

is equivalent to the mass of the bulk material multiplied by the value of the

horizontal acceleration due to earthquake α.

(2) The reference value of the additional normal loads on the silo walls due to seismic

effects is given,

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For a silo with a circular cross-section and diameter dc, by the foll. equation:

2.c

sohd

gp αγ=∆ (G.1)

And for a rectangular silo with the width b the equation is:

2.b

gp soh

αγ=∆ (G.2)

Where

γ is the bulk material density;

α is the horizontal acceleration due to the earthquake;

g is the acceleration of the fall.

(3) The additional loads normal to the silo walls may be assumed to be evenly

distributed across the height of the silo. At the upper end of the silo wall one has to

add the resultant forces – acting from inside outwards -- of the bulk material loads

due to filling and discharging, and the additional seismic horizontal loads – never

smaller than zero (no negative values).

(4) The assumed horizontal distribution of the additional loads ∆ph.s = ∆ph.s is shown

in diagram G.3.

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For a circular silo the additional load is to be found using the equation:

θcos.. sohsh pp ∆=∆ (G.3)

For a rectangular silo ∆ph.s has to be fixed using the equation:

∆ph.s = ∆ph.so (G.4)

a) cross-section of circular silo b) cross-section of rectangular silo

∆Ph,s∆Ph,s

b

a∆Ph,s

∆Ph,so

θ

FIGURE G-3 Cross-section across the vertical silo shaft with details of the additional horizontal loads due to seismic actions

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ANNEX H (NORMATIVE)

ALTERNATE RULES FOR THE DETERMINATION OF HOPPER LOADS H.1 General

(1) This annex gives two alternate procedures for estimation of bulk material loads on

hoppers.

(2) H.5 can be used for the description of loads not only for fill loads but also for

discharge loads. It must however be noted that the sum of these loads is not equivalent

to the weight of the bulk material stored in the hopper. The given load formulation in the

hopper is to be regarded as an envelope load profile which acts on the hopper walls

during filling and during discharge.

(3) For fill loads in the case of steep hoppers, the equations given in H.7 can be used

as an alternative to the formulations given in 8.3.

H.2 Definitions

The following definitions are applicable to this Annex.

H.2.1 Peak Load (Kick Load)

Peak load which can occur at the hopper junction in case of a mass flow during the

emptying of a silo

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H.3 Symbols

hl Distance between the hopper peak and the hopper junction along the inclined

surface (see fig. H.1)

np Loads acting vertically upon the inclined hopper wall

inp Different load components acting vertically upon the inclined hopper wall (i = 1, 2

and 3)

sp Load peak at the hopper junction

H.4 Dimensioning Conditions (1) The hopper is to be designed for the state prevailing after the filling and for

discharge loads.

(2) The flow pattern of the bulk material that is to be expected for the hopper is to be

determined by fig. F.1

(3) In case both core flow and mass flow can occur in the silo, these effects are both

to be taken into account during dimensioning.

H.5 Loads on the Hopper Walls (1) For an inclination of the hopper walls vis-à-vis the horizontal α that is greater than

20° (see fig. 1b), the loads acting vertically on the inclined hopper walls are to

be calculated as follows:

np

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NOTE see NOTE in H.4

( )n

nnnnn lxppppp 2133 −++= (H.1)

With

( )ββ 221 cossin += bvfn Cpp (H.2)

(H.3) β22 sinbvfn Cpp =

βµ

γ 23 cos0.3

h

sn

KUAp = (H.4)

Where

β Inclination of the hopper walls vis-à-vis the vertical (see fig. H.1)

x Distance between the lower end of the hopper and the observed position (amount

between 0 and xx) according to fig. H.1 (with ref. to the inclined surface)

1np And are parts which describe the hopper loads caused by filling of the hopper 2np

hµ Lower characteristic value of the coefficient of wall friction in the hopper

sK Upper characteristic value of the horizontal load ratio of the stored bulk material

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3np The part of the load portion caused by the vertical pressures (of the bulk material

stored in the vertical silo shaft) at the hopper junction/ hopper’s starting-point

bC Bottom load enlargement ratio

vfp Vertical load at the hopper’s staring point after the filling in accordance with

equation (11) or (86)

