Hopper Design Indian Standard

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है” ह” ह

IS 9178-3 (1980): Criteria for Design of Steel Bins for Storage of Bulk Materials, Part 3: Bins Designed for Mass Flow and Funnel Flow [CED 7: Structural Engineering and structural sections]

IS : 9178

(Part

III

) -

1980

Indian Standard

Reaffirmed 2010

CRITERIA FOR DESIGN OF STEEL BINS FOR

STORAGE OF BULK

MATERIALS

PART 111 BINS DESIGNED FOR MASS FLOW

AND FUNNEL FLOW

I N D I AN S T A N D A R D S I N S T I T U T I O N

BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

N E W D E L H I 1 1 0 0 0 2

January 1982

© Copyright 1982

Is :

9178 ( Part

III ) •

1980

Indian Standard

CRITERIA FOR DESIGN OF STEEL BINS FOR

STORAGE OF BULK MATERIALS

PART III BINS DESIGNED FOR MASS FLOW AND FUNNEL FLOW

Structural Engineermg Sectional Committee, SMllDC 7

Chairman

DIRECTOI: Sl'ANIJARDS ( CIVIT, ) A[""bers

SnRI R. i\f AGAR'VAL

DIt Puuv KurSUN~ (Alternal. )

SUIH A K IlAXLltJEI'.

Repr;se"llng

Mimstry of Railways

Insriturion of Engineer' ( Inrha }, Calcutta

Metallurgic d and Engrncerrng Consultants

l India) Ltel, Ranchi

Sum S. SA"KARAN (Allerrral' )

Slim P. G. ihnDIIAN Brauhw.ntc & Co Lt,l, Ca lcutra

:::. HI":::' K t;,,,COPAllIlY, Y (Altemale )

SlIIlI S, N BASU Inspccuon Wing, Drrecrorate General of Supplies

ami D.'pm"h, New Delln

SII'" D Il I ~1'1 (AIJ,mal' )

Sru.t P. C JIll 1"'1 Mrmsrrv ofS!Jippilll'; -md Transport (Department

ut I'rnnvpor-t ) ( Road, WIIII'; )

DIt 1'. N CIH'." L"TEl" Government 01W"'tBengal

DR P D,YA"A I'1A" Indr.m Institute of Technology, Kanpur

i:>lilti D S

J)""

1\1. N. Dastur & Co PH Ltd, Calcutta

:::'1I1<lS R. KIILhA,,,t (.Ilfemate)

Dnui rou l l",A~~~l«"liN) Ccntr.rl Elccnrcitj Authority, New Deihl

D,.'un ])JLtI' 1"" l11"'5-l\l1~~IO"'f) \ Allemllte)

Sunr Z II"'N Cenn al Water Comrmss ion, New Ddln Suut V. NAr:AL'" ' " (.W,mal')

JOI:>l1' DIRJ.~j'O" ST \ " "AuJI 8 Muustry of Railways

(B& S)

1\88'81'\'1" Dllnl run ( B& S)-sn (Alternate )

jvr" r DIHLLrllI' (D.,,,,",,") Natronal Burldrngs Orgaruzution, New Delhi

Sum K S S1U"I\AS,':>I ( .Jllernal.)

SIIHI KAH.'llK PR~S\U Indian Roads Congress, New Delhi

SHIU:::' C, CIHK"'llAllTI (.lllernal' )

{ Cnnllnwd on page:2 }

@ COPYrlghl 198t

INDIAN STANDARDS INSTITUTION

Thu publicanon II protected u.ider the Indian Copy"ghi Acl (XIV of 1957) and reproducllon 10 whole or ID part by any means except with written permission of the pUblisher shall be deemed to be an inCflngement oC copyright under the ,aId Act.

IS z9118 ( Part DI) • 1980

Ind ia,

Representlll,

Jessop & Co Ltd, Calcutta

( COflhlllUdftl1/1l

"",e

I ) Members

SHIU P. K. MALLICK

8Hm T S. BAGCHI (AlttTMte )

SHIU S. K. MUKHEIlJEE Bridge & Roof Co ( India) Ltd, Howrah

SHIll

n.

K CHATTERJEll (Alternate)

Salll P V. NAIK RIchardson & Cruddas Ltd, Bombay

SnRI V. G. MANORULKAR (Allernate )

SHill DILIF PAUL Industrial Fasteners Association of

Calcutta Bmny Ltd, Madras

SHin N RADHAKRISHNAN

SHIn P. ApPA RAO (Alternate)

SIun N. V. R ....tAN Structural Engineermg Research Centre, Madras

DnT. V.S. R. ApPA RAO ( Alternate)

SHIll C. S,

s

RAO Engmeer-in-Ohrefs Branch, Ministry ~r DeCellce

REPIlESENTATlVE Tata Consultrng Engmeers, New Deihl

REPRESENTATIVE Hindustan Steel Works Construction Ltd,

Calcutta

Rail Indian Technical and Economics Services, New Deihl

Slun A B.RIBEIRO

SHIll S K BUANDT ( AlltTnate)

SHillP SENGUP1'A Stewarts & Lloyds of India Ltd, Calcutta

SHIll M. M. GnOSH (A.lternate)

SH1UM. M. SUENOY JOInt Plant Committee, Calcutta SHRl D. SRINIVASAN (Allt:rnale)

Snm C. N. SRINIVASAN CR. Narayana Rao, Karpagambal Nagar, Martras

SIIIlI C N RAG1IAVENDIIAN (AlltrMle)

SHIll G SIlmp'A"AN llharat HeavyElectrrcals Ltd, "I'iruchirapalh

~HJlJH. K. TANJ!JA Indran Register of Shipping, Bombay SHEI D SAIlANGDIlAR (Alternale)

SHIll M. D. [HAMDEKAR Bombay Port Trust, Bombay

Oil D. N TI<lKIIA UllIverSity uf Roorkee, Roorkee

SHIll L. D W"IlHWA Engineers India Ltd, New Delhi

S"III 1l fl. NAG ( Altemate )

SlIIlI C R. RAMA Rw Director General, lSI (&-offim Membn)

Director ( Struc& Met)

Secrefarres

S1InI S. S SETHI

Deputy Director ( Struc & Met l,lSI

SnRI V G HIREMATH

ASSIStant Drrecror ( Struc & Met ), lSI

Subcommittee for Use of Steel in Bulk Storage Structures, 5MBDC 7 : 4 COfll.Jener SURI N K. Roy !>l,mN's SHRI S. K. CHATTERJEE SHI<I S. GOJ'ALAE:RISHNAN

SHRI S. SELVARAJ (Alter,..lel

SHill GUI'CHAIUN SINGH Sunr K VEEIlARAOIlA \'Al'UARY

The Fertilizer (Planning and Development}

India Ltd, Smdn

Cement Corporation ofIndia Ltd, New Delhi Structural Engmeerrng Research Centre, Madtas Food Corporation of India, New Delhi

Bharat Heavy Electrrcals Ltd, Tiruchlrapalli

MARCH 1984

AMENDMENt NO. 1

'to

IS: 9178 ( Part III )-1980 CRITEIUA FOR

DESIGN OF STEEL BINS

FOR

STORAGE OF

BULK

MATERIALS

PART'"

SINS DESIGNED FOR MASS FLOW AND

FUNNEL FLOW

Col'rilead1lm

<

( PQge 31, claus« ]2.2.~.2, lfUQIWII 10 ) - Substitute the followingf,

the existing equation:

H [

~- (-~

r.

P, .

~.d

]

( 2 - O"hin 8)lD X

{sin

6

+

cosI} • tan

a

h ) . ... (ll

IS: 9178 (Part JIJ ) .1980

Indian Standard

CRITERIA FOR DESIGN OF STEEL BINS FOR

STORAGE OF BULK MATERIALS

PART III BINS DESIGNED FOR MASS FLOW AND FUNNEL FLOW

e,

FOREWORD

0.1 This Indian Standard (Part III) was adopted by the Indian

Standards Institution on 7 July 1980, after the draft finalized by the

Structural Engineering Sectional Cornrmttee had been approved by

the Structural and Metals Division Council and the CIVIl Engineering Division Council,

0.2 Bins are known as silos if they have circular or polygonal shape in plan. When square or rectangular in plan they are known as bunkers. In this standard. bin shall mean both silos and bunkers unless otherwise stated.

