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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]
“!ान $ एक न' भारत का +नम-ण”
Satyanarayan Gangaram Pitroda
“Invent a New India Using Knowledge”
“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता ह”
है”
ह
Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”
IS : 9178 (Part III ) -1980
Reaffirmed 2010
Indian Standard
CRITERIA FOR DESIGN OF STEEL BINS FOR
STORAGE OF BULK MATERIALS
PART 111 BINS DESIGNED FOR MASS FLOW
AND FUNNEL FLOW
© Copyright 1982
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
MANAK
BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
N E W DELHI 110002
January 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
Repr;se"llng
Mimstry of Railways
DIRECTOI: Sl'ANIJARDS ( CIVIT, )
A[""bers
R. i\f AGAR'VAL
DIt Puuv KurSUN ~
SUIH A K IlAXLltJEI'.
Insriturion of Engineer' ( Inrha }, Calcutta
SnRI
(
Alternal. )
Metallurgic d
and Engrncerrng
l India) Ltel, Ranchi
Consultants
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 01 W"'tBengal
DR P D,YA"A I '1A"
Indr.m Institute of Technology, Kanpur
i:>lilti D S
1\1. N. Dastur & Co PH Ltd, Calcutta
J)""
:::'1I1<lS
Dnu i rou l
D,.'un
R.
KIILhA,,,t
(.Ilfemate)
l",A ~~~l «"liN)
])JLtI'
l\l1~~IO"'f ) \
Ccntr.rl Elccn rcitj Authority, New Deihl
1"" l11"'5-
Allemllte)
Sunr Z II" 'N
Cenn al Water Comrmss ion, New Ddln
Suut V. NAr:AL'" '" (.W,mal')
JOI:>l1' DIRJ.~j'O" S T \ " "A u JI 8
Muustry of Railways
(B & S)
1\88'81'\'1" Dllnl run (
sn ( Alternate )
B & S)-
jvr" r DIHLLrllI' (D.,,,,",,")
Natrona l 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 z 9118 ( Part DI) • 1980
( COflhlllUd ftl1/1l
"",e I )
Representlll,
Members
Jessop & Co Ltd, Calcutta
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 Ind ia,
Calcutta
Bmny Ltd, Madras
SHin N RADHAKRISHNAN
SHIn P. ApPA RAO ( Alternate)
SIun N. V. R ....tAN
Structural Engineermg Research Centre, Madras
Dn T. V. S. R. ApPA RAO ( Alternate)
SHIll C. S,
RAO
Engmeer-in-Ohrefs Branch, Ministry ~r DeCellce
REPIlESENTATlVE
Tata Consultrng Engmeers, New Deihl
REPRESENTATIVE
Hindustan
Steel Works Construction Ltd,
Calcutta
Slun A B. RIBEIRO
Rail Indian Technical and Economics Services,
New Deihl
SHIll S K BUANDT ( AlltTnate)
SHill P SENGUP1'A
Stewarts & Lloyds of India Ltd, Calcutta
SHIll M. M. GnOSH (A.lternate)
SH1U M. 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 Heavy Electrrcals Ltd, "I'iruchirapalh
~HJlJ H. 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 R w
Director General, lSI ( &-offim Membn)
Director ( Struc & Met)
Secrefarres
S1InI S. S SETHI
Deputy Director ( Struc & Met l, lSI
SnRI V G HIREMATH
ASSIStant Drr ecror ( Struc & Met ), lSI
s
Subcommittee for Use of Steel in Bulk Storage
Structures, 5MBDC 7 : 4
COfll.Jener
SURI N K. Roy
The Fertilizer (Planning and Development}
India Ltd, Smdn
!>l,mN's
SHRI S. K. CHATTERJEE
SHI<I S. GOJ'ALAE:RISHNAN
SHRI S. SELVARAJ (Alter,..le
SHill GUI'CHAIUN SINGH
Sunr K VEEIlARAOIlA \'Al'UARY
l
Cement Corporation of India Ltd, New Delhi
Structural Engmeerrng Research Centre, Madtas
Food Corporation of India, New Delhi
Bharat Heavy Electrrcals Ltd, Tiruchlrapalli
2
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 ) the existing equation:
H [
~- (-~
r.+
( 2 - O"hin 8)lD X {sin 6
(SMBDC 7:
Substitute the following f,
P, .
~.d ]
cos I} • 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 III the analysis and
design of steel bins for storing various materrals of different 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
3
IS I 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 so lvcd 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 is explamed. 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 lunit auons 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
Design crrreria,
Part III Bins designed for mass flow and funnel flow.
rr
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
4
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 of bulk 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 horizon tal or near horizonta I.
Field in which the major pressure is
·Rules for rounding off numerical value. (w.ued).
5
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.
3. NOTATIONS
3.1 For the purpose of this standard the notations as given below shall
apply:
bo
10
h
m
r
w
A
B
F
R
V
S
]
=
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
= Bulk density of the solid, kg/m 3
= Area of horizontal section of a cylinder, m S
= 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/m l
= Frictional stress on the hopper wall, kgf/m l
6
IS I 9178 (Part 111 ) • 1980
As
Rj
if, ill
v
r
Shear cell area (cross-sectional area of the test
sample), m 2
= Radius of curvature at transition
V
=
= Flow factor of a channel (hopper)
=
r
= Major consolidating force, kgf
= Major force in a dome or a pipe ( bulk material under
flow), kgf
= Flow function of bulk material
=
=
=
=
=
=
=
=
=
=
=
=
En
wn
=
=
=
=
=
=
H (O)
=
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/m 2
Initial pressure on a hopper wall at the vertex, kgfjm l
Peak pressure at the transition, kgf/m l
Initial pressure on a hopper wall at the transition,
kgf/m 2
Radial pressure on a hopper wall at the transition,
kgf/m 2
Peak pressure at an effective transition, kgf(m 2
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. kgfjm 2
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 ()
7
IS I 9178 (Part 111) - 1980
= 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, kgfJm 2 •
rP
=
G (1))
ii
ii'
a
4. DESIGN CONSIDERATIONS
4.1 In the design of bins for bulk storage, the two important considerations 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 Sl ze of the bID. These are dealt wlth'in detail In Section 2
and Section 3 of the code for mass flow and funneL /low respectively.