(2) The wall friction loads are given by: tp

hnt pp µ= (H.5)

Where

np represent the hopper loads acting vertically on the hopper wall according to

equation (H.1)

(3) For silos with possible mass flow, allowance is to be made for an additional load

portion at the hopper junction (see fig. H.1). this load portion is to be calculated

actively from the hopper junction, measured across a length of and along the entire

periphery of the hopper.

sp

cd2.0

(H.6) vfts Kpp 2=

Where is the vertical load portion of the fill load in the bulk material at the hopper’s

starting point, calculated according to equations (11) or (86).

vftp

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0.2dc

β Pn3

x

pt Pn3

Pn1

Ps

Ps

Pn2

lh

Phft

Figure H.1 – ALTERNATIVE RULES FOR THE HOPPER LOADS

H.6 Determination of the Connecting Forces at the Hopper Junction

The connecting forces in the hopper at the hopper junction are to be derived using the

equilibrium conditions. For the loads arising from covering up of the hopper, the bottom

load enlargement ratio is to be calculated. bC

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H.7 Alternate Equations for the Hopper Load Correction Value xx for Discharge

Loads

In case of discharge loads in a hopper with steep walls, the mean vertical pressure at any

position in the bulk material is to be calculated according to the equations (116) and (117)

using the following parameter : eF

( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛+

++⎟⎟⎠

⎞⎜⎜⎝

⎛+

=β

βεεφ

φβµ sin

sincossin1

sin121

cot11

i

ieF (H.7)

In which

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎭⎬⎫

⎩⎨⎧

++=i

whwh φ

φφβε

sinsin

arcsin21 (H.8)

hwh µϕ arctan= (H.9)

Where

hµ Lower characteristic value of the coefficient of wall friction in the hopper

iϕ Angle of internal friction of the saved bulk material

NOTE The equation (H.7) is to be used instead of the equation (128). The equation (H.7)

for is founded on the somewhat complex Theory of Enstad for discharge press eF

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ANNEX I (NORMATIVE)

INFLUENCES DUE TO DUST EXPLOSIONS I.1 General

This Annex contains instructions for making allowance for dust explosions in silo

structures.

I.2 Application

(1) This section is applicable to all silo structures and other comparable structures

where non-toxic combustible and explosive powders are processed or stored or

accumulate in large quantities in the form of waste matter.

(2) It does not apply to those structures in which explosions are ruled out by means of

specific measures.

(3) This annex can be used for the retrofitting of the existing structures. In such case

the actual state of the structure is to be taken into account, not its planned state. In case

of doubt an expert opinion has to be sought.

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DIN 1055-6:2005-03

I.3 Additional Standards, Guidelines and Regulations

Listed below are the additional standards, guidelines and regulations that are relevant to

the planning and the operation of a silo structure.

- DIN-Fachbericht 140, Silo Structures designed against Dust Explosions

- DIN EN 26184-1, Explosion Protection Systems – Part 1: Determination of Explosive

Characteristics of Combustible Dusts in the Atmosphere

- DIN EN 1127-1, Explosive Atmospheres – Explosion Protection – Part 1: Basis and

Methodology

DIN EN 50014, Electrical Equipment for Explosion Hazard Areas – General Rules

VDI 2263, Dust Fires and Dust Explosions; Risks, Evaluation, Protective Measures

I.4 Explosive Dusts and their Characteristic Values

(1) The dust from several bulk materials which are normally stored in the silo

structures are explosive in nature. Explosions can occur when organic or inorganic dust

having sufficiently small particle size reacts exothermically with acid and thereby causes

a swiftly progressive reaction.

(2) During an explosion of dust from bulk material normally stored in silos,

overpressures ranging from 8 bars to 10 bars can occur in closed spaces without vents.