0.3 The functions of bins as storage structures are very important in power stations, fertilizer complexes, steel plants, cement plants and other similar industries for efficient storage and use of bulk material in both granular and powdery form. On the agriCultural front bins are used to store food. grains for ensuring their supply throughout the year. Bulk storage of materials in bins has certain advantages over other forms of storage. An Indian Standard on this subject has, therefore, been a long fclt need and this standard is armed at givmg the necessary guidance IIIthe analysis and

design of steel bins for storing various materrals ofdifferent characteristics and flow properties.

0.4 Bins have been designed on the basis of Janssen's Theory (with modifications to the original). From experimental investigations and a study of the performance of the existing bins, it has been noticed that the pressure distribution is influenced by the size and shape of the material to be stored ( that is granular or powdery), moisture and temperature, bulk density, which, in turn, are affected by storage and flow characteristics. Besides, there is increase in the imposed loads during filling and emptying, the latter being more predominant.

0.5 For reasons mentioned above, in the bins designed by conventional methods, materials do not easily flow due to arching and piping. This

ISI 9178 (Part III) • 1980

requires frequent poking - manually, pneumaticallv, with steam or by other mechanical means. With rr-sr-arch data available, this problem has been successfully solvcd by adnpting mass Iluw or funnel flow bins where the shape of the bin hopper and the size of the openmg, are based on the flow properties of the stored material.

0.6 In this part of the code the present thmking on the design of mass flow and funnel flow bunkers based on jernke's work isexplamed. Further research in this field is cnntinuJO'; and it will not be possible to give

a

umvcrsal approach for all rnaterrals under varymg scrvrce conditions. This standard has lunitauons winch are explained in Appendix A with proper reference. It i" therefore, suggested that designers should consider all these aspects while adopting the recommendations given in this code.

0.7 In order to deal with the subject 10 an effective manner this standard has been prepared in three parts, namely,

Part I General requirements and assessment of loads. Part

rr

Design crrreria,

Part III Bins designed for mass flow and funnel flow.

0.8 This standard keeps in view the practices being followed in India and elsewhere in the field. Assistance has also been derived from the following publications:

I. DIN 1055 (Sheet 6) Design loads for building bins, issued by Deutsche Norrnenausschluss.

2. Pressure distribution in bins (in German) Pioper

K.,

and Wenzel, F. Verlag Vom Wilhelm Erust & Sohn, Berlin, Munchen, 1964.

3. Bins and bunker for handling bulk material" Reisner, \V" and Rothe, M E. Trane-Tech. Publication, Ohio, USA

4. Jenike, A. W.; Storage and flow of solids, Bull 123 (Utah Engmeering Experiment Station, Unice. of Utah, U.S A. ),

1964.

5. Jenike, A. W.;Johanson, JR.; Carson,J. W.; Bin loads - Part 2~

Concepts, bin loads - Part 3: Mass flow bins, bin loads - Part 4: Funnel flow bins, Published in the' Journal of Engineering fon Industry' Feb 1973 by American Society of Mechanical Engineers.

0.9 Recommended literature for reference is given in Appendix B.

0.10 For the purpose of deciding whether a particular requirement of this standard is complied with, the final value, observed or calculated, express, ing the result of a test or analySIS, shall be rounded off in accordance with

IS: 9178 (Part III) • 1980

IS : 2-1960"'. The number of significant places retained in the rounded off value should be the same as that of the specified value in this standard.

SECTION I GENERAL

I. SCOPE

1.1 This standard (Part I II) dl'.lls with the design of steel brns for

storage ofbulk materials ensuring satisfactory mass How and funnel How ( plug flow) under gravity flow In the case of powdery and granular

materials.

2. TERMINOLOGY

2.1 For the purpose of this standard, the definitions given in Parts I and

II in addition to the following definitions shall apply.

2.1.1 Active Pressure Field- The field in which the major pressure is

vertical or near vertical.

2.1.2 Arched Pressure Fields - In arched pressure fields major pressure

lines arch across flow channels, synonymous with "passive pressure" in soil mechanics.

2.1.3 Charger - Deposition of bulk solid into a bin, usually hy dropping in or blowing III from above.

2.1.4 Cylinder - Vertical part of a bin.

2.1.5 Draw - Withdrawal or feeding of bulk solids from a bin.

2.1.6 Flow Channel - Space through which a bulk solid is actually

flowing during draw.

2.1.7 Flow Pressure - Pressure which the material exerts on the walls of a bin during flow

2.1.8 Funnel or Plug Flow - The flow pattern in which the material

flows primarily in the central region of the bin or hopper.

2.1.9 Initial Pressure - Pressure exerted by bulk solids on the walls of the bin during and after charging, but before any withdrawal of the

material.

2.1.10 Mass Flow - Flow in which the entire mass of material flows without stagnation.

2.1.11 Passive PrUSUTt Field - Field in which the major pressure is horizon tal or near horizontaI.

·Rules for rounding off numerical value. (w.ued).

IS

I

9178 (Part III) .1980

2.1.12

Peaked Pressure Fields - In peaked pressure fields major pressure lines from peaks at the centre of the bin, synonymous wrth "active pressure" in soil mechanics.

2.1.13

Radial Pressure Field - Field which occurs in the lower part of

a hopper and in which pressures are proportional to the distance from the vertex of the hopper.

2.1.14

Strain Energy - The energy of a flowing mass of solid which could be recovered by a relaxation of boundary forces and displacements.

2.1.15

Switch - Region of change of an active pressure field towards a passive pressure field.

2.1.16

Transition -Joint between the cylinder wall and the conical

flow channel in a funnel flow bin, In mass flow it is the joint between cylinder and hopper.

standard the notations as given below shall

=

Mmor dimension of the outlet, m

= Major dimension of the outlet or length of the opening ( slot length ), m

= Diameter of the opening of hopper, m

= Diameter of a circular cylinder, that is. dia of vertical,

portron of storage system, width of rectangular Or square cylinder, m

- Height of the cylinder, m

= Coefficient, m = 0 for wedge hopper

m = I for conical hopper

= Distance from the axis of symmetry. ill

= Bulkdensity of the solid, kg/m3

= Area of horizontal section of a cylinder, mS

=

Diameter of hopper, width of a hopper, m = Unconfined yield force of bulk solid, kgf

=

Hydraulic radius

=

A/V

= Perimeter of the cross-section of the stored material, m = Shearing force, kgf

= Janssen's pressure line

= Depth of the fill in the cyhnder, m

= Fnctional stress on the bin wall, kgf/ml = Frictional stress on the hopper wall, kgf/ml

w A B

F

R V S ] r

m

h

3. NOTATIONS

3.1 For the purpose of this

apply:

b_o

10

As

R

j

if, ill

v

r

En

wn

H (O) ISI 9178 (Part 111 ) • 1980

= Shear cell area (cross-sectional area of the test

sample), m2

= Radius of curvature at transition

V

=

r

=

Flow factor of a channel (hopper)

= Major consolidating force, kgf

=

Major force in a dome or a pipe ( bulk material under flow), kgf

= Flow function of bulk material

= Instantaneous flow function of bulk solid

= Time flow function of bulk solid stored for a period'I '

before delivery starts

= Pressure normal to hopper or cylinder wall, kgf/m2 = Initial pressure on a hopper wall at the vertex, kgfjml

= Peak pressure at the transition, kgf/ml

= Initial pressure on a hopper wall at the transition, kgf/m2

= Radial pressure on a hopper wall at the transition, kgf/m2

= Peak pressure at an effective transition, kgf(m2

= Non-dimensional vertical force acting within a bulk solid at the level of the transition due to radial stresses

in the hopper

= Vertical force developed in cylinder walls due to wall friction, kgf

= Pressure normal to cylinder wall. kgfjm2

= Total vertical force acting within the bulk solid at the level of transition due to stresses in the cylinder, kgf

= Effective yield locus of the How of bulk solid

= Wall yield locus of the flow of bulk solids for a

particular hopper wall

= Hopper slope measured from vertical, deg

= Conical hopper slope measured from vertical, deg

= Plane flow hopper slope measured from vertical. deg

= Slope of flow channel with respect to vertical, deg

= A function depending on ()

IS

I

9178 (Part 111) - 1980

rP G (1)) ii ii' a

= Kinematic angle of internal Irrction of bulk solid, deg

=

A function depending upon r/l

- Effective angle of wall friction of bulk solid on the walls of the bin, deg

= Kinematic angle of wall friction between bulk solid and wall of bin, deg

I::: Angle of friction between bulk solid and hopper wall, deg

= A function depending on ii'

= Coefficient of friction between the bulk solid and the cyLinder wall

= Pressure ratio, that is, horizontal to vertical pressure

= Pressure, kgfJm2•

4. DESIGN CONSIDERATIONS

4.1 In the design of bins for bulk storage, the two important considera-tions involved are:

a) flow characteristics, and

b) load distrrbution characteristics of the stored material.

