Design of Silos & Tanks

8/10/2019 Design of Silos & Tanks

1/17

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M17 -DESIGN OF SILOS AND TANKS

CONVINOR ' nil BoARDo' EXAMINDS:

EXTl.RNAL I.XAMINER:

UN)VI:RSITV OF

URGH

DINB

Wednesd8Y 6th M8rt"h 2002

3.00pm - 4.30pm

Professor 0 A Barry

ProfessorH. D. Wricbt


2/17

On-ground silos

When building structuresare designed, he ultimate limit state s related o the

characteristichighest oad state,which might be the highest ive load or wind

load. However. n silo design,different extremevalues of the propertiesof the

storedmaterialsmust be considered s different load cases. Give the reason or

this, and state he extremes f storedsolid properties hat shouldbe used or each

condition. [8]

1.

a)

Determine he design wall loads for the following cylindrical on-ground mild

steel silo. The silo is constructed rom rolled stnM:tural teel plate and has a

vertical wall height of 25.0 m and a diameter of 10.0 m. It is ~ to store

alumina,and is concentrically illed and discharged.The roof slopesat an angle

of 300 o the horizontaland he silo is filled until the solid ust touches he top of

the vertical wall.

i) Identify the design value of the angle of repose,and the stnICturaldesign

value of the unit weight r [2]

ii) Find the Wlit weight hat shouldbe used or the purposeof detelmining he

reliable storage apacityof the silo, anddeduce his capacity. [3]

iii) Determine the surface c~ of the wall for which the silo should be

designed. [2]

iv) Identify the upper and lower values of wall friction angle that should be

used or the design. Deduce he upper and lower characteristic alues of

wall friction coefficientJL [3]

v) Identify the upperand ower characteristic aluesof lateral pressure atio ).,

as given n the able ofpro petties. [2]

vi) Identify the upper and lower characteristicvalues of effective internal

friction

~

for the solid from the table of properties, nd then use an

appropriateequation o deduce he upperand ower characteristic aJues f

lateralpressureatio).. Comparehese aJcu1atedalueswith thosegiven n

the table of properties. Statewhy the equation s given at all, if it can ead

to different values rom those n the able.

Note: Use he values rom the able n all subsequentaJculations. [5]

vii) Find the total weight of solid that can be placed n the silo at the structural

designunit weight, and determine he height of the effective surfaceabove

the base. [3]

b)

University of fAinoorgh

Schoolof Civil and EnvironmentalEngineering

HODoun Module M.t7: Designof Silos

mination April 2002

egreeExa

Answer any two questions

Eachquestion s worth 40 marks

IIf2 hours

ime allowed:

This exam s open book


3/17

viii) FCX'he colXlition of maximmn normal ~ against the silo

identify the appropriate aluesof wall friction coefficient, ateral pI'1

ratio and Wtit weight o be used.

f


4/17

Patch loads and discharge

All standards hat define silo pressures egin by defining a filling pressureand

then modify it to obtain a dischargepressure. Briefly explain why this is, and

indicate he differences etween illing and discharge ressures. [4]

2.

a)

The Europeailsilos loading stalxlardENV 1991-4also requires silo designs o

include a "patch" pressure o be placedat any position on the silo wall. Briefly

explain its purposeand the featuresof real silo pressureshat it is intended o

reprexnl [4]

A cylindrical on-groundsilo of diameter 12.0m s made rom polished stainless

steel and is used o store barley flour. The condition to be considered n your

design s the maximum pressure ase,and for this the appropriatepropertiesare

as follows: unit weight 8.5 kN m3; .u

= 0.255; A.=

0.550; internal friction angle

;; =

28. It has a vertical wall height 18 metresand s concentrically illed level

(flat top surface) o the top of this wall. Discharge s through an outlet which is

slightly eccentric o the silo axis, with eo= 1.2 m.

