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Load Development and StructuralConsiderations in Silo Design1

ByJ.W. Carson, Ph.D.

andR.T. Jenkyn, P.Eng.

1 Source: Carson, J. W. and R. T. Jenkyn: Load Development and Structural Considerations in Silo Design. Presented atReliable Flow of Particulate Solids II, Oslo, Norway, August 1993. Used with the permission of the publisher.

SYNOPSIS

Each year an alarming number of silos, bins,and hoppers fail due to bad design, poorconstruction or improper use. Jenike &Johanson engineers have been called in toinvestigate more than 50 structural failures inthe last five years alone.

Many failures are the result of loadingconditions not anticipated by the designer. Inthis paper we describe design procedures thatwe have found to be successful. In particular wecover bin load calculations for various fillingconditions and flow patterns, force resultants,and design requirements.

INTRODUCTION

Although statistics are not available, hundredsof industrial and farm silos, bins, and hoppersfail in one way or another each year. Sometimesthe failure is a complete dramatic structuralcollapse. Other times cracks are found in a

concrete wall, or dents in a steel shell, either ofwhich might appear harmless to the casualobserver. Nevertheless, these are danger signalswhich indicate that corrective measures areprobably required.

The economic cost of repairs to this essential –though frequently neglected – component of abulk material handling system is never small.The owner faces the immediate costs of lostproduction and repairs, personnel in the vicinityare exposed to danger, and the designer andbuilder face possible litigation because of theirliability exposure.

What can be done to avoid these problems? Inthis paper we show some of the problems thatcan occur, why they occur, and the straight-forward steps that can be taken to avoid, or atleast minimize, such problems.

2

SILO DESIGN

The design of bins and silos to store bulk solidsinvolves bulk material, geometric, and structuralconsiderations.

Bulk material considerations are importantbecause the frictional and cohesive properties ofbulk solids vary from one solid to another, andthese properties affect material behaviorconsiderably. In addition, a given bulk solid’sflow properties can vary dramatically withchanges in numerous parameters, includingparticle size, moisture, temperature, andconsolidating pressure. This variability ofproperties makes testing at actual conditionsmore important for proper bin and silo designthan may at first appear.

When considering the geometric design of asilo, potential problems include arching acrossan outlet, ratholing through the material, and theflow pattern during discharge. A bulk material’spropensity to arch or rathole is primarily relatedto it’s cohesiveness, while its flow patternduring discharge depends upon internal frictionas well as the friction that develops between thematerial and the silo’s hopper walls. The goal ofgeometric design is to maximize the useablecapacity of a silo while minimizing its capitalcost, overall height, etc.

Established design procedures [1] includeselection of the optimum hopper angles andminimum outlet dimensions. The idealdischarge mode is one where, at steady state, allmaterial flows without obstruction. This isreferred to as mass flow. The discharge modewhere only some of the material flows is calledfunnel flow. In mass flow, the material does notnecessarily move at a uniform rate throughout:velocity variations across any horizontal cross-section are possible.

The structural design of a silo requires, amongother things, knowledge of the distribution ofpressures and shear stresses on its walls (causedby the stored material) and how that distributionvaries during charging, storage at rest,discharging, and recharging.

Of the three major aspects of silo design (bulkmaterial, geometric, and structural), the binloads aspect of structural design is the leastunderstood. But unless the structural design isdone properly, the integrity of the silo may becompromised. Silo collapse is far too common,yet agreement amongst designers on proceduresfor determining silo loads has not beenforthcoming. This is very apparent when oneconsiders existing codes of practice. There isvery little detailed guidance concerning thevarious loading conditions – some static, somedynamic – which can co-exist.

Even if existing codes were “better,” it isunreasonable to expect that any code of practicewould contain a definitive set of instructionscovering all cases that might have to beconsidered. Usually none but the simplest casescan be described. Over-enthusiastic compliancewith the letter, to the exclusion of the spirit andintent of a code of practice, can be misleading,and even dangerous.

In some countries, codes are recommendationsonly, so compliance with them is notmandatory. However, for practical purposes inthe event of a failure, a code (assuming thatone exists) is a minimum mandatory standard.In other words, an engineer may have the rightto exercise independent engineering judgmentwhen creating a design, and may even go backto first principles. But if a problem occurs andthe engineer must justify his design, he willhave difficulty doing so unless it is as good asthe minimum provided by the applicable code(or codes), or the inapplicability of the code hasbeen documented [2].

3

Codes are particularly weak in the area ofeccentric flow channel formation. In fact evenflow experts often cannot agree on where a flowchannel will form in a funnel flow bin or silo, itssize, shape, etc. Because of this uncertainty inthe ability to predict the occurrence of flowchannels, some designers feel that it is prudentto assume the occurrence of worst case flowchannels if there is any doubt at all. Part of theirrationale is that they consider it to be dangerousto fine tune a design on the basis that somedefinite predicted flow regime will occur, thatoperators will operate the silos according to adefinite set plan, or that the material’s flowproperties will not vary [3]. While such anapproach should be conservative, it may be toocostly to implement.