".1.1 The now characteristics determine the slope of the hopper portion of the bill and the outlet dimeusions wlnch indrrecrlv lead to the selecnon

of shape and Slze of the bID. These are dealt wlth'in detail In Section 2

and Section 3of the code for mass flow and funneL /low respectively.

4.1.'2 Load distrrbution characteristicsgive the actual loading conduion

on the walls of the bm and at the ouuct, The-se govern the structural design of the bin as well as the selection of the feeder system to be incor-porated at the outlet. This has been dealt with In detail in Section 4 of

the code.

SECTION 2 DESIGN FOR MASS FLOW

5. GENERAL

5.1 In mass flow, the contents of the hopper move at all points and sliding takes place at the walls whenever any solid is drawn through the outlet of the bin, Inactive or dead regIOns are absent III the stored mass. Mass

Is

t

9178

(I'art

tit) •

1910

5.2

Mass flow has the fallowing characteristics which guide the selection of the design parameters:

a) Channelling, hang-ups, surging and flooding are absent,

b) Flow is uniform, and steady state flow can be achieved closely, c) Pressure throughout the mass and at the walls is relatively low,

which results in low consolidation or packing,

d) There are no dead regions within the bin; hence there is minimum of consolidanon at rest.

e) A first-in-first-out How pattern may be obtained, if desired This IS useful in the storage of solids which either deteriorate With time or segregate during charging

f) By circulating a mixture around a suitable bin, blending may be attained.

5.3 Mass flow storage bins may be designed with a variety of hopper shapes listed below ( see Fig. I ):

a) Conical or pyramidal hoppers with circular or square outlet, b) Chisel hoppers with rectangular outlet or slot,

c) Transition hopper with rectangular outlet,

d) Wedge hopper with full slot or rectangular outlet.

5.4 This standard covers the various hopper shapes given in 5.3 under the following two distinct grou ps:

a) Conical channel with square or circular outlet,

b) Plane flow channel with rectangular or full slot outlet.

6. FACTORS INFLUENCING THE DESIGN

6.1 Flow Properties of Stored Bulk Solids - The flow properties of

bulk solid stored in the bin is the principal factor affecting the design. These properties shall be determined under similar conditions of the bulk mass as It is stored in and delivered by the bin being designed. Factors affecting the flow properties are as follows:

a) Particle size and shape,

b) Bulk density and consolidation, c) Moisture content,

d) Temperature,

e) Surface finish of bin walls, and f) Period of storage.

The flow properties shall be determined after considering these factors in the actual storage conditions. The flow properties thus

IS I 9178 (Part III ) • 1980

determined will help in determining the outlet size, the slope of hopper and the load distribution on the walls of the bin.

Z, I- - -

t---

I-~ d

V'''\

1

10

-r

j , - l I

i

8_c

(a) Conical (bl Pyramidal (c) Chisel

d

~-T

,1 IZ,

_J

_Sp 8_e 8,

I~

10

~

b.

(d) Transrtron (e) Wedge

FIG. 1 HOPPER SHAPES FOR MAss FLOW BINS

6.1.1 Slope of Hopper - For a good design, the hopper slope angle shall be so selected (see7.4) that the stored mass moves in a first-in-first-out fashion and each point of [he mass moves when flow starts. The bin shall fully clear itself Without any flow promoting device.

IS I 9178 ( Part 111 ) .1980

6.1.2 (hdlet - For a satisfactory flow in a mass Row storage system, the outlet shall be large enough (see 7.5) so that plug flow, piping and doming do not occur and the flow continues without the aid of flow pro-moting devices.

6.2 LUlDp Size - The flow is also influenced by lump size with respect to a certain outlet size. For uninterrupted flow, the outlet shall be designed for an optimum lump size. Normally, the lumps are free flowing and are suitable for mass flow.

7. DESIGN PROCEDURE

7.1 Design procedure involves the following stages:

a) Collection of information about the stored bulk solids and

the wall material of the bin,

b) Determination of the flow properties of the bulk material to be stored,

c) Estimation of the hopper slope 8, d) Estimation of the size of outlet.

7.2 Collection of Information About the Stored Bulk Solids and the Wall Material of the Bin

7.2.1 The size, unpacked bulk density ( aerated bulk density) and the

lump size (if lumps are present) of the powdered and granular

solid shall be determined.

7.2.2 The condition of the bulk solid to be stored shall be conformed. This requires information about the moisture content and temperature of the bulk material of actual service and the time period for which the bulk material is stored at rest in the bin.

7.2.3 The wall material and its surface condition ( finish, lining finish) shall be determined or the information shall be obtained from the prescribed specifications of the bin.

7.3 DeternUDatioD of the Flow Properties of Bulk Material

7.3.1 The bulk material shall be tested on a shear tester ( flow factor tester) to obtain Itdistribution curve with respect to major consolidating force V and flow function FF. The test shall be done With the sample of bulk material representing the actual material to be stored (size, moisture content, time period, temperature, etc, shall be similar). The r/J

distribution with respect to various consolidation and wall yield loci

(wri )

shall be determined (

see

Appendix C).

7.3.2 The values of shear cell area AB, mean values of

a

and

a'

at the outlet conditions shall be determined from the flow property data. ~' shall be estimated from WYL (see Fig. C-3 of Appendix C ).

IS

*

9178 ( Part III) • 1980

7.4 E.timation of Hopper Slope Angle 9

7.'1.1 Flow factor (.fJ) corresponding to the assumed 8 and 8' values

at outlet shall be estimated from the.fJ contours for conical and plane flow channel ( see Fig. C-1S to C-15 of Appendix C). Thelf values should be

so selected that the point ( &', 0 ) IS very close to the extreme boundary.

7....2

e,

shall be selected from

Fig. C-B

of Appendix

C

such that the point ( 0" 8' ) lies _5~ within the boundary of the selectedff for the case of conical flow.

1.... 3 In the case of plane flow channels, 0]. shall be selected very close to the left of the dotted extreme boundary. In the case of a smooth tran-sition zone ( trantran-sition from vertical portion of storage equipment to the hopper) with a radius of curvature R_t

;>

d13, OJ' may be increased by 5° from the optimum value selected earher.

7.5 Estimation of Outlet Size

7.5.1 The estimated flow factor

if

(see7....1) shall now be plotted

against flow function FFof the bulk solid FF is a plot of Vand Fwith

Vas abscissa and Fa~ ordrnate, whereas

if

is the plot of Vand Vwith V

as ordinate, scale of (' and F being same for the plot.

7.5.2 II ( 6 ) corresponduig to the estimated 6 for the selected shape of

outlet IS determined from FJ!j C-12 of Appendix C.

7.5.3 If there is no intersection of.f! with FF, and FF lies below

if,

it shows that the material stored IS free flowing and any dimension of outlet

based on the rate of discharge and lump size shall be sufficient. An outlet size _bo = G ;~ (m.lximum lump xize ] or the size based on discharge whichever IS greater shall be selected. The following relation yields the

value of [' at the outlet condition:

V

~ ~o_w A~

- H (0)

When

r

so determined is located on .fJline, V at the outlet is also obtained.