4.1.'2 Load distrrbution characteristics give 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 incorporated 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
flow IS a gravlt)' flow without any flow promoting device.
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
9
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.
-r
j
I- - - t--d
,
-
I-~
Z,
l
I
i
V'''\
8c
1
10
(bl Pyramidal
(a) Conical
(c) Chisel
d
~-
,1
T
IZ,
_J
Sp
8e
8,
(d) Transrtron
FIG.
I~
b.
1
10
~
(e) Wedge
HOPPER SHAPES FOR
MAss
FLOW BINS
6.1.1 Slope of Hopper - For a good design, the hopper slope angle shall
be so selected ( see 7.4) 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.
10
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 promoting 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 It distribution 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 aand 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 ).
11
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 I n 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 transition zone ( transition from vertical portion of storage equipment to the
hopper) with a radius of curvature Rt ;> 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 (see 7.... 1) shall now be plotted
against flow function FF of the bulk solid FF is a plot of V and F with
Vas abscissa and F a~ ordrnate, whereas if is the plot of Vand V with 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 xiz e ] 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~
-
When
obtained.
r so determined
H (0)
is located on .fJline, V at the outlet is also
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 factor jf shall be selected.
Based on this modified.o; the intersection point ( V, V ) is noted.
7.5.5 If there is an intersection of ffwith FF, it shows that the bin of a
particular slope an~ outlet size can be desisned for mass flow, The intere
section point ( V, r ) is noted.
IS : 9178 ( Part III ) • 1980
7.5.6 After plotting If over FFo and FF, if It I~ found that lhe,ffline
lies between FF0 and FF t , that 1~, JrIS above FF 0 hut below FF t • the stored
material shows a tendency of consolidation wit h 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 di rnensrons, ho shall be calculated from the
following formula'
bo=_~,-H(Ot
.r, w
7.6 Check for Estimated Design Data
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.
7.6.1 Corresponding
\0
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 offf and 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 correspending 11 ( hopper slope) shall be obtamed from Fig C-13 to C-15 of
Appendix C. H ( ll) shall be obtained from Fig C-12 of Appendix C.
V is obtained 111 the manner shown under 7.5.3 to 7.5.6. The outlet size
bo 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.
13
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 bo 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 opening 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>6b o 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 ( see Fig. 2). It is 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.
14
IS: 9178 ( Part III ) • 1980
DRAW MOSTL¥
COARSE
2
FIG
\
PLUG FLOW
I
\
I
\
\
I
DRAW SAME
AS CHARGE
I
\
I
I
I
I
I
\
"
/
la) FLAT BOTTOM
lblCQNICAL
FIG. 3
PLUG FLOW BINS
15
(e 1PYRAMIDAL
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
a certain outlet size. For uninterrupted flow, the outlet shall be
designed for an optimum lump size.
10
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.
16
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 (see Appendix 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 corresponding to the average 1\ and the if 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 91l 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 of V and F with 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 of Appendix C.
10.4.3 If the outlet shape selected for design is square or circular, the
major dimension of the outlet will represent 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 If the 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
VH
(6)
As. w
10.4.5 The dimension of the rectangular outlet is given by bo X 10 ,
The dimension 10 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. It shall 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 during the initial stage of charge into a bin and during 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 .. peaked II pressure field.
18
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[
---;-
l-e
19
-~
;<1]
(I)
IS r 9178 (Part 111).1980
and the hydraulic radius R
d
2(I+m)
= --=---~--,----c­
.oo
(2)
where'
m = I for circular bin,
= 0 for long rectangular or square cylinder. and
A = 0'4.
I n the cylinder, the frictional stress lw is related to normal pressure
Ph by
•• , (3)
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
-:4
=
wR [
---;T
Values of
=fi!!"J
I - e
~~1.- are
... (4)
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
OJ
w.d
= 2( tan 6-+-t-an~8~h""')
,.. (5)
The initial pressure at the transition. PnU, is given by
(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
... (7)
JS I 9J78 ( Part III ) ·1••
d
\
\I/
\
\
I
\
\ I
"I
FIG. 4
a
INITIAL PRESSURES IN A CONICAL HOPPER
21
II t 9171 (Part UI)· 1910
o
~----------~-.-,
8
I
I
10
12
I'
g
coo
.... N -
oW
"0"
'8
18
20
o
•
8
20
12
wR
~----
-/L
FIG.
5
FUNCTION
Qcl A
-"~-
wR
-
>. (hIR)
l-e
-----;----
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 nODdimensional form ( Phlwd )max in 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 ) - • •
e
I
,
~
,...--"''': 0 '0
. - - _ : 0 15
-0·20
'11\
'1\\.
1'
j
-o
~o
lit,
111 1
'11\
I
I
, of
JANSSEN
r
It""'"
J
.1
(Phlwd lmal<'
" : '0
,4-025
= 0-]7'S
'0· 50
I' . ,-
I
FIG.6(a)
SlRAIN ENER:a.,.
_ _ _ =0 7$
:;: I
o
2
IPhl .... ) m•• - - _
FOR CIRCULAR CYLINDERS,
hId = 3
0F::""------,
STQAI~
ENUGl
}.lA,o 10
.0 15
: 0 20
: 0 )0
JANSSE~
)."-"0
"
d
r
\
)1,0 25
,0 315
·0·50
'0·15
_----'
)
............................
o
----IP"lwd)
FrG.
6(b) (Phlwd )wu.
I'r\U
FOR CIRCULAR CYLINDERS,
hId = 5
The vertical force Pw caused by the frictional stress tw and Pressure
Ph is computed from
[
Pw
p.., ]
red = (" W.dB 1 mal<
wdS
.. , (8)
X -;-
Ty pical results in non-dimensional form ( Pdw_)
W
ted in Fig. 7 for circular cylinders,
23
a
are represenWBJ;
N
A.
\
1
(N(IlG~
2
,
3
(I' w fWd 3) rn . . ____
"
~=o,o
~=OI5
/J.A = Q·30
BASED aN SIRA'N
{P"/wdS)ma,,. FOR CIRCULAR
CYLINDERS h/d= 3
o
),
1.