(3) The characteristic values for the explosive behaviour of dust are:

-- The dust characteristic value stK

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-- The max. Explosive overpressure maxp

(4) The dust parameter corresponds to the max. Speed stKdtdp of the rising pressure

(5) Both values are determined in accordance with standardized procedures (see

DIN-Fachbericht 140 and DIN 26184-1)

(6) The principal explosive dust-types are: brown coal, cellulose, pea-flour, fly ash,

fodder, feed-mix concentrate, barley, corn flour, rubber, resin, wood dust, coffee, potato

flour, coke, maize flour, maize starch (dry), milk powder, paper, pigment, Soya meal,

Soya flour, hard coal, wheat flour, washing agents and sugar.

I.5 Sources of Ignition

Small quantities of energy are generally adequate for igniting these dust particles. The

following sources of ignition are of particular significance in silo bins and associated

spaces e.g. silo cellars, connecting passages and stairwells

- hot surfaces e.g. those which are caused by friction of defective structural

components, or sparks such as those caused by foreign bodies in the hoisting devices,

sparks during welding, grinding and cutting during repairs, smoulder spots which can also

enter into the silo bin from outside along with the bulk material.

- Unsuitable or defective electrical equipment (e.g. incandescent bulbs)

- Heat generated due to drying

- Self ignition due to electrostatic discharge

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I.6 Protective Measures (1) The damage caused by a dust explosion can be minimized by containing the

explosion as far as possible within the area in which the igniting occurs. For this purpose

explosion zones have to be demarcated. The spreading of the explosion to another area

is to be avoided. The explosive overpressures are to be minimized.

(2) The consequences of an explosion can be minimized by providing for suitable

precautionary measures during planning (e.g. the provision and demarcation of relevant

explosion zones).

(3) The individual building sections between the explosion barriers are to be

dimensioned for one of the following two conditions:

-- If no pressure relief has been provided, the zones must be dimensioned for the

max. Explosive overpressure maxp

-- If a suitable relief has been provided, the zones must be dimensioned with the

largest reduced overpressure or . redp gesredp ,

(4) The amount of the reduced explosive overpressures or depend on the

type of the dust, the size of the zone where pressure relief has to be effected and the

vents, and the opening pressure and the inertia of the depressurizing system.

redp gesredp ,

(5) The inflammable emission coming out of a vent should not have any adverse

effect on the surroundings nor be allowed to transmit the explosion to any other explosion

zone.

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(6) There should be no danger to people on account of splinters from panes or other

components. Vents should therefore lead out directly into the open – above roof tops in

case of silo bins, and above high-lying window faces in case of other spaces such as silo

cellars, connecting passages and stairwells.

(7) The opening pressure of the depressurizing system should be as small as possible

And its mass inertia should be low. Here it must be kept in mind that with an early

actuation of the depressurizing system a substantially larger quantity of the combustible

dust-air mixture is passed on than with systems which have a greater inertia.

I.7 Dimensioning of the Components

The dimensioning of the concerned components is to be executed in accordance with the

rules for extraordinary loads (catastrophic loads).

I.8 Dimensioning for Explosive Overpressure (1) All the load-bearing and space-enclosing components of an explosion zone are to

designed for the dimensioning pressure.

(2) The dimensioning pressures should be determined in accordance with the

procedure given in the DIN-Fachbericht 140.

I.9 Dimensioning for Sub pressure

After a pressure relief has taken place, a sub pressure may arise in the explosion area

caused by the forces of mass inertia in case of swift gas emission and subsequent

cooling of the hot flue gases. This sub pressure is to be taken into account with the

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dimensioning of enclosing components and the components which are situated in the

cross-section of the current.

I.10 Securing the Closing Elements of the Vents (1) All the closing elements are to be secured such that do not fly open as a result of

the explosion’s pressure, e. g. shutters to be secured with joints, and covers with

catches, ropes or other attachments.

(2) The velocities of the closing elements that were moved for estimating the

anchoring forces can be determined using the calculating methods laid down in DIN-

Fachbericht 140.

I.11 Recoil Forces through Pressure Relief (1) Recoil forces arise during pressure relief, for which allowance may - if required -

need to made in case of stability verification. This is to be specially checked in case of

lightweight structures with horizontal vents which are distributed across the cross-section.

(2) The recoil forces can be calculated as per the specifications in DIN-Fachbericht

140.

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Transcript of 51989151 din-1055-6-2005 silos