i) A patch ~sure load will be applied o the tilling pressures. Locate he

position of the centreof this patch as a depth zp below the surfaceof the

flour. [4]

ii) Determine he filling vaJueof normal pressure gainst he wall at the level

of the centreof the patch, gnoringpatchpressures. [4]

iii) Determine he filling value of the co-ex.isteDt atch pressureand identify

the vertical and horizontalextentof the patch. [4]

iv) Deduce he total horizontal orce appliedby the filling patchpressure. 4}

v) Find the flow pressuremultiplier C for normal pressures. nd so d~. ~.e he

flow pressure t the evel zp. gnoringpatchpressures uring discharge.4]

vi) Determine he dischargevaJueof the co-existentpatch pressureand the

total force appliedby the filling patchpressure. [4]

vii) Find the vertical stress esultantN,rSdeveloped t the baseof the silo wall

at the most highly stressed osition causedby the dischargepatch alone,

using he appropriate artial safety actor YF. [6]

viii) If the wall is made of stainlesssteel of thickness = 12 mm, deduce he

corresponding ertical stress ue o the patch oad aJooe. [2]

3


5/17

3. Elevated ilos1rit~ boppen

a) Name the two principal modes of solids flow from a silo, and st8te the key

differences between them, with the aid of sketches. An elevated silo with a

hopper can be designed so that the flow of M)1ids n diJCblrge is in either of these

two m


6/17

Strength of metal silo walls

Where a metal silo is symmetrically illed and discharged,he cylindrical walls

must be designedagainst two key failure modes due to bulk solid loading.

Identify the two modesand ndicate he aspects f bulk solids oading which are

most important n inducing that failure mode. Deduce he bulk solids property

limits which shouldbe usedwhen assessinghe silo for resistance gainst he two

modesof failure. [8]

4.

a)

A cylindrical on-groundsilo of diameter 12 m is made rom mild steel with a

yield stressof 230 MPa and Young's modulusof 2xlOSMPa. It bas a vertical

wall height 18 m and s concentrically illed level (flat top surface) o the top of

this wall. The stress esultants valuated or the silo wall at threedifferent levels,

including the partial factor on actions, YF, re shown n Table 1. The internal

pressure,without a partial factor, s also shown.

b)

If the wall thickness at z

= 10m is proposedo be t = 6 mID,detennine he

safety margin against a yielding (bursting) failuret using the partial

resistance factor YM

=

1.10. To what value could the wall thickness be

reduced f this is the key failure mode? [10]

The silo is built to FabricationQuality Class B "High quali~tt and the

proposed wall thickness at z = 12.5 m is t = 8 min. Ignoring the

strengtheningeffect of internal pressure,determine the safety margin

againsta buckling failure, using he partial resi~ce factor YM 1.10. Is

the designadequate? [22]

ii)

5


7/17


8/17


9/17


10/17

2. Patch oads and dischup

a) All standards hat define silo pressuresbegin by defining a filling pressureand

then modify it to obtain a dischargepressure. Br~j1y explain why this is, and

indicate he differencesbetweenilling and discharge ressures. [4]

Underconditionsof filling, the pressure egime s relatively well definedand matches

values given by Janssen's heory quite well, provided appropriateval~s for the

material properties are used. This is therefore used as the referencecase when

defining silo pressures, nd all other pressure onditionsare nonnally referredback o

this as a basis. However, when dischargebegins, parts of the silo wall may be

ex}X)sed

o significant increasesn pressure,hough someof thesemay be transient

However. heir duration s sufficiently ong for them o be classedas static short enD

loads rather than dynamic oads, and the flow pressuremultiplier, or flow pressure

factor s used o attempt o relate he discharge ressureo the filling pressure. n the

Eurocode, he value of the flow pressuremultiplier dependson the solid being

considered its angle of internal friction) and the aspect atio of the silo (squat or

slender).

b) 1'18e uropeansilos loading standard ENV 1991-4aho requires silo designs o

include a "patch" pressure o be placed at any position on the silo wall. Briefly

explain its purpose and the eatures of real silo pressures hat it I.s ntended o

[4J ., 111.

Underboth filling and discharge onditions, he pressures gainst he walls of silos are

not symmetrical with respect o the silo axis, even under apparentlysymmetrical

conditions. The loss of symmetry s causedby geometric mperfections n the silo

walls, andKCidentalasymmetriesn the filling and granularsolids packingprocesses.

To account or this asymmetryand to ensure hat the structural design has some

margin of safety againstunsymmetrical oads, he E\D'ocode efinesa patch pressure

that must be added o the filling pressures, nd a secondpatch pressuremust be

applied to the dischargepreSS\D'Cs. hilst in principle the patch pressuremay act

anywhere, he standarddefines he position at which it should act to give the worst

effect.