FlO. 7 (a)
,
,
z
ol
•
'
i
\
FIG. 7
I
(b)
~
2
CYLINDERS
,
'
,
l
I
•
CIRCULAR
3
,
ON STRAIN ENERGV
(F'tN/Wd), mill(
1
6AS,ED
(Pwfwd8 )ma". FOR
hjd=5
o
5'
•
1'
, I
a(
i
le
-•
-
.-...~
;;
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
FlO.
8
Po
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.
25
JI.9178 ( Part III ) .1980
I
30·,...--~....---....---....,...--....,..--......,..----.
0
01••• ,.,
~ 20k==~~--J....L
IJJ
0::
eo
•
s:~ 10
<0
10·
20·
30·
et
FIG.
'1( a)
f1
wE
•
• DEGREES - - - -
CONTOURS FOR CONICAL CHANNELS,
B= 30·
1,0'
t
30·
lfl
W
w
n::
l:l 20·
w
0
s:
wB
.
s:
2· 0
<0
10·
20·
30·
•
at. DEGREES ---0FlO. 9(b)
a
wB
CONTOURS FOR CONICAL CHANNELS,
3 = 40·
IS I 91'18 ( PBl"t til ) • 1980
•
40 Plr--.,.--.....,..---,.-----,---..,
r 30 ~~~~~t--__+_--t--_1
If)
w
\oj
a:
•
20 ~-"x-
l:3
o
L.
10
10•
20·
30·
•
ee.DEGREES----
:B
FIG.9(c)
CONTOURS FOR ComCAL
CHANNEL', 3 = 500
40·
I
)0•
lfI
uJ
uJ
a:
~
w
20
0
0
,
.J::
<0
~~200
10·
L=3·0
wB
o'
FIG, 9(d)
a·
10'
40·
20·
30·
Se,DEGREES - - -
..
(J
wB
CONTOURS FOR CONICAL CHANNE.Ls, 11
27
50·
= 60·
IS I 9178 ( Part III ) • 1!18O
so' ,----,------,-.----r---"""T'"--.....,
I
"o·
30·
III
IIJ
IIJ
Q:
C)
w
20'
0
.c•
co
10'
10·
&=20
!s-'>] 0
!-'IO.
r1
9(e) - wB-
20·
30·
-
50'
Sc.OEGREE5 - - - -
CONTOUR~ FOR CONICAL CHANNELS,
a=
70°
30°nl"'~:-r-,,::;:;:>,........,r-~T"'""'I---n--"""T--"""
t 0c=~4~r--=f:~~~H
,
1/)20
UJ
~
h1
"-
,....._~
1-'::""'-1
'0 ),39
<,
0
o.lo'k-=~~~--+---=:::::t:=-~j...L~-l
<,
s:
"" loS'-
IC
min VAlU E:
SOO
..
t!
FlO.
10(a) wB
CONTOURS FOR SYMMETRIC PLANE FLOW CHANNELS. ~
28
= 30
0
Is I 9178 ( t-art 111 ) • Ill"
1/1
~ 20° po~--+-.=........,
n::
a
o
-
50°
60·
8 p.DEGREES - - - - FlO.
a
10(b) wE
CONTOURS FOR SYMMETRIC PLANE FLOW CHANNEL,
10°
20·
30·
Il = 40°
50°
•
8 p.DEGREES - - - - FIG.
lO(c)
(1
wE
COr-.TOURS FOR SYMME1RIC PLANE FLOW CHANNEL,
29
Ii = 50·
IS • 9178 ( Part 10 ) • 1980
60· ,....---...,....--r"""'T............,.-,,'It""""--...,....---;-----,
so·
I-----l-----,I---++------\---\-t\---\--\-~---t----t
40·
!
oJ)
w
-.SL
....e =0·'0
30·
W
IX
C)
W
Q
. 20·
.J::
10
10·
10°
20°
30°
Sp DEGREES
FIO.lO(d)
11
wB
40°
-
CONTOURS FOR SYMMETRIC PLANE FLOWCIIANNEL,
30
3 = 61.,0
IS: 9178 ( Part III ) • 1918
0
60
-"wB I
-
~~O4
wB
~f05
CJ
W"lr~12
0
50
1
'"
UJ
W
Q:
w~ "'01
"if
C>
.
UJ
0
s:
<0
0
30
ep,DEGREES
FIG.
rt
10(e) wB
..
CONTOURS FOR SYMMETRIC PLANE FLOW CHANNEL,
a=
70~
17.2.2.2 The peak pressure P nt can be calculated from
~)"'. P r • Wod.J
sin II ) m ( sin II + cos 0 + tan ISh )
33 [(
( 2 -- 0
04
~c
-
31
••• (10)
III 9178 ( Part III ) ~ 1988
This equation is based on the overpressure at the transition being
distributed over 03 d of the hopper wall. The value of Qc/A is computed
from Eq. (4). Typical plots of P r contours are given in Fig. II and
Fig. 12 for conical channels and symmetric plane flow channels
respectively.
30·~~;;;:-I-T-T-I---'
20·
30·
..
8c,DEGREES---
FIG. 11 ( a) Pr
I
III
llJ
W
CONTOURS FOR CONICAL CRANNELS,
8
=
30°
30·
20·
a:
l!)
w
•- 10·
0
<0
0°
30"
20·
8 c·DEGREES
FIG ll(b)
Pr
•
CONTOURS FOR CONICAL CHANNELS,
32
8
=
40°
IS: 9178 ( Part III ) - 1980
/.,0·
1 30"
III
lJJ
lJJ
a:
~
lJJ
0
,
20"
s:
10
10·
20°
DEGREE S
FIG. lI(e)
Pr
•
CONTOURS FOil, CONICAL CHANNELS,
3
=
50°
30',--~---,-""""-""-"""",-""""------,,,,,,,,--_,,,,,,,,,,,,,-,
Lo~;:';>--]r,O·5:-0-+-: : . . . ". .- - 1f\- - +-~
!oJ
!oJ
~ •
0.10
!oJ
.c.
10
20·
30·
..
60·
8 p,OEGREES - - - FIG.
12(a) P,
CONTOURS FOR SYMMETRIC PLANE-FLOW CHANNELS,
33
3 = 30·
IS I 9J18 ( Part
rJl
W
~
in ). J980
o
20"
:.3c
0358
~-~+--'","--';-'--~---f"-;;:--~-+--~;:t-----':~-i
o·
10°
20·
30·
-
ep,OEGREES---FIG.