Several committees in various countries arecurrently working to revise silo design codes.Many are having great difficulty in enactingnew procedures for the design of silos toaccommodate flow channels even though theyknow that they occur and they know that manysilo failures have been caused by such flowchannels. Every day there are new engineerswho are charged with the design of new silos.Most of these new engineers look first to thecodes for information on the design of thesestructures, hoping and expecting that the codeswill point them in the right direction. To do this,a code need not be perfect, but it must reflectthe latest in technology and be rational.Hopefully, papers like this one will fill some ofthe gaps while codes are being revised.

CAUSES OF SILO FAILURES

There are many different causes of silo failures[4]: shortcomings in the design procedure,construction, usage, maintenance, or somecombination thereof. This, in turn, means thatmore than one individual or group often bearssome responsibility when a failure occurs.

Potentially responsible parties include thedesigner, builder, building material supplier,owner, user, and others.

Failures Due to Design Errors

Silo design requires specialized knowledge. Thedesigner must first establish the material’s flowproperties, then consider such items as flowchannel geometry, flow and static pressuredevelopment, and dynamic effects. Problemslike ratholing and vibration have to beprevented, while assuring reliable discharge atthe required rate. Non-uniform loads, thermalloads, and the effects of non-standardfabrication details must be considered. Aboveall, the designer must know when to be cautiousin the face of incomplete or misleadinginformation, or recommendations that comefrom handbooks, or from people with the “it’salways been done this way” syndrome.

Having established the design criteria, acompetent design has to follow. Here thedesigner must have a full appreciation of loadcombinations, load paths, primary andsecondary effects on structural elements, and therelative flexibility of the elements. Specialattention must be given to how the most criticaldetails in the structure will be constructed sothat the full requirements and intent of thedesign will be realized.

Flow-related loading conditions which,unfortunately, many designers fail to anticipateinclude:

• Bending of circular walls caused byeccentric withdrawal. If the withdrawalpoint from the hopper is not located on thevertical centerline of the silo, and if theresulting flow channel intersects the silowall, non-uniform pressures will developaround the circumference of the silo leadingto horizontal and vertical bending moments.

4

Many silo designers incorrectly account forthese non-uniform pressures by onlyincreasing hoop pressures. The problem ofbending moments is particularly commonwhen using silos with multiple hoppers inwhich only one or two of the hopper outletsare used at a time.

• Non-symmetric pressures caused by inserts.Support beams and other types of internalscan impose non-symmetric pressures on thesilo wall leading to unacceptable bendingstresses.

• Self-induced vibrations. Bins and silossometimes vibrate. This can be either a highfrequency, low amplitude type of cyclicvibration, or a low frequency, highamplitude erratic vibration leading toshocks. The latter have been known to causestructural failures [5].

• Local peak pressure at a point where afunnel flow channel intersects a silo wall.

• Mass flow occurring when funnel flow wasexpected.

• Migration of moisture from wet to dryparticles within the stored solids, whichcauses the dry particles to expand andimpose large radial loads on a silo. (This isan uncommon problem.)

Failures Due to Construction Errors

In the construction phase there are two ways inwhich problems can be created. The morecommon of these is poor workmanship. Unevenfoundation settlement and faulty construction(such as using the wrong materials or not usingadequate reinforcement, such as insufficientquantity of rebars) are but two examples of sucha problem. This can usually be avoided byhiring only qualified builders, by close

inspection during construction, and by enforcinga tightly written specification [6].

The other cause of construction problems is theintroduction of badly chosen, or evenunauthorized, changes during construction inorder to expedite the work. Any changes indetails, material specifications, or erectionprocedure, must be given careful considerationby both the builder and silo designer.

Failures Resulting from Silo Usage

If a bulk material other than the one for whichthe silo was designed is placed in it, the flowpattern and loads may be completely different.The load distribution can be radically changed ifalterations to the outlet geometry are made, if aside outlet is put in a center discharge silo, or ifa flow controlling insert or constriction is added.The designer should be consulted regarding theeffects of such changes before they areimplemented. Some of the problems which canoccur include:

• Collapse of large voids. A collapsing arch orrathole induces tremendous dynamic loadson the structure, which can cause thestructure to fail. Vibrating bin dischargershave also been known to fall off bins andsilos because of this mechanism.

• Development of mass flow in silos designedstructurally for funnel flow. Mass flow candevelop if the walls become smoother withtime or if the properties of the bulk solidbeing stored change. This generally resultsin much higher loads at the top of the hoppersection, which can result in structuralfailure.

• Drastic means of flow promotion. Highpressure air cannons and even dynamite aresometimes used to restore flow. The result

5

may be more dramatic than the user anddesigner anticipated!