7.5.4 If FF lies above jJ, it means that the solid will not flow in a channel w.th flow factor assumed. lflower values ofJfare available and if an intersection can be obtained, the new flow factorjf shall be selected. Based on this modified.o; the intersection point ( V,

V )

is noted.

7.5.5 Ifthere is an intersection offfwith FF,it shows that the bin of a particular slope an~ outlet size can be desisned for mass flow, The

IS :9178 ( Part III ) • 1980

7.5.6 After plotting

If

over FF_o and FF, if It I~ found that lhe,ffline lies between FF0 and FF_{t ,} that 1~,JrIS above FF0 hut below FF_{t •}the stored material shows a tendency of consolidation with time. In these cases, vibrators are specified, so rhat the flow may be started, and the outlet is designed with a factor of safety to allow for any unfavourable effect of

~ibration. This shall be accomplished by so selecting V that at outlet

V

=

1'5 F.

7.5.7 From 7.5.3 to 7.5.6 according to tile case f.tced in design

V

shall be selected and

H

(0) shall be revalued from Frg, C·12 of Appendix C if any modification in 11 has been done dunng the location of ( V, V).

7.5.8 Minimum outlet dirnensrons, h_o shall be calculated from the following formula'

bo=_~,-H(Ot

.r,

w

7.6 Check for Estimated Design Data

7.6.1 Corresponding \0 the I' value obtained under 7.5.3 to 7.5.6,

S shall bc read from plot 0 and I', This v.iluc of Swill determine the EYL of the stored rnass at outlet conditions.

7.6.2 The Mohr's semicircle shall be drawn through ( V,0 ) such that it shall be tangential to ElL The WYL shall then be drawn over this Mohr's semicircle. The point of iniersecuon shall determine 8' at outlet. This should check with the estimated 0',

7.6.3 If the estimated 0' does not tally WIth the check value of 5', a further estimation offfand 0' shall be done, so that the check value of 0'

is dosdy reached.

7.7 Recalculation for Slope of Hopper and Outlet Size on Basis of

Corrected Data

7.7.1 The corrected values ofjJ, 0 and

o'

shall be noted and the corres-pending 11 ( hopper slope) shall be obtamed from Fig C-13 to C-15of Appendix C. H (ll) shall be obtained from Fig C-12 of Appendix C.

V is obtained 111the manner shown under 7.5.3 to 7.5.6. The outlet size b_{o shall then be obtained according to 7.5.3.}

7.7.2 A check is done once again to ascertain the recalculated values in a similar way as shown in 7.6.1,7.6.2 and 7.6.3

7.7.3 The check and recalculation shall be continued until corrected and check values of

o'

are equal.

IS: 91'78 ( Part III ) • 1980

7.8 Adopted Values of Outlet Size aod Slope of Hopper for Design

7.8.1 The hopper slope angle shall be equal to or less than the

calculated values It shall not exceed the calculated value in any case. 7.8.2 In the case of conical hoppers or steep pyramidal hoppers, the outlet shall be circular or square. The diameter of the circular outlet or the side of the square outlet shall not be less than the calculated minimum dimension boo

7.8.3 In the case of plane flow hopper, the outlet shall be rectangular or full slot. In the case of rectangular opening, the small side shall not be less than b_o Incase the stored solid contains lumps, the smaller side shall be atleast four times ( preferably silt times) the maximum lump size. The greater side of the rectangular outlet shall not be less than three times the smaller Side. In the case of full slot opening, the width of open-ing shall be greater than the calculated boo For lumpy stored solid, it shall always be more than four times (preferably six times) the maximum lump size. The length of slot shall be at least six times the width of slot

(lo>6bo

l .

7.8.4 A recommended calculation sheet is given in Appendix D for the design of bins for mass flow, including determination of outlet size and slope of hopper.

SECTION 3 DESIGN FOR FUNNEL OR PLUG FLOW

8. GENERAL

8.1 In funnel flow ( plug flow). the hulk solid flows towards the outlet of the bin in a channel formed within the mass, while the mass around the channel remains stationary (seeFig. 2). Itis a gravity flow without any flow promoting devices.

8.2 Funnel flow bins are used for storage when segregation is unimportant and there is no problem of deteriorauon with time of the stored material. Since there is httle wear in the hopper walls during service, this storage system is useful for the storage of hard, abrasive and lumpy solids.

8.3 Funnel flow bins ( Fig. 3) may be classified in the following types: a) Flat, bottom bins without hopper,

b) Bins with conical hopper, or c) Bins with pyramidal hopper.

8.4 The shape of the outlet may be circular, square or rectangular.

IS: 9178 ( Part III ) • 1980

DRAW MOSTL¥ COARSE

DRAW SAME AS CHARGE

FIG 2 PLUG FLOW

\ _I \ I \ \ _I I I \ _I I I \ I

"

/

la) FLAT BOTTOM lblCQNICAL (e 1PYRAMIDAL

FIG. 3 PLUG FLOW BINS

IS

I

9178 ( Part III ) - 1980

9. FACTORS INFLUENCING DESIGN

9.1 Flow Properties of Stored Bulk Solid - The flow properties of

bulk solids stored in the bm is the principal factor affecting the design. These properties shall be determined under similar conditions of the bulk mass as It is stored in and delivered by the bin being designed. The factors affecting the flow properties are as follows:

a) Particle size and shape,

b) Bulk density and consolidation,

c) Moisture coni ent, d) Temperature,

e) Surface finish of bin walls, f) Time period of storage.

The flow proper\les thus determined will help in arriving at the outlet size, the slope 01 hopper and the load distribution on the walls of the bin.

9.1.1 Outle: - For a sausfactory flow in funnel flow bins, the outlet shall be large enough so that pipmg and doming do not occur and the flow continues WIthout any 110w promoting device.

9.1.2 Slope oj Hopper - The hopper slope shall be so selected that the moving channel 01 the mass attains a maximum possible size and there IS no possibihty of plpmg and doming.

9.2 Lump Si:,;e - The flow is also influenced by lump size with respect

10 a certain outlet size. For uninterrupted flow, the outlet shall be designed for an optimum lump size.

10. DESIGN PROCEDURE

10.1 Collection of Information about the Stored Bulk Material and

Wall Material of the Bin

10.1.1 The size, aerated bulk density and packed bulk density of the powdered and granular solid shall be determined. The lump size ( if lumps are present) shall also be determined.

10.1.2 The condiuon of the bulk solid to be stored shan be confirmed. This requires information about the moisture content and temperature of the bulk material at actual service and the time period for which the bulk material is stored at rest in the bin.

10.1.3 The bin wall material and its surface condition (finish, lining finish) shall be determined or the mfnrmauon shall be obtained from the specification sheet of the bin.

IS

19178

(tart

ttl) .1...

10.2 Determination of the Flow Properties of Bulk Material

10.2.1 The bulk material shall be tested on a shear tester ( flow factor tester) to obtain 1\ distribution curve with respect to major consolidating force, V, and flow function FF. These tests shall be conducted with the sample of bulk material representing the actual material to be stored (size, moisture content, time period, temperature, etc, shall be similar). The

r/l

distribution with respect to various consolidation shall also be determined (seeAppendix C ).

10.2.2 The values for shear cell area As, mean values of

8

and

r/l

shall be determined from the flow property data.

10.3 Determination of Hopper Slope Angle

.p

10.3.1 Flow factor (ff) corresponding to the average 8 and <p shall be fixed with reference to Fig. C-9 of Appendix C. The value offfshall not be less than 1'7.

10.3.2 Referring to Fig C-IO, the hopper slope may be fixed corres-ponding to the average1\and theif obtained under 10.3.1. The maximum

9 values for conical and plane flow channels shown in Fig. C-IO of

Appendix C shall not be exceeded If doming is to be avoided.

10.3.3 In the case of plane flow (rectangular outlet) hoppers, the slope 9_1l shall always be more than 30", If 1\ is greater than 40", which represents the rnajonty of bulk solids. In the case of pyramidal hoppers, the slope angle refers to the valley angle.