12(b)
Pr
CONTOURS FOR SYMMETRIC PLANE-FLOW CHANNELS,
0=40°
50' ~--........:--_:-1'""---.::c-r_,.._........,........--;__--..,
40·
t
30·
rJl
UI
UI
0::
I!)
w 20·
0
.
s:
ItO
10"
I:q"'~
(~
~
O·
O·
FIG
12(c)
P,
10'
JO"
20'
8 p, DEGREES
40"
-
50'
CONTOURS FOR SYMMETRIC PLANE-FLOW CHANNELS,
34
60'
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. 13 shows the general bin configuration and some of the useful
variables.
LOCUS OF
PEAK PRE-
SSURE
OWEST LOCAl-
.,-;-.-
--j'ON OF
EFFECTIVE
TRANSITION
d
JANSSEN
r
FIG. 13
o
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 of hid may be drawn are given in clauses 13.2.2 to 13.2.4.
NOTE - For a height to diameter ratio less than 2. It rs suggested that] an.sen'.
equation may be used, for the flow channel seldom intersect. the cylmder wall.
35
IS I 9178 ( Part III ) • 1980
•
u A= 0·02
, I
"0·10
wO·20
"0'30
~
j
""-1/
1
2
3
(f'h!wdl",..
FlO.
14(a) (Pb(wd )mox.
I
4
-
FOR CIRCULAR CYLINDERS,
hid = 2
a
I
I
<\
jJ.'!I:0·02
: 0'06
=0·10
=0· '5
=0·20
=0,30
0
d
2
1 2 4
(Ph fWd''''
FlO.
14(b)
( Pblwd )mox.
I...
FOR CIRCULAR CYLINDERS,
)6
•
hid = 3
......
w
FIG.
14(e)
~
d
(
)
CYLINDERS,
hid = 4
FOR CIRCULAR
lPt'/w d) rna'
'
I' )
3
rf
2
,
j
"0,15
=0 ·20
=0 ·30
IiX,,0·02
,,0-06
=0 ·10
111/,1 ( ,
ff
(Ph/wd )m..,,'
o
~ L
31
l2
d
z1
OK
I
I
FIG. 14(d)
~
d
2
'
/
/'
rI 1f f
r
I
CYLINDERS,
7
I
A=
I
>
I
h/d=5
FOR CIRCULAR
(Ph fWd Imax
rIll
}I
).J
0 02
,,0 Of;
"0" 0
= a 15
=0·20
:....c~=0,30
( Ph!wd )ma".
o
-5'
41
L
d
2,
DK
I
4
I
~
-=
...•-
...~
~
.....
(C
...
II>
....
IS, 9178 ( Part III ) • 1980
13.2.2 Figure 15 shows the equilibrium at an effective transition.
Assuming that the ratio of horizontal to vertical pressure at an
effective transiuon, .\1 is equal 10 that ratio m the radial stress field, lower
in the conical channel, the peak pressure at an effective transition
is given by
uik [ I -e
PI = "1--
-e', Z. ]
R
,.,. ~g
(ll)
c!
~c
--"
(1-
,
\
s
0""
.:
\
e'
9
FlO.
15
~'
f
\1/
,/
~;P'
p.
/
/
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 IT and Ph, assuming that the wall of the
flow channel to be a velocity characteristic, and
b) a relationship between
\ =
"
.\ =
(24 tan 0'
IT
and Pr :
+ 1r1.Pr) ( 1 - sin 8 .
+ tan 6' )
16 ( sin 8
tan 6' )
(12)
..
Value of P r and 6' as function of 8 can be determined. By taking
A, PI can be calculated from Eq (11).
38
IS a 9178 ( Part III ) • 1980
13.2." Frictional stresses accompany P b 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;
-- =
.,. d
( P..,)
wd S
--3--'
(wd )max
.•. (13)
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
and
tb =
Ph [(
+-
+ cos
3
e) + 2;
1 ) sill 6 cos 6
[l
+ ~r
(1
++) sin €I cosa]:
r ...
po (COS! 6 -
Si~26
)]
(14)
J
The variable r is defined in Fig. 13.
For a flat bottomed bin, the above equations reduce to:
Ph
=
tb =
Pb!;>'
-2 rpo P b
1
r.. (15)
--dA
J
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'iIumber
III
paranthesis refer to the lueratur e given m 0.8.
39
IS .9178 ( Part III ) .1980
A-2. Arching just below the transition is frequently reported (3).
does not seem ro cover that.
This
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
1 metre across requires knowledge of material characteristics at major
principal stresses of less than 70 kgjm 2 . 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 assumpnons 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.
40
IS : 911& ( l'art til ) . 1980
APPENDIX
B
( Clause 0.9 )
RECOMMENDED LITERATURE FOR REFERENCE
1.
Enstad
2.
Molerus, a and ' Auslegungsdiagramme fur Schuttgutbunker "
Chemie-Ing-Techn, Ed. 43 (1971), Nr. 13,
Schoneborn,
P. R.
S.741/45.
3.
Wright, H.
• An evaluation of the ]enike Bunker design
Method' Transactions of ASME, Journal of Engg.
for Industry, Feb. 1973, pp. 4B-54.
4.
Walker, D. M.
• A basis for unker design', Powder Technology,
1 ( 1967), pp. 228-236.
Carr,]. F.
and Walker,
D.M.
I An
annular shear celt for granular materials',
Powder Technology, I (19b7/6B), pp. 369-373.
6.
Ashton, M. D.
Farely, R. &
Valenun
F.H.H.
, An improved apparatus for measuring the tensile
strength of powders'; ]ournal of Scienufic Instrument41 ( 1961 ), pp 763-755.
7.
Schwedes, J.
, Measui ement of powder properties for Hopper
8.
Proposed, ACI
Standard
'Commentary on Recommended Practice for
Design and Construction of Concrete Bins,
Silos and Bunkers for Storing Granular MaterialsACI Journal, Title No. 72-38, pp. 550, Oct. IY75.
9.
Walker, D. M
, An approximate theory for pressures and arching
in hoppers' Chemical Engineering Science, 1966,
21, pg. 975.
10.
'On the theory of arching in mass flow hoppers' Chemical Engineering SCience, 1975, Vol. 30,
pp. 1273-1283.