A cylindrical on-ground silo of diameter 12.Om f made rom polished stainless

steel and is used to store barley flour. The corJdition to be considered in your

design is the moxim"", prUSfl1'e CD8e, nd for this the appropriate properties are

as ollows: unit weight 8.5 k;NW; ,II

=

0.255; .4.

=

0.550; nternal riction angle

;; - 280: It has a vertical wall height 18 metres and is concentrically filled level

(flat top surface) to the top of this wall. Discharge is thrmlgh an outlet which is

slightly eccentric to the silo axis, with eo = 1.2 In.

i) A patch pressure load will be applied to the filling pressures. Locate the

position of the centre of this patch as a depth zp below the surface of the

}lour. [4J

c)

Locationoftbe patch s given by z,: Eq. 7.17: z, is the esserof Zo and hJ2

For theseproperties,Zo=R/2~ =

6.0/(2xO.2SSxO.SSO)

21.39m

The height s identical o heso bJ2 - 18/2 9.0 m

9


11/17


12/17

Thus patch pessure is p,,- 02x P xi"l - 0.2xl.10x46.37-

The total borimntal force applied by the patch plaS\D'e is Ppc

Ppc

=

1[ s

R p,. =

[ x 2.4 6.0

10.20= 461.5 N

KsRp,.

vii} FlIwl 1M verlical.Jtn-u ".nIlt- N&t.-."loped ,. 1111 of 1111ilo wall

at 1M most highly stn.f.redposition CaU.f.d y 1M dLrcharrepatch alont,

IIIIng the apprOpI'iDIecrtlDl s.afetyaclor 'fF. [6]

~ of die a..e of thesilo wall belowdiee:rtive ~ -

z

- 18m

The most bisbiY U ~ position s at e - 0, when~ ~ 1.0

Vertical tIe8I resultantN&t.- eveloped t the molt highly .~ position n the wall

at z (Eq. 10.20)

Val~ of YF s taken fnMn Table 10.2: this is . ~ 8:tion. uotber solids"

\mfavourable ':f~~ ~ die vaI~ is YF 1.50.

N~ = - 'YF , sz

,)/R) COt 9 - 1.SOxI0.20x2.4x18.0-9.0)'6.0) -

SS.08 kN/m

viii}

If lilt 'MIalJ.f ... of 1tGtMc.ulftl of

iI.::.~-==-~

2-. ~ 1M

correSINJrwlingrticaI.rtre.uue 0Iw chDIId.. [2]

{5]

Vertical~brane stressn thewall s liven by ~

- N.sJ1

- -SS.08/12

- ..S9 MPa

{5]

V mica membrane ftSS n the wall is given by

,

Units: (kN/m)/mm - (N/mm)/mm N/mm:

11

10.20Pa

where

,= Nasi'

=MPa

~-

2 -'


13/17

3. Elevated .ilos wit~ lIoppen

a) Name he two principal modes f solldf flow fro," a Itlo, and .ftatl the by

differetk"Ubetweenhem.with the aid of It.tcllu. All ekUed IUD with a

hoPIWr Q1Iedesignedo hai tile low of solidi. 4SlCUp i.r ll "" of tIIt.JI

two1IIodes. [8]

The ~ ~peI flow mc:NIesn silos are Mass Flow and FUlmeIFlow. The key

differencebetween hem s IS follows. In Mass Flow all ~cles of the storedsolid

are n motian when he outlet is o~. In FunnelFlow, only someof the solid is in

motion: different peuemscan occur n ft8mel flow, with the moving solid IOmetimes

entirely internal to the silo: in other ciICumstances,he Oowina ~ will spread

outwards rom the outlet and reach the wall, above which all material will be in

motion.

If

a circIIlIr pi.,.. sUo Iwu a conica/1tOppeT with a 1IDIIangle of 100 aIwJ he

wall fHction angle between he solid a1ki 1M #tDppIr .f 15, dele""ine the

IN'O~ modeofjlow ill 1111Uo according o EIII'c* J Part 4. [4]

b)

The DM)(ie f flow can be fOtBMIrom die chart of flow mode predictions:Fig. 6.2 w

Fig. 1.5:

The hopper is conical so Fig. 6.2c applies.