10.3.4 The conical channels for plug flow are usually very steep and this leads to the adoption of flat bottom bins 10 place of a conical

channel.

10.4 DeterlDination of Outlet Size

10.4.1 The flow factor

ff

determined as per 10.3.1 IS plotted against the flow function FF of the bulk material. FF is a plot ofVand Fwith Vas abscissa and F as ordinate, whereas

ff

is the plot of V and

V

with

Vas

ordinate, scale of

V

and F being the same. The Intersection of ifwith FF

yields a point ( V,

V).

10.4.2 Functions G (

.p)

and

H (

a) are evaluated from Fig. C-II and Fig. C.12 respectively ofAppendix C.

10.4.3 Ifthe outlet shape selected for design is square or circular, the major dimension of the outlet willrepresent the side of square or diameter of circular opening. The major dimension, 10 for rectangular or do for circular opening shall be calculated by the following formula:

10 or do =

VG(.p) A• .w

IS ,9178 (Part III ) ·1980

10.4.4 Ifthe outlet is rectangular in shape, the minor dimension bo of

the outlet ( apart from the major dimension 10 ) shall be obtained to avoid

any doming. bo is calculated by the following relation: b

o =

V

H (6)

As. w

10.4.5 The dimension of the rectangular outlet is given by bo X 10 ,

The dimension

1

0 shall be so adopted that is always greater than three

times boo

10.5 Adopted Valaes of Outlet Size aDd Slope of Hopper

10.5.1 Adopted values for the outlet dimensions shall be larger than the calculated values to accommodate the uninterrupted flow of lumps also. The dimenslon of outlet shall be at least sill: times the diameter of the size of lump being handled.

la.5.2

Adopted slope of the hopper shall be equal to or smaller than the calculated value. Itshall not exceed the calculated value in any case. 10.6 A recommended calculation sheet is given in Appendix E for the design of bin for funnel flow.

SECTION 4 LOAD DISTRIBUTION FOR DESIGN

OF

BULK

STORAGE

BINS

11. INITIAL AND FLOW PRESSURES

11.1 The method of calculation is based on the principle of minimum recoverable strain energy (For full details of the concept and pressure distribution, reference may be made to the papers • Bin Loads Part II concepts; Part £II - Mass flow bins and Part IV - Funnel flow bins' by

A. W. lemke,]. R. Johansen and] W. Carson, published In

tne

Journal

of Engineering for Industry of ASME, February 1978 ). There are certain limitations of this theory as pointed out by different research workers which are outlined in Appendix A. The procedure for determining pressure distribution as given in this section may be adopted subject to these limitations. The loads which act on the bin walls are different dur-ing the initial stage of charge into a bin and durdur-ing the flow stage from a bin, because the deformations which the stored materials undergo during these two stages are different. In the initial stage when the bulk material is charged into an empty bin with the discharge gate closed or the feeder at rest, the bulk material settles down as the head of bulk material rises. During this process, the material contracts vertically in ,the cylinder as also in the hopper. The major pressure tends to align with the direction of contraction of the bulk material. Hence. these initial pressures are close to vertical throughout the bin thus forming a .. peakedI I pressure field.

IS t 9178 ( Part III ) • 1980

This initial pressure corresponds to load calculated by Janssen's method in the cylindrical part of the bin and by a linear distribution in the hopper. This assumes that the bulk materials are not charged with significant impact and the bulk storage materials in powder form are charged at sufficiently low rate so that they deaerate. If granular bulk materials are to be dropped from some height the bins have to be

designed with safety for impact and wear in impact areas. Powdery

material when charged at high rate may develop close liquid pressures on the walls. Also, it should be ensured that the storage materials are suffi. ciently free flowing without obstruction; otherwise, stable arches of the stored materials may form. When this arch collapses, a large amount of bulk material falls and induces dynamic loads in the bin.

11.2 When the gate is open or the feeder is started, the stored material starts flowing out to the outlet, and in this case, a vertical expansion of solid takes place within the flow channel. The minor pressures may tend to align with the direction of expansion of the stored material. As a rule, the flow channel diverges upwards from the outlet. Hence, the flawing mass of stored material also contracts laterally. The major pressures with. in the flow channels tend to align with the lateral contractions. Hence, major pressures are essentially lateral, minor ones are vertical and the pressure field is arched.

11.3 The region of switch from peaked to arched fields originates at the outlet of the bin when the gate is first opened or the feeder is slarted and rapidly travels upwards into the bin as the stored material is withdrawn from the bin. At the level of the switch, the equilibrium of the mass imposes a sharp overpressure on the walls of the flow channels. This overpressure travels upward with the switch at least to the level at which the channel intersects the cylindrical part of the bin to the level of the transition in mass flow bins and effective transmission in the case of funnel flow bins. In a cylinder, above a transition, experimental data indicate wide oscillation of low pressure with time and this along with the peaks need be predicted. This has been analysed as a strain energy, based on the second law of thermodynamics and the pressure distributions for the mass and funnel flow bins are worked out.

11.4 The procedure for load distributions suggested in this code may be applied to bins designed for mass and funnel flow.

12. PROCEDURE FOR CALCULATION OF LOAD DISTRIBUTION IN MASS FLOW BINS

12.1 Initial Pressure

12.1.1 Cylinder -

Initial pressure

Ph'

on the walls of cylinder is:

W

R[

-~

;<1]

---;- l - e

19

IS

r

9178

(Part

111).1980

d and the hydraulic radius

R

= --=---~--,----c­

2(I+m) where'

m= I for circular bin,

= 0for long rectangular or square cylinder. and

A= 0'4.

.oo

(2)

Inthe cylinder, the frictional stress lw is related to normal pressure

Phby

•• , (3)

... (4)

12.1.2 Hopper - The surcharge, due to the stored material in the cylinder. exerts a vertical load Qc ( see Fig, 4-) on the stored material of the hopper. This force becomes maximum when the cylinder wall pressure is minimum (Janssen's distribution ). This is given by

Qc wR [

=fi!!"J

-:4

=

---;T

I - e

Values of

~~1.-

are plotted in Fig. 5.

The initial pressures perpendicular to the hopper wall are assumed to vary linearly from the apex to the transition, as shown in Fig. 4. The value at the apex, Pnl is given by

P

w.d

OJ = 2(tan 6-+-t-an~8~h""')

The initial pressure at the transition. PnU, is given by

,.. (5)

(2

+

m)

( 1+

m)

tan II

• tan

6

+

tan

8h

... (6)

The parameter m is 0 for long edged shape hopper and 1 for conical hopper.

The frictional stress /" is related to normal pressure Po by

I" = Po tan ll"

2J

JS

I

9J78 ( Part III ) ·1• •

d

\ I /

\ I \ I "I

a

\ \

\

FIG. 4 INITIAL PRESSURES IN A CONICAL HOPPER

II

t

9171 (Part UI)· 1910

o ~---~-.-,

I'

g c o o oW ....N -"0" 12 20 • 8

~----

wR o 8 20

I

10

I

12 '8 18 -/L

>.

(hIR) l - e Qcl A FIG. 5 FUNCTION -"~- - ;

-wR

12.2 Flow Presaures

12.2.1

Cylinder - The pressures exerted by a mass of stored material

in a cylindrical vessel are governed by

a) Slight deviation in shape of the vessel from cylindrical, and b) thin stable or unstable boundary layers of solid which forms at

the wall of the cylinder.

As a result, only bounds on wall pressures can be established. Janssen's formula nearly gives the lower bound and the upper bound is calculated by the consideration of strain energy of the mass of stored material.

An example of the loci of maximum cylinder pressure computed from strain energy and modified for the hopper effect is plotted in nOD-dimensional form ( Phlwd)maxin Fig. 6. These pressures are a function of the distance from the top of cylinder and the product pl., Janssen

pressures are also plotted as a reference.