Design', Trans. of ASME, Journal of Ep.gg. for
industry, Feb. 1~73, pp. 55·59
Walters,
J. K
'A theoretical analysis of stresses in silos with
vertical walls', Chemical Engineering Science,
Bd. 2B ( 1973), NT I, pp. 13-21.
41
18 J 91'78 ( Part DI ) .1980
11.
Walters, J. K.
12.
Walters, J. K.
• A note on the stress distribution at great depth in
and Neederman, silo', Chemical Engineering Science, Vol. 28
R. M.
( 1973) Nr. 5, pp. 1907/8.
13.
Doeksen, G.
• A theoretical analysis of stresses in axiallysymmetric hoppers and bunkers; Chemical Engineering
Science, Bd. 28 ( 1973 ) Nr. 3, pp. 779/89.
• 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 measurement 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 arrangement 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 12 m 2
42
15 I 9178
I Part III ) • 1910
NORMAL LOAD
Pl ANE OF SHEAR
OF AREA As
RING
SHEA~lfrG=.;;;::;:::;=-n- 'f~-~4+-L_..........4I..
BASE
LOAD
FRAME
/
(a)
Shear Cell
MAJOR
CDNSOLIDAT-I V
ING FORCE ,
MOULD
RING
BASE
FRAME
(b)
Preconsolidation of a Shear Cell
NORMAL
LOAD
/COVER
~:::;==l---l+l-----L~
SHEARING
LOAD
S-
~~H J4l
u:::
-\-_--'-_----.J.u-----,
RING
SAMPLE OF
WALL MATERIAL
FILLER
L STEM
FRAME
-,
(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
43
III 9178 ( Part DI ) • 1t80
C-l.l Shear cell which is the main tool in finding out the design parameters 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
44
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 maximum 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
IA
1400
1300
1200
j
JJ
l.l.
10
ROUND SIZEl-200MESH1DRh
G'iPSUMIG·
I_
e
1/
, IlOO
"'e
Or 1000
""
~.
....>'
900
Ul
z BOO
\l.l
o
~
\7
V~
~-j
I
i
700
---'
ffi
TSPIPOWDER.$IZE 1-35MESHIMOI5TURE 3°101
e
I
,
COAL I PULVERISED SIZE 1-20uMt:SH}. DRY I
1
600 ---
/
500
400
o
~
I
20
40
60
80
100
CONSOLIDATING LOAD, V, kgl
120
140
[60
_
NOTE - To convert consolidating load to consolldanng pressure (kgr/cm')
divide by 3 t -20.
FIG. C-2
CONSOLIDATING LOAD VERSUS BULK DENSITY CURVES FOR
GYPSUM, TRIPLE SUPERPHOSPHATE AND PVLVERISED COAL
45
1819178 ( Part
II[ )
·1980
f0-
--
l.-L~~~
-
\.o9:l~
~V
""
.
LATHE MA(,HINED•
MEDIUM FINISH
COAL SIZE. -200 MESH
CO,NDI;'O~'
lOR; I
I
7
3
4
S
6
NORMAL lOAD, Vn.(J... t) - - -
8
t>
o
-
,.~
sn EL SAMPLE
V
2
I
I
9
r10
- Similar charts for various other materials should be drawn.
Flo. C-3
so
'l!~~
",.,-
~ .....
I
V
./
f-- fo- f---
NOT~
oL
...
WALL YIELD
V~RY
Locus ( COAL
ON STRUCTURAL STEEL)
.
I
VkRY
F
POOR
l
VE R V
POOR
F
0
L
W
>- 35
....
:;
iii 30
~
w
I
P
'" 25
~
~
P
a
R
PASSABLE
20
~
15
l'
10
0
F
l
W
L
0
0
W
I
.
r- GOOD
FAIR
EXCElLENT
FlOW
0
f
I
,
0,
2S'
F
F
L
0
W
)0'
l
o
W
)S·
W
'0'
'5"
50'
ss"
60'
65"
10'
15'
80'
ANGLE OF REPOSE. DEGREES ~---
FlO. G-4 ANGLE OF REPOSE VERSUS COMPRESSIBILITY
( PACKED BULK DENSITY - AERATED BULK DENSITY)
PACKED BULK DENSITY
46
85" 9
IS I 9178 (Part
..
obd
:l<>/
t
lY'
Q
i/
...-
E
--
-
-
en
-" -
~..
'v~;
~"
h_
~
~'=' ~o/
!>cO .'L/
,~:2l ~~~v
,,~ ;' ~ -tft'
If' (j- 1 /
I ---r/'
/:/
-,-1---
,,~"D
-----1---_ "D\S~-
f/l
.J
z
..,~
0
0
0
/
~
\)y
"?
m) .1910
/
o
vtz
17
---
f~
e--
7
tFF -DRY SAND
Po
CONSOLIDATING FORCE, V, k g t -
FIG. C-5
SOLID FLoW FUNCTION FF AND HOPPER FLOW FACTORfj
,
,
,
w
...
V
llI:
o
...
'"w<
:r
III
/
./
V
01'E.51 VE
_ o~ C
.,~
1
e.~V ~ "/ ~
\'II'."'~
~1.0'll",\" V
.I'
cO
e.~e.j~
...;:!.'i<'.....
,//~
/
~V
NORMAL LOAD, Vn---
FIG. C-6
TYPICAL YIELD LOCI FOR FOUR CLASSES OF POWDER
47
00
.j>.
o
",If)
....
....
O·
HOPPER
•
)
•)
20";
r-,
<,
-
20
- .0
.
)0
4.0·
fcUNNfL FlJ)W
SLOPE ANGLE, 8. DEGREES
_.
10
.
~
.,.
, ~,
:J.
MAS S Fl 0 W " " - .
.~ 1"-..
30)
40•
I
s I•
FlO. C-7
RANGES OF MASS FLOW AND
FUNNEL FLOW IN CONCCA.l.. HOPPERS
Z<II
00
..
~
...........
"0"
""... ;
~
.. 0
QIo-
ZU
o
",lU
",Z
;JoO
.. .
l:j.&
zo
'"
<110
",,,,
0'"
_II:
)0
t,6
•
•
I
I
II
)0
r-,
r-
10·
,
"'",
FLOW
-,
r-,
I'-
"
200
'!'-...