The wall 6'ictiOI1qie is I 50

-

Using the iKJPper alf qIe of 200 8M ... = I So, t is clear hat this hopperwill

exhibit MassFlow.

c) A" ,.J.YQted silo, COIUI1'.:ted e8ftiy from all.iIIi.-, Iwu a ~/er of

8.3",.tres and is used o storematz,.with a unit wig#rl r

-

8.5 k,N1",J. It is

COIICe.,.;caliy tJ/d aIKl dUchDI-geil /rough a hopper with QII apex JWJlf ngle of

200. n. wrtica/

.rIre.J.fwlthill tile solid at tIle trtDI.rilicm Iwu bee" ,.~d Q$

45.1 kPa wi... tIle Of'OJ"'iDle 1Itat,.rlG/ W'Opertiel wnJe." Kfed (A -

0.45 aIKl

.u-

0.268).

(I) o.tet-- WMtMr,. .""" I.r.rlftpM.tWIow,. [5J

Eq. 7.26 8i'\'a a'iterion for --=-+~~

The hoppei' s shallow if:

tm.8>{ :&}

2P11

that is if t8I2OO> (1-O.4S)I(2xO.268)

(fI)

,... ,. wGll

r8io F .for lU,. co.JlIjONJo ~

Eq.7.31:Tt. hopperwall pressureatio or filling is

Ff

- ~.~~;;;~

(I + 0.8xO.268xCQC200)I(1

0.268x~)

-

0.915

12

O

0

1

. . .

,

._~ .~~

0.364> 1.026 No, m this IM~ is steep.

.

(S)


14/17

(Iii) FIIwl ,1M ."" NI JWWS.I~ . "

,.",

,. f '" r N/

"..,. flam,. (6]

The nonna1 ressure n the wall on filling me (Eq. 7.27)p. F PY/

in whichhe~ P-1s aivmby

~{(~-(fJ}h

n - 2(F~co~+Ff-l)

Pvf - D-Il~~-~~ J . ~t~

~ n - 2(F~ cotp + Ff- I)

and he raDSitionertical tress aabeen iven n thequestion s Pvft- 45.2 kPa

In this ~ the ~ to be ~ areat the top of the oopper.10

X - ~ ~1Ih ~ ~~ may IXJt ecoIn~ tb8t Ibis Ie.Is to . coasidcrable JX)rt

cut in the questicxl:

~

{ n}

n

Ifx - ~ thenPvf= -;;:t 1.0 1.0 + Pvft1.0 - Pvft - 45.2 kPa

The normal JXaSUIe XI fi11iIII at .. TOP of the OOAJel's then

PM- F(Pvf- O.915x4S.2 41.4kPa

If the It.xIaIt ck>es Ot~lIIise that aUother ams ~ tIxn it is i:~:~~ -,. to ~

~ density, o determine he hopperheipt, to look up the appr\Jf'i:'aateal~ ofoopper

wall friction angle taking cognisance f whether his should be an upper or lower

bow1dva1~, to evaluate he hopper wall friction coefficient, and to use aU these o

find n - ~ thepessure t anyheightp.r. Sadly ll dleseermswill cancelo

leaveonly die above,aIKIdlis hugeeffort will be ratherwasted n this question. This

question s dlerefore athereasy or tOOIewho have8 aood mderstanding onerous

for thosewho lack it.

Give" 1.IkIt M ,."..,. 'wall rlclloll angle is ;.,

- J O, IftlIM iIIIenkll friction

angle of 1M solid I.J~

-

18,

l""

"" designwall ,...,/ JW'e.f.nl1'e"'" ~ry lOp

of 1M hopperwall dwl"g di.Jclrarp. [11]

d)

TheditcI.- ~ ia .. IMw- i81i'w81y Eq8.1 )

Pac FePw

~Pw -

~{(~

( J}

P.I( J

1

+_a8

IIxt Fe - 1

- lint ~2P+e)

.:

=+-+ sin-'{~}

Onc:e gain, he vertical ~ at the TOP of the hopper~~ to:

Pw=Pvft

However, he val.. of F am must be fotmd.

The hopperwall friction is given by 1.111tan .. - tan 1So 0.261

The ntaD81 riction angle s +1 280

13

".(rJ

- 45.2 Pa


15/17

so E -..+

sin-I{~} -15+ sin-I{~} -15+ 33.46 -48.460

Now Fc = 1 _1

:"'-=+8)

(1 + 1iD2rc0e48.46~ I - siD2JOcoI(2x200+48.46

- .328

at the iMJPPerop, PM

-

. - 8M

1.321~S.2

-

O.0kPa

Now

PM-

14

Pw

-,.. m


16/17

Strength of metal sUo waUs

Where a metal silo is symmetrically filled and discharged, the cylindrical walls

must be designed against two key failure modes due to bulk solid loading.