22

1819178 ,PartlD ) - • •

2 IPhl .... )m•• - - _

~

SlRAIN ENER:a.,. ,...--"''': 0 '0 '11\ . - - _ : 0 15

'1'

-0·20 1\\. ~o-o lit, 1111 JANSSEN " : '0 '11\ _,4-025 , ofr ₌ 0-]7'S I' . ,- _{'0· 50} It""'" _ _ _ =0 7$ : ; : I J o e

I

,

j

I I I .1

FIG.6(a) (Phlwd

lmal<'

FOR CIRCULAR CYLINDERS, hId= 3

0F::""---, \

...

_----'

o ) IP"lwd) I'r\U

---JANSSE~ )."-"0 )1,0 25 ,0 315 ·0·50 '0·15 STQAI~ ENUGl }.lA,o 10 .0 15 : 0 20 : 0 )0

"

d

r

FrG. 6(b) (Phlwd )wu. FOR CIRCULAR CYLINDERS, hId

=

5

The vertical force P_{w caused} by the frictional stress tw

Ph

is computed from

Pw [

p..,

]

wdS

red = ("W.dB

1 mal<

X ;

-Typical results in non-dimensional form ( _{Pdw_)} W

a

WBJ;

ted in Fig. 7 for circular cylinders,

and Pressure

.. , (8)

are

o l i

l

e

;;

-

.-

...

~

-

-

•

i

6AS,ED ON STRAIN ENERGV ~ a ( I

•

, I

1

'

•

/J.A = Q·30 ~=OI5 ~=o,o 2 3 (I' w fWd 3) rn .. ____ BASED aN SIRA'N (N(IlG~ ), "

,

' o z 1

1.

, , \ N A.

•

3 1 2 (F'tN/Wd), mill( , 5' , ' , l o I

\

FlO. 7 (a) {P"/wdS)ma,,. FOR CIRCULAR CYLINDERS h/d= 3 FIG. 7 (b) (Pwfwd8 )ma". FOR CIRCULAR CYLINDERS hjd=5

IS 19178 ( Part III )

.1980

12.2.2 Hopper - Flow pressure variation in a mass /low hopper consists of a pressure peak at the transition, then a lmear decrease to an intermediate value and another linear decrease to zero at the apex

( see Fig. 8 ).

o

Po

FlO. 8 FLOW PRESSURE IN A CONICAL HOPPER

12.2.2.1

The radial pressure component at the transition PII~r is

given by

Pllt r = (

:B ).

w.ri. ••• (9)

Typical plots of ( :B ) as a function of

e

and 8h are given in Fig. 9 and Fig. 10 for conical channels and symmetric plane flow channels respectively.

JI.9178 ( Part III )

.1980 • 20· 30·

e

t •DEGREES -10·

30·,...--~....---....---....,...--....,..--...,..----.

I

0 01••• ,.,

~ 20k==~~--J..

..L

IJJ 0::

e

_{o •} ~ 10 s: <0 f1

FIG. '1( a) wE CONTOURS FOR CONICAL CHANNELS, B= 30·

•

20·

30·

at.

DEGREES

---0-1,0'

t

30·

lfl W w n:: l:l _20· w

s:

0

.