~
I-
l--
•
RANGES OF CONICAL AND
PLANE FLOW
40
"'\
'\
]0 0
"",
OF
hNGE
"'"
CONIC /I.l
"-
t'---
1"-..
UNGE
OF
"L ANE
FLOW
...........
,",OPPER S1.0PE ANGLE> 6.
DEGREES
..
o" O·
•l
I
I
]0 ' "
_
Fla. C 8
i
::I
...z
= .. r
u:t
.
"0
:011 ,
...
o ~ sCiI
...........
<3;
~r
z
~;C
;=
00
ZO.O.
oil ...
"'",
"'",
<,
'I-l
o
...... ,.f'~ ~ ]0
g
o
:;
I~
s
...-
i
•
--=
:l
-•:P
-.J
~
1A
IS I 9178 ( Part III ) - 1"0
FIG. C-9
if-FLOW.FACTOR FOR
49
No
PIPING
18 19178 ( Part: III ) ·1980
C)
60~-+--I-------~:---:-'L--t----t---+---+~-+---l
I)
SO f---+-+-~--+--:!ooI.:----+--F"IoOO:::+--+----1
,f
= 1'8
f t _I,
~
I
If = 1·4
FIG. C-lO
ffCONTOURS FOR DOMING IN PLUG
so
FLOW
IS 19178 ( Part III ) -1980
12
J
10
I
II
/
/
)
~
4
V
2
30°
1/
V
V
V
V
40°
50°
60°
70°
KINEMATIC ANGLE OF INTERNAL
FRICTION OF BULK souo.e, DEGREES
•
FIG. C·Il
FUNCTION
51
G ('" )
IS.9178 ( Part IU ) .1980
3·0
2·5
----- ---
t-""
1r.\~CIJ~
P
SO\l ...~t
I/"
-
I-""
.- ....
~
lo--'
~
1·5
lbnl
~ECl"NGUlA~ ll~'"
0
1·0
I
.i
0
0
10°
0
20
HOPPER SLOPE,
FIG. C·12
20·
FlO.
C-13(a)
30°
I
..
40°
e,
DEGREE - - FUNCTION H (ll)
3D·
'D·
Ge,DEGREES
50·
-
ffCONTOURS FOR CONICAL CHANNELS, ~=30°
[S : 9178 ( Part III ) - 1980
11'1
°
m
o
e
.... 20
....
Q:
-<0-10
0
20
30°
•
9c, DEGREES ----<FIG.
C-13(b)
jjCONTOURS FOR CONICAL CHANNEL~,
8=40°
40° ~---r-----"---~--'T"""---r---,
I
30°
II)
au
au
Q:
lA1
20°
0
-CO.
10°
20°
30°
-
ee, DEGREES --__e_
FlO. C-13(c)
ffCONTOURS FOR CONICAl. CHANNELS,
53
a=50°
18~
9178 ( Part III ) - 1980
'00
1 30°
l/'I
W
W
a::
0
w 20
a
C)
..
110
0
1O
10°
20°
30°
8c,DEGREES - - - - FIG, C-13(d)
ffCONTOURS FOR CONICAL CHANNELS, ~=60°
54
IS 19178 ( Part lJI ) .1980
40 t-~-t---+-----t----+-----1
0
La'
(/1
ILl
ILl
a:
~
~ 20
-.
0
k----"'.......-''''''d--'''
20°
30°
ee, DEGREES
FlO. C.13(e)
40°
..
1f CONTOURS ]lOR CONICAL CHANNELS,
~=70°
... ..
10°
20°
30°
ep
FIG. C.14(a) ffCONTOURS
40°
50°
.. DEGREES
FOR SYMMETRIC PLANE-FLOW CHANNELS,
55
60°
11=300
IS .9178 ( Part III ) - 1980
t 30° =-~---+--~,----~--=:~~.----"-:
111
w
W
a:
l:3
o
ff = '.,
20° 1....::---+---=~;,;,;,.:.:.._--~--'''----4-.:s..t,
"
<,
<,
<,
<,
<,
<,
10°
20°
30°
8p DEGREES
FlO.
C·14(b)
40°
fll
50°
..
ffCONTOIJRS FOR SYMMETRIC PLAIN-FLOW CHANNELS,
8=40°
50°
-,
<,
-,
-,
-,
"-
0°
0°
10°
30°
20°
8p DEGREES
FIG. C-H(e)
40°
-
50°
60
ffCONTOURS FOR SVMMETRIC PLANE-FLOW CHANNELS, ~=50°
56
IS I 9178 ( Part III ) • 1910
e
50
r"'--.--~~~~~..--~,
Lo'~~~
\fl
UJ
UJ
a::
~ 30" ~---.:~----+--'"
o
•10•
10"
FIG. C-14(d)
..
20"
3D"
DEGREES - - -
ep.
If CONTOURS FOR
CHANNELS,
57
SYMMETRIC PLANE-FLOW
3=60°
I•• '178 (Pan
m ) .1'80
7o· r::::"'l::::::~I:""'=::::::--O:;:::~--I--r--,--,
,
.
10
10'
10·
20'
JO'
ep,DEGREES
FIG. C-14(e)
40'
50·
•
ffCONTOURS FOR SYMMETRIC PLANE-FLOW
CHANNELS,1)=70'
58
IS 19178 (Part III ) .1980
III
W
W
ll:
C)
ILl
c
".0
2 [ j f - - - - '.......:-+-----",
•
aO~·--"*"=---::*="-"""""""I-::--......7---±~-~
20·
30·
40·
..
8p,DEGREES--------1FIG. C-15(a)
ffCONTOURS FOR ASYMMETRIC PLANE-FLOW CHANNELS WITH
ONE VERTICAL WALL, 3=50°, ~v=200
59
IS I 917B (Part
III
ll.J
ll.J
m
i- 1980
30°
<,
<,
a:
Cl
W
0
.
10
<,
<;
"-
20°
0° '":-_ _........
~
if
FlO.
-,
C-15{b)
_ _.......
20°
....L.-_ _""'-"'-_ _~'-:-_ _.......
30°
-
e p , DEGRE ES -------<1_
~o
ffCONTOtJRS FOR ASYMMETRIC PLAN1!-FLOW CHANNELS WITH
ONE VERTICAL W!lLL,
0=50°, l/iy=30°
-
'"
0
20°
FlO.