Identify the two modes and indicate the aspects of bulk solids loading which are

most important in inducing that failure mode. Deduce the bulk solid\' property

limits which should be ILJedwhen assessing he silo for resistance against the two

modes offailwe. [8)

4-

II)

The two key modesare:

+ plasticcollapse, uptureor bursting

+ buckling underaxial compression

Key aspects:

+ Plastic failure: high internal pressures, induced by solids flow (so discharge is

critical). Low wall friction causes ncreases n these pressures

+ Buckling under axial compression: high wall frictio~ leading to cumulative vertical

loads in the wall. Geometric imperfections seriously affect the strength.

+ Plastic failure verification must be perfonned using a von Mises check

+ Buckling under axial compression verification may include the effect of a patch load

on the wall, and the strengthening effect of internal pressm'eat all positions

The material property extremes which are needed o address hese two modes are:

+ Plastic failure: Maximum lateral pressure ratio A, and minimum wall friction

coefficient ~

+ Buckling: Maximwn lateral pressme ratio

~ and maximumwall friction coefficient

1.1

A cylindrical on-ground silo of diameter 12m is made rom mild steel with a

y;eldstress of 230 MPa and Young'smodulusof2xloS MPa. It has a vertical

wall heighl 18 m and ;s concentrically illed level (flat top surface) o the top of

this wall. Thestress esultantsevaluatedor the silo wall at three different evels,

including the partial factor on actions. YF.are shown n Table I. The internal

pressure,without a partial factor, is also shown.

b)

IS


17/17

Jfthe wall thickness t z - 10 m is proposedo be t = 6 mm, determine

the safety margin against a yielding (bursting) ailure, using the partwl

resistanceactor ru = 1.10. To what value could the wall thicknessbe

reduced f this is the Uy failure mode? [10]

I)

Choose he valuesarising rom Max. PreIS1ft.

NeSd 444 kN/m andNxSd=1~ kN/m.

So NvmSd

=

..J(NeSd2Ne~xSd + NxSd2)

389kN/m

Check or 6mm wall: Nv8Rd 230.6/1.1

=

1254kN/m

So safetymarginagainstbursting s 1254/389 3.23

Requiredwall thickness s given by:

~uired =

(NvmSdfrM)/fy

- 1.71mm

This value is too thin to be realistic on a diameter of 12 m. so JX'Obably mm wall

would be used f this were he critical

ii) The silo is built to Fabrication Quality Class B "High quality", and the

proposed wall thickness at z = 12.5 In is t - 8 mm. Ignoring the

strengthening effect of intemaJ presnlFe, determine the safety margin

against a buckling failure, using the partial resistance actor YM

= 1.10. Is

the designadequate? [16J

Choose he valuesarising rom Max. Friction.

NOSd

= 445kN/m andNxSd 230kN/m.

Buckling assessment:

Radius to thickness ratio: R/t = 6(XM)I8 750

Fabrication quality class is High, so Q

=

25

Characteristicmperfectionamplitude

=Wk

Unpressurised lastic mperfection eduction actor a cr(

For uniform meridional compression", =1.0, 80 ~ - 0.195.

Elastic critical stress

=

O'xRt

= 0.605Ei = 161.33MPa

Dimensionless lenderness: .. ..J(f.,lO'xaIt) ..J(230, 161.33)=

1.194

Limiting dimensionless ler.derness:

..,

-

..J(2.5aJ

="'(2.5.0.194)-

0.698

Since 1..>

1.., .

this silo wall is in the mne 3, elasticb~kling

Kx=aJ~2 = (0.195/1.1941-0.137

Characteristic uckling strength s giVal by

xn

= Kx' fy = 0.137.230 31.46MPa

So buckling resistances NxRd (O~)~ - (31.46/1.1.8 - 228.8kN/m

Compare esignvalue of stress esultant:NxSd

=

230 kN/m

Safetymarginagainstbuckling s 228.8/230

=

0.995 ust unsafe But JX'Obably K.

16

verysafe

consideration.

.LI

\J

= 8.005)

..J(7S0)

=8.76 mID

- 0.62

~-;:;~;:;

Design of Silos & Tanks

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Transcript of Design of Silos & Tanks