wB 2· 0 s: <0

10·

IS

I

91 '18 ( PBl"t

til ) •

1980

• 20· 30·

ee.DEGREES----•

10

•

40

Plr--.,.--...,..---,.---,---..,

r

30

~~~~~t--__+_--t--_1

If) w \oj a: •

l:3

20 ~-"x-o L. 10

FIG.9(c)

:B

CONTOURS FOR ComCAL CHANNEL', 3= 500

..

40· 50· 20· 30· Se,DEGREES -10' 40·

I

₎₀

•

lfI uJ uJ a: ~ 200 w 0 _, .J:: <0 ~~200 10· L=3·0 wB

o'

a·

FIG, 9(d) (J CONTOURS FOR CONICAL CHANNE.Ls, 11

=

60·

wB

ISI

9178 ( Part III ) • 1!18O

so'

,----,---,-.----r---"""T'"--..., 50'

-20· 30· Sc.OEGREE5

-10·

&=20

!s-'>]

0

I

"o·

30·

III IIJ IIJ Q: C) 20' w 0

•

.c co 10' "" loS'-min VAlUE: SOO <, <, "-

,

'0

),39 r1

!-'IO. 9(e) -wB- CONTOUR~ FOR CONICAL CHANNELS,

a

= 70°

30°nl"'~:-r-,,::;:;:>,...,r-~T"'""'I---n--"""T--"""

t

0c=~4~r--=f:~~~H

1/)20

UJ ,..._~ ~ 1-'::""'-1

h1

0

o.lo'k-=~~~--+---=:::::t:=-~j...L~-l

_s: IC

..

t!

FlO. 10(a) wB CONTOURS FOR SYMMETRIC PLANE FLOWCHANNELS. ~

=

300

Is

I

9178 (

t-art

111 ) • Ill"

1/1 ~ 20°po~--+-.=..., n::

a

o 50° 60·

-8p.DEGREES -a

FlO. 10(b) wE CONTOURS FOR SYMMETRIC PLANE FLOW CHANNEL, Il = 40°

50°

•

10° 20· 30·

8p.DEGREES

-(1

FIG. lO(c) wE COr-.TOURS FOR SYMME1RIC PLANE FLOW CHANNEL, Ii= 50·

IS • 9178 ( Part 10 ) • 1980 60· ,....---...,....--r"""'T...

...,.-,,'It""""--...,....---;---,

so·

I---l---,I---++---\---\-t\---\--\-~---t----t

!

40·

-.SL_....e =0·'0 oJ)

30·

w W IX C) W Q 20·

.

.J:: 10

10·

10° 20° 30° 40° Sp DEGREES -11

FIO.lO(d)

wB

CONTOURS FOR SYMMETRIC PLANE FLOWCIIANNEL, 3= 61.,0

IS: 9178 ( Part III ) • 1918 600

-"

- ~f05

1

~~O4 wB

I

wB _CJ 500 W"lr~12

'"

UJ

"if

w~ "'01 W Q: C> UJ 0

.

s: 300 <0 ep,DEGREES .. rt

FIG. 10(e) wB CONTOURS FOR SYMMETRIC PLANE FLOW CHANNEL,

a

= 70~

17.2.2.2 The peak pressure P_nt can be calculated from 33 [(

~c

-

~)"'.

Pr •

Wod.J

( 2 -- 00 4

sin II ) m (sin II

+

cos0

+

tan ISh )

31

III 9178 ( Part III ) ~ 1988

..

20· 30·

8

c,DEGREES---This equation is based on the overpressure at the transition being distributed over 03 dof the hopper wall. The value ofQc/A is computed from Eq. (4). Typical plots of Pr contours are given in Fig. II and

Fig. 12 for conical channels and symmetric plane flow channels

respectively.

30·~~;;;:-I-T-T-I---'

FIG. 11 (a) Pr CONTOURS FOR CONICAL CRANNELS, 8

=

30°

I

30·

III

_20·

llJ W a: l!)

w

0

-

10·

•

<0

0°

20·

30"

8_c·DEGREES

•

FIG ll(b) P_r CONTOURS FOR CONICAL CHANNELS, 8 = 40°

IS: 9178 ( Part III ) - 1980

/.,0·

1

30"

III lJJ lJJ a: ~ 20" lJJ 0_, s: 10

10·

20° DEGREE S •

FIG. lI(e) P_r CONTOURS FOil, CONICAL CHANNELS, 3 = 50°

60·

..

20· 30· 8_p,OEGREES -30',--~---,-""""-""-"""",-""""---,,,,,,,,--_,,,,,,,,,,,,,-,

Lo~;:';>--]r,O·5:-0-+-::::..."...----1f\----+-~

!oJ !oJ ~ !oJ • 0.10 .c. 10

FIG. 12(a) P,CONTOURS FOR SYMMETRIC PLANE-FLOW CHANNELS, 3 = 30·

ISI 9J18 ( Part

in ).

J980

-10° 20· 30· ep,OEGREES----0358 o

o·

rJl W ~

20"

~-~+--'","--';-'--~---f"-;;:--~-+--~;:t---':~-i

:.3

_c

FIG. 12(b) P_r CONTOURS FOR SYMMETRIC PLANE-FLOW CHANNELS, 0=40°

50' ~--...

:--_:-1'""---.::c-r_,.._...,...--;__--..,

40·

t

30· rJl UI UI 0:: I!) 20· w 0

_.

s: ItO 10" I:q"'~_(~

O·

~

O·

10' 20' JO" 40" 50' 60' 8p, DEGREES

-FIG 12(c) P, CONTOURS FOR SYMMETRIC PLANE-FLOW CHANNELS, 0=50·

IS: 9178 ( Part III) • 1980

12.3 Appendix F may be referred to for a typical procedure for the

application of the above-mentioned method for calculating load

distribution in mass flow bins

13. PROCEDURE FOR CALCULATING THE LOAD

DISTRIBUTION IN FUNNEL FLOW BINS

13.1 In tall funnel flow bins, the flow pressures are larger than the initial

Janssen's pressure. Hence, for design purposes flow pressures have to be used. Fig. 13shows the general bin configuration and some of the useful variables. JANSSEN

o

d r

LOCUS OF

PEAK PRE-SSURE OWEST LOCAl-.,-;-.- --j'ON OF EFFECTIVE TRANSITION

FIG. 13 FUNNEL FLOW BIN PRESSURES

13.'2 Cylinder - The loci of (Pblwd )max, the maximum non-dimensional horizontal wall pressures exerted by a mass of stored materials on the walls of a vertical cylinder are drawn in Fig. 14 for different hid ratios with

~l

as y-axis, These pressures are a function of the height from the top of the cylinder and the product rA. A value of 0'4 is taken for .\.

13.2.1 The equations on the basis of which the figures for different values ofhid may be drawn are given in clauses 13.2.2 to 13.2.4.

NOTE - For a height to diameter ratio less than2. It rs suggested that] an.sen'.

equation may be used, for the flow channel seldom intersect. the cylmder wall.

IS I 9178 ( Part III ) • 1980

•

""-1/

, I ~

j

u

A= 0·02 "0·10 wO·20 "0'30 1 2 3 4 (f'h!wdl",..

-FlO. 14(a) (Pb(wd)mox. FOR CIRCULAR CYLINDERS, hid = 2

I

_a

I

I <\ jJ.'!I:0·02 0 _{: 0'06} d =0·10 =0· '5 =0·20 =0,30 2 1 2 4 (Ph fWd''''

I...

•

FlO. 14(b) (Pblwd)mox. FOR CIRCULAR CYLINDERS, hid= 3

FIG. 14(e) (Ph/wd )m ..,,' FOR CIRCULAR CYLINDERS, hid = 4

....

II> (C

...

~

...

~

...

=

--

•

...

~

4 ).J A= 0 02 ,,0 Of; "0" 0 = a 15 =0·20 :....c~=0,30 41 I Iff I I } r 1 r 7 > (Ph fWd Imax DK I ( Ph!wd )ma". FOR CIRCULAR CYLINDERS, h/d=5 2

2,

-5' rIll / /'

o

'

I I I d

L

FIG. 14(d) d

~

IiX,,0·02 ,,0-06 =0 ·10 "0,15 =0 ·20 =0 ·30 2 3 ~ L 111/,1 (, ' I

o

,

lPt'/w d) rna' 3 1 f ( f ') ) f j r I OK I z 1 d

l2

d

~

w ...

IS, 9178 ( Part III ) • 1980

13.2.2 Figure 15shows the equilibrium at an effective transition.

Assuming that the ratio of horizontal to vertical pressure at an effective transiuon, .\1 is equal10 that ratio m the radial stress field, lower

in the conical channel, the peak pressure at an effective transition

is given by uik [

-e',

Z. ]

PI = " 1 - - I

- e

R

_(ll) ,.,. ~g c!

~c

- - " (1- f

~;P'

~'

p. ,

\

0""

s

.:

/

\

e'

/

/

,

9

\1/

FlO. 15 EQUILIBRIUM AT AN EFFECTIVE TRANSITION

13.2.3 Considering the radial stress field, .\ is to be determined as given in Eq. (12) after establishing

a) a relationship between ITand Ph, assuming that the wall of the

flow channel to be a velocity characteristic, and b) a relationship between ITand P_{r :}

\ = (24 tan 0'

+

1r1.Pr) ( 1 - sin 8 . tan 6' ) (12)

" 16 ( sin 8

+

tan 6' ) ..

Value ofPr and 6' as function of 8 can be determined. By taking .\ = A, PI can be calculated from Eq (11).

IS a9178 ( Part III ) • 1980 .•. (13)

1

r..

(15)

J

wdS

13.2." Frictional stresses accompany Pb and are computed from the

following:

tw = po Pb

These stresses cause vertical force P.., in the walls and are the same

as those worked out for mass flow bins. The vertical force per unit length is calculated from the equation:

r;

(

P..,)

- - = - - 3 - - '

.,. d (wd )max 1f

13.3 Hopper - The pressure field computed for the cylinder is assumed to extend into the hopper. The normal stress Pn and shear stress th on

the hopper walls are computed from the equations:

r,

= Ph

[Ci~2

6

+

cos3

e)

+

2; [l (1

++)

sin €I cosa]:

and

r ...

(14)

t_b = Ph [(

+-

1 ) sill 6cos6

+

~r

po (COS! 6 -

Si~26

) ]

J

The variable r is defined in Fig. 13.

For a flat bottomed bin, the above equations reduce to:

Ph = Pb!;>' -2 rpo Pb tb =

--dA

13.4 Reference may be made to Appendix G for a typical procedure for

the application of the aforernenucned method for calculating load

distribuuon in funnel-flow bins.

APPENDIX

A

( Clause 0.6 )

LIMITATION OF jENIKE'S THEORY

A-I. Experimental evidence reveals overdesign of the cntical outlet

widths 11l mass flow hoppers when the standard Jenike's method is

followed (1)*. This IS due to the fact that Jellike does not account for the possibility that an arch across the outlet may slide along the wall (2) and for the fact that the arch in addition to its own weight will have to sustain the weight of the powder above.

*i'iIumberIIIparanthesis refer to the lueratur e given m 0.8.

IS .9178 ( Part III )

.1980

A-2. Arching just below the transition is frequently reported (3). This does not seem ro cover that.

A-3. Actual stresses close to the transition zone between parallel part of the silo and the hopper section deviate strongly from those predicted by the radial theory (1).

A-4. It does not adequately allow for the impact loading which often occurs on filling and can easily cause arching (3). This is believed to be a major reason for the discontinuity of flow that commonly occurs in bunkers designed based on ]enike's method.

A·5. Jenike's shear cell which is the main tool in finding out the design parameters of the bulk materials used in this theory ( which has been described in Appendix A of the draft code) could be used only in the case of samples with particles top size of only about 1-6 mm and is subjected to the foHowing Jimuations (4).

A.5.1 The limited shear displacement available makes necessary a rather arbitrary and laborious preparation of the sample prior to the shear consolidation.