0°
C-15(c)
0°
-, co- 10
a
cr.
(.!)
w
UJ
w
If)
30°
40°
50°
20°
ep, DEGREES
30°
'.3
40°
<,
50°
" ...
60"
VE~TICAL WALL,
B= 50°, ¢'l=400
ffCONTOVJlS FOR ASYMMETRIC PL~NE·FLOW CHANNELS WITH ONE
10°
ff::
<,
la
g
...
~
...
:'..
........
~
~
\Cl"
...
fIl
..
...
IS I 917. (Part III ) • l!IBO
APPENDIX D
( Clause 7.8.4 )
RECOMMENDED CALCULATION SHEET FOR DESIGN
OF BINS FOR MASS FLOW
0.1. DESIGN WITH CONICAL ( SQ.UARE/CIRCULAR ) OUTLET
a) Bulk Material
i) Material:
it) Size:
iii) Condition:
IV) Average Bulk Density w:
b) Hopper Wall
i) Material:
ii) Fmish:
c) Flow Properties of
Bulk Material
i) Shear Cell Area, A.:
it) Estimated 8 at outlet:
iii) Estimated 8' at outlet:
d) Estimated Hopper
Slope Angle Bo
i) Estimated if:
(Fi.'(.C-13)
ii) Estimated Be:
(FIg A-B, stay 5° within boundary)
e) Estimation of Outlet
Dimensions:
i) H ( 6e ):
(FIg. C-12)
ii) Estimated jJ
iia) For no interaction of .lJwith FF:
Case I : FF lies below if
( free flowing material)
Case 2: FF lies below
if
JJ ( correction if any):
I ntersection if with FF of
V.R(S)
bo =
A•. w
Select lower jJ for an
intersecuon il possible,
Selectedj(:
stored material ( V, V):
iib) ForJJlying between FF 0 and FF t : Select a point ( V. p) on
if such that V = 1'5 F
( V, V):
( V, F):
Min outlet dimension
P. H (8e )
bo = --,---'--=-A. w
62
IS : 9178 (Part III) • 1988
f) Check
V
Corresponding
=
I)
=
By drawing Mohr's semicircle through (V, 0 ) and tangential to
ErL and its intersection with HTL.
S' at outlet =
Corrected =
Corrected
Corrected ll' =
ff =
Corrected Oc
=
v=
H (Oc) =
Minimum outlet dimensions, ho=
r' ~U~ol
A.
w
g) Adopted Values for Design
Hopper slope angle Bo =
Outlet dimensions Eo = Circular/Square
D.2. DESIGN WITH PLANE FLOW CHANNEL -
Rectangular/full
slot outlet
a) Bulk Material
I) Material:
]1) Size:
b) Hopper Wall
111) Condition:
IV) Bulk density w:
i) Material:
ii) Finish:
c) Flow Properties of
Bulk Material
i) Shear cell area, As =
ii) Estimated II at outlet =
iii) Estimated S' at outlet =
d) Esurnated Hopper
Slope Angle Op
i) Estimated ff'
( FIg. C-14 or Fig. C-lS )
ii) Estimated Op =
( Flg. C-B )
e) Estimated outlet
Dimensions
Estimated .if
i) H ( Bp ) =
ii) Estimated if:
63
IS I 9178 (Part lit) • 1980
Hal For no intersection .ff
Case I : FF lies below
jJ ( Free flowing material)
with FF.
b =
o
F.
H (0)
A•. w
Case 2 : FF lies Select lower .fJ
above .fJ
for an intersection,
if possible
=.!!l
jJ ( Correction, if any):
Lntersection of if
wuh FF of bulk
material ( V, V) =
Select a point ( V, V) on if
such that V = 1'5 F
(V,V)=
(V,F)=
iib) for.fJ I} ing between
FF o = and FF t
V=
H (Op) =
( C orrection if any)
Min outlet dimension bo = V.
9)
A•. w
He
I) Check
V =
,
Corresponding II =
By drawing Mohr's semicircle through ( V, 0 ) and tangential to
EYL and its intersection With WrL.
11' a t outlet =
Corrected 11 =
Corrected.ff =
H (Op)
, Corrected 11'
l Corrected Op -
V
=
Minimum outlet dimensions,
g) Adopted Values for Design
Hopper slope angle Ill' =
Outlet dimensions
Circular, Square)
( Rectangular 1 :> 3bo, Full slot 10 :> 6 bo )
=(
64
IS: 9178 ( Part Dr) .1980
APPENDIX E
( Clause 10.6 )
RECOMMENDED CALCULATION SHEET FOR THE DESIGN
OF BINS AND HOPPERS FOR FUNNEL FLOW
a) Bulk Material
i)
ill
iii)
iv)
Bulk size:
Average bulk density:
Lump size:
Condition:
b) Hopper Wall
i) Material:
ii) Fmish:
e) Flow Properties of
Bulk Material
i) Shear Cell area, A.
ill Average S =
iii) Average,'" =
d) Hopper Slope Angle, 6
i) Flow factor, if =
( see Fig. C-9 of Appendix C )
ii) 6. or Bp =
( see Frg. c-io of Appendix C )
e) Outlet Dimensions
i)
.ff =
ill Intersection of.ff with flow function
of bulk material
( V, V) =
iii) V
=iv) G (1)) ( see Fig. e-n of
Appendix C )
v) H (8) ( see Fig. 12 of
Appendix C)
Major dimension of outlet, do
d
o or I0 =
V.G(r/»
A
•. w
Minor dimension of outlet,
bo =
V JL£~
As. w
Square outlet side, bo = 10 1v' :!
Circular outlet Diameter, do =
Rectangular outlet Smaller side,
bo =
, Bigger side 10 =
65
=
18 I 9178 ( Part UI ) • 1980
Adopted outlet dimensions ( Circular/square/rectangular)
(Minor dimensions >0 6 X maximum lump size)
Adopted slope of hopper =
(9c or 9p )
APPENDIX F
( Clause 12.J }
PROCEDURE FOR CALCULATING LOAD DISTRIBUTION
IN MASS FLOW BINS
Step 1 - Define the bin geometry and the flow properties of the stored
material
d, h, 8, m, ~, lib, 8, and ~.