A·5.2 To obtain design data for hoppers with outlets less than about 1metre across requires knowledge of material characteristics at major principal stresses of less than 70 kgjm2 . At the low normal loads required for this, llftinR or pivoting of the cell lid, assocrated with non-uniform stress distribuuon becomes nouccable.

A.S.3 The tensrle strength of material may be measured in the annular shear celI designed by Walker and Carr (5) instead of a split Jenike-type ceU as recommended by Ashton, Farley and Valentin (6).

A.S.4 Professor Schwedes (7) points out that in the flow factor tester of Jenike, the state of stress cannot be determmed completely and assump-nons regarding the positions of slip planes are necessary to evaluate the test results.

A.G. Other research work has been in progress and the relevant references are included (8).

Conclusions: The theories presented by Walkar (9), Walkers (10.12) and Enstad (I) are meant to cover the limitations of Jemke's theory but they are approximate a fact also pointed out by the authors themselves.

Reference to the work done by Docksen (I3) may be made for the precautions that have to be observed while designing the bIDS.

IS : 911& (

l'art

til ) .

1980

APPENDIX

B

( Clause 0.9 )

RECOMMENDED LITERATURE FOR REFERENCE

1. Enstad 'On the theory of arching in mass flow hoppers'

-Chemical Engineering SCience, 1975, Vol. 30,

pp. 1273-1283.

2.

Molerus,

a

and ' Auslegungsdiagramme

Schoneborn, Chemie-Ing-Techn, Ed.

P. R. S.741/45. fur Schuttgutbunker " 43 (1971), Nr. 13, 3. 4. 6.

7.

8. 9. 10. Wright, H. Walker, D. M. Carr,]. F. and Walker, D.M. Ashton, M. D. Farely, R. & Valenun F.H.H. Schwedes,

J.

Proposed, ACI Standard Walker, D. M Walters,

J.

K

• An evaluation of the ]enike Bunker design

Method' Transactions of ASME, Journal of Engg. for Industry, Feb. 1973, pp. 4B-54.

• A basis for unker design', Powder Technology,

1 (1967), pp. 228-236.

I An annular shear celt for granular materials',

Powder Technology, I (19b7/6B), pp. 369-373.

, An improved apparatus for measuring the tensile strength of powders'; ]ournal of Scienufic

Instru-ment41 ( 1961 ), pp 763-755.

, Measuiement of powder properties for Hopper Design', Trans. of ASME, Journal of Ep.gg. for

industry, Feb. 1~73, pp. 55·59

'Commentary on Recommended Practice for

Design and Construction of Concrete Bins,

Silos and Bunkers for Storing Granular Materials-ACI Journal, Title No. 72-38, pp. 550, Oct. IY75.

, An approximate theory for pressures and arching in hoppers' Chemical Engineering Science, 1966, 21, pg. 975.

'A theoretical analysis of stresses in silos with vertical walls', Chemical Engineering Science, Bd. 2B ( 1973), NT I, pp. 13-21.

18J91'78 ( Part DI ) .1980

11. Walters, J. K. • A theoretical analysis of stresses in axiallysym-metric hoppers and bunkers; Chemical Engineering Science, Bd. 28 ( 1973 ) Nr. 3, pp. 779/89.

12. Walters,

J.

K. • A note on the stress distribution at great depth in

andNeederman, silo', Chemical Engineering Science, Vol. 28

R. M. ( 1973) Nr. 5, pp. 1907/8.

13. Doeksen, G. • Precautions in order to attain design capabilities or Mass-flow system', Journal of Engineering for

Industry, Transactions of ASME, Feb. 1973;

pp.93-96.

Bunker Design-Transactions of ASME Journal of

Engmeering for Industries November 1977 by

Americal Society or Mechanical Engineers ( Pages 809 to 827 )

Part I Bunker outlet design and initial measure-ment of wall pressures by PC Richards Part II Wall pressure in mass flow

Part III Wall pressure and flow patterns in funnel flow

Part IV Recommendations

APPENDIX

C

( Clause

7.3.1 )

PROCEDURE FOR TESTING OF FLOW PROPERTIES OF BULK SOLIDS

Col. The tests for determination of flow properties are performed on the flow factor tester which consists or a shear cell with cover and arrange-ment for applying normal and shearing load on the sample packed in the shear cell. The normal load is applied through the hanger and weights and the shearing load is applied gradually by an advancing screw stem operated by electric motor, causing a stem displacement of 0'9 mm/min, The shear load is measured by a proving ring placed between the screw stem and shear cell

[see

Fig. C-I (a)].

The inside diameter or shear cell is 63 mm, and the height is 38 mm, which yields the shear cell area,

A. = 0 003 12m2

15 I 9178

I

Part III ) • 1910 NORMAL LOAD Pl ANE OF SHEAR OF AREA As

SHEA~lfrG=.;;;::;:::;=-n-'f~-~4+-L_

...4I.. LOAD RING BASE FRAME /

(a) Shear Cell MAJOR CDNSOLIDAT-I V ING FORCE , MOULD RING BASE FRAME

(b) Preconsolidation of a Shear Cell

FILLER FRAME SAMPLE OF WALL MATERIAL NORMAL LOAD /COVER ~:::;==l---l+l---L~ RING -, L STEM SHEARING

LOADS -

~~H

u::: J4l -\-_--'-_----.J.u---,

(c) Measurement of the Kinematic Angle of Friction Between Bulk Solid and Wall Material

FIG. C.l DETERMINATION OF THE FLOW PROPERTIES USING A FLOW- FACTOR TESTER

III9178 ( Part DI ) • 1t80

C-l.l Shear cell which is the main tool in finding out the design para-meters of the bulk materials used in this theory could be used only in the case of samples with particle top size of I 6 mm,

C-2. Bulk density of the aerated bulk material is determined without any packing. Thereafter, the bulk densities of packed bulk solids shall be recorded as further tests proceed under various consolidating loads. Typical curves giving bulk density at different consolidating loads are given in Fig. C-2 for gypsum, trlple superphosphate and pulverised coal. Similar curves should be drawn for the material to be stored.

C-3. The bulk solid to be tested is placed in the cell set-up shown in

FIg. Col (b) for preconsolidation One layer after another is packed up to the top of the mould and excess material is scraped off. The twisting top is placed over the packed solid. A normal load is applied on the top with the help of hanger and weights. A number of oscillating twists are applied to the top by means of a special wrench. This completes the preconsolidation.

C·4. The load applied for preconsolidation is removed and the twisting top and the mould is removed with precaution SI) that the base and ring

of the shear cell are not disturbed. The excess material over the ring is scraped ofT lever with the top of ring. The test cover is placed over the material and the consolidation load is applied to the cover. The screw stem ( shearing device) is advanced against the bracket so that the shear of the laver of material starts. The shear load attains a steady maximum

value for a certain consolidation normal load. This completes the

consolidation and shear yielding of the bulk solid. The values of normal loads and shear load are recorded.

C-5. The shearing of the material is done at various normal loads under the same consolidation. This is done by consolidating the test sample following the same procedure as under C-'\- shearing until 95 percent of the maximum shearing force as obtained under C-4 is reached. At this point, the normal consolidation load is replaced by smaller normal loads for further shearing of the sample. The maximum steady shear force values thus obtained shall be recorded.

C-6. Yield locus shall be plotted by locating various normal loads vs shear load values for a particular consolidation load. A number of suitable consolidation loads selected shall yield a family of yield loci.

Mohr's circles, when drawn, yield major consolidating force V and

unconfined yield force, F. These plots shall also give kinematic angle of internal friction and effective angle of friction of the bulk solid.

C-7. Plots of Wall Yield Locus - The shear cell shall be arranged as shown in Fig. Col (c). The sample of wall material is placed as the base,

representing the actual material and surface condition of the bin

IS , 9178 ( Part IU ) • 1980

or hopper wall. The bulk material is placed inside the ring up to the top. The cover is placed and normal load IS applied on the cover. The

maxi-mum steady shearing forces are recorded for varrous normal loads yielding

the points on wall yield locus (WrL). A typical WrL for coal on

structural steel is plotted in Fig C-3.

C-.8. The charts and curves given in Fig. C-2 to C-IS are based on the

tests explained in this appendix and they apply for typical bulk solids. They are given for information only. Such data should be worked out for each of the stored materials for which the Inns are to be designed.

1500 1400 1300 1200 , IlOO

"'e

Or1000

""

~. >' 900

....

Ul z BOO \l.l o 700 ~ ---'

ffi

600 500 IA

j

JJ

l.l.

10 ROUND SIZEl-200MESH1DRh G'iPSUMIG· I_ e

1/

TSPIPOWDER.$IZE 1-35MESHIMOI5TURE 3

V~

e

\7

~-j I

I

i

COAL I PULVERISED SIZE 1-20uMt:SH}. DRY I , 1 ---~ I

/

°101 400

o

20 40 60 80 100 120 140 CONSOLIDATING LOAD, V,kgl _ [60

NOTE - To convert consolidating load to consolldanng pressure (kgr/cm')

divide by 3t-20.

FIG. C-2 CONSOLIDATING LOAD VERSUS BULK DENSITY CURVES FOR GYPSUM, TRIPLE SUPERPHOSPHATE AND PVLVERISED COAL