Slep 2 - Calculate" fd and
~
,\ ( Use ,\ £ : Q. 4 )
Step:1 - Calculate initial and maximum cylinder wall pressure P b and
friction stress I." using Fig. 6 for ( Ph/rod )mall and Eq. (3) for t.".
SlfP 4- -
Calculate maximum vertical force P." and force per unit
length of circumference developed in walls using Fig. 7 for
( P."Jrods )mu and Eq. (8)
Slip 5 -
Calculate R from Eq. (2)
Step 6 - Calculate average vertical pressure Qc/A at transition from
Fig. 5.
Step 7 - Calculate initial pressure in hopper from Eq. (5), (6) and (7).
Step 8 - Calculate the radial component of prrssure P ntr from Eq. (9)
and Fig. 9 or Fig. 10 as appropriate for (a/roB).
Step 9 - Calculate peak pressure P n \ at the transition from Eq. (10) and
Fig. 11 or Fig. 12 as appropriate.
Step 10 - Calculate the slant height 0'3 d over which the overpressure
acts.
IS I 9178 ( Part
APPENDIX
( Clause 13 4 )
m ) . 1980
G
PROCEDURE FOR CALCULATING LOAD DlSTRmUTlON
IN FUNNEL FLOW BINS
Sltp 1 - Define the bin geometry and flow properties
h, d, m, 8h, ~, Il, W, and ~
Sttp 2 - Calculate the maximum cylinder wall pressure Ph and friction
wall stress t." using Fig. 14 for ( Pb/wd)mu and Eq. (3).
Sttp 3 - Calculate the normal stress Po and shear stress
tb
for the hopper
wall by Eq, (14) or (15) as the case may be.
Sttp 4 - Calculate the maximum vertical force P." and force per unit
length of circumference of the cylinder wall by Fig. 7 for mass
flow bins and Eq. (13).
67
INDIAlil STANDARDS
ON
STRUCTURAL ENGINEERING
Struc/llral S,./lon
IS:
808-1964 Railed steel beam channel and angle sections (,erns,d)
808 (Pa,t I )-1973 Dimensrons for hot-rolled steel Iloaml: Part I MB series (second
"011;01/ )
811-1965 Cold formed light gauge structural steel sections ( rev;"d)
1252-1958 Rolled steel sectrons bulb angles
1730 (Part I )-1974 Dirnensrons for steel plate, sheet and strip for structural and
general engmeenng purposes: Part I Plate (fi's/ "v....n )
1730 ( Part II )-1974 Dimensions for st ee l plate. sheet and strip for structural and
general engrneermg purposcs: Part II Sheet (first "onIOn)
1730 ( Part III )-1974 Drmcnsrons for steel plate, sheet and strip for structural and
general cng meerrng purposes: Part III Strip (first reo",.n )
1852-1973 Rolling and cuttmg tolerancrs for hot-rolled steel products (s<COl1d reV'SI.n )
2713-l969 Tubular steel poles for overhead power lints (ji"l reolHon)
3908-1966 Aluminium equal leg angles
3909-1966 Alumunurn unequal leg angle.
3921-1966 Aluminium channcls
395-1--1966 Hot rolled steel channel sectrons for general engineering purposes
5384-1969 Alumimum I beam
6445-1971 Aluminium tee sect ions
Coder of Praetue
800-1962 Use of structural steel in general buildmg construction (reois,d)
801-\975 Use of cold formed light gauge steel structural members 10 general buildmg
construction
802 ( Part I )-1977 U,e of structural steel in overhead transmission hne towers:
Parr I Load, and perrmssible stresses ( second revisIOn)
803·1976 Dcsrgn, Fabrrcation and erection of vert ica l mild steel cylindrical welded
all storage tanks (first reolSlOo )
805·1968 Use of steel in gravity water tanks
806·1968 Use of steel tubes in general burlding construction (reo<Jed)
807.1976 Design. manufacture, erectron and testing (structur.l portion) of cranes
and hoists (first ,eoUlon )
3177-1977 Electrrc overhead travellIng cranes and gantry cranes other than steelwork,
cranes (fifjt revISIon)
4{}OO·1967 Assembly cf strucrura! jornrs USing !Ilgh tensile fClctwn gelp fasteners
4014 ( Part I )-1967 Steel tubular acatfcldings: Part I Defimtrons and materrals
4014 ( Part II )-1967 Steel tubular scaffoldings. Part II Safety regulations for
scaffoldmg
IS:
4137-1967 Heavy duty electric overhead travelling cranes including special service
machines for use in steel works
6533-1971 Design and construction of steel chimney.
7205-1973 Safety code for er ectron of structural steelwork
8147-1976 Code of practrce for use or alumimurn alloys in structures
8640-1977 Recommendations for dimensronal parameter' for industrial huildings
G.n.,al
81H-1957 Rectangular pressed steel tanks (firs' remsion )
72[5-1974 Tolerance. for fabrication of steel structure.
808[·1976 Slotted sections
HandlJo.lcs for Structural Engln."s
No. I
No.2
No.3
No."
No.5
No.6
No.7
Structural steel sectrons
Steel heams and plate girders
Steel column and Slruts
High tensile friction grip bolts
Structural use of hght gauge steel
Application of plastic theory in design of steel structure,
Simple welded glrders
INTERNATIONAL SYSTEM OF UNITS (SI UNITS)
B••• Unltl
Quantity
Length
Unt!
Symbol
Time
melre
kilogram
second
Electric current
ampere
m
kg
s
A
Thermodynamic
tern peratu re
kelvin
K
LumInous Intensity
Amount of substance
candela
mole
cd
mole
Mall
Supplementary Unite
Quantity
PIUe angle
Solid angle
Unit
Symbol
radian
slerad Ian
rad
sr
Utut
Symbol
Derived Unit.
Quantity
Force
Energy
Power
Flux
Flux denslly
Frequency
Electric conductance
Eleclromollve [orce
Pressure, streSS
newton
louie
wall
weber
tesla
hertz
siemens
volt
pascal
N
J
W
Wb
T
Hz
5
V
Pa
Definition
1 N = 1
~g.m/Sl
1 J - 1 N.m
1 W = 1 J{s
I Wb = I V s
1 T = 1 Wb/m!
1 Hz = 1 cis (S_I)
1 S = 1 A{V
1 V = 1 WIA
1 Pa = 1 N/mt