• Buckling of an unsupported wall below anarch of stored bulk material.

• Metal fatigue caused by externally-mountedbin vibrators.

• Dust explosions.

Failures Due to Improper Maintenance

Maintenance of a silo comes in the owner’s oruser’s domain, and must not be neglected. Thereare two types of maintenance work which arerequired [7]. The first is the regular preventativework, such as the periodic inspection and repairof the liner used to promote flow, protect thestructure, or both. Loss of a liner may beunavoidable with an abrasive or corrosiveproduct, yet maintaining a liner in properworking condition is a must if the silo is tooperate as designed.

The second area of maintenance involveslooking for signs of distress, (e.g., cracks, walldistortion, tilting of the structure) and reactingto them. If evidence of a problem appears,expert help should be immediately summoned.An inappropriate response to a sign thatsomething is going wrong can precipitate afailure even faster than leaving it alone,including the common instinct to lower the silofill level.

Wear due to corrosion and/or erosion can beparticularly dangerous. For example, as carbonsteel corrodes, the reduced wall thickness caneventually lead to a structural failure. Thisproblem can be compounded through erosivewear of the silo wall. Erosive wear can also be aproblem in reinforced concrete silos handlingabrasive bulk materials such as coarse ores.

SILO LOADS

The loads which bulk materials exert on silostructures can generally be divided into twocategories: those due to initial fill and thosewhich are as a result of flow. Initial fill loadsdevelop, as the name implies, when a silo isfilled from an empty condition without anywithdrawal taking place. The term flow-inducedloads, on the other hand, is somewhat of amisnomer since it implies that the material mustbe in motion for these loads to develop. In fact,the only requirement is that there be somewithdrawal of material which allows the flowinduced loads to develop. Once this occurs, flowcan be stopped and then restarted withouthaving any appreciable effect on the silo loads.In addition, the rate of discharge is usually not asignificant variable in affecting the magnitudeof the silo loads. The primary reason for this isthat most bulk materials are not viscous orvisco-elastic, so their rate of movement has littleeffect on their frictional properties.

Initial Fill

As with all of the loading conditions describedherein, it is convenient to consider first thevertical-sided portion of the silo (generallycalled the cylinder section), and then the hopper(i.e., sloped section of the silo in which thecross-sectional area is changing with height).

If a silo is filled at a point which coincidesclosely with the silo’s centerline, the loadswhich develop on the cylinder walls aregenerally less than those which are flow-induced and are therefore of little interest as faras structural design is concerned. If there issome reason to consider these loads, werecommend the use of the Janssen equation witha K j value (ratio of horizontal to verticalpressures) of 0.4 and with wall friction angle f¢equal to a value determined from tests (seesection MATERIAL FLOW PROPERTIES

6

below). For a circular cylinder of diameter D,the Janssen equation is:

p =g D4 m

1 - e-4 m K j z / D[ ] (1)

t = m p 2)

m = tan ¢ f 3)

See NOMENCLATURE section at end of paperfor a description of each term.

Other types of fill conditions can result in loadson the cylinder walls which are larger than thosewhich are flow-induced. In particular, considerthe conditions which occur when a silo is filledoff-centered, or if it is filled along a ridge (suchas would occur if a continuous belt tripper fillsystem were used). Pressures around the siloperimeter at any elevation caused by theseconditions, can be calculated using thefollowing procedure:

• At any point on the cylinder’s perimeter,measure vertically up the wall to theelevation where the material surfacecontacts the wall, z1.

• Cut the surface profile with a horizontalslice at the elevation just determined (i.e.,where the material surface contacts thewall). Calculate the volume of the surchargeabove that slice, then divide that volume bythe area of the slice, to give an effectiveadditional head above the slice, z2.

• Apply Janssen’s equation, usingz = z1 + z2.

• Repeat this for sufficient points around thesilo perimeter to define the distribution.

While this condition is usually rather localizedto a region immediately below the materialsurface, it can occur at any elevation as the silois being filled.

As far as the hopper section is concerned, webelieve that the following equation adequatelypredicts the initial fill pressures which actnormal (i.e., perpendicular) to the walls of aconverging conical hopper no matter what typeof flow pattern occurs during discharge.

p = gh - z

ni

+qg

-hni

Ê

Ë Á Á

ˆ

¯ ˜ ˜ 1 -

zh

Ê Ë Á

ˆ ¯ ˜

ni +1Í

Î Í Í

˙

˚ ˙ ˙

(4)

ni = 2 1+tanf'tanq c

Ê

Ë Á Á

ˆ

¯ ˜ ˜ - 3 (5)

Note that “z” in equation (4) starts with a zerovalue at the top of the hopper, not at the top ofthe cylinder as in equation (1). The value of qcan be calculated by taking the Janssenhorizontal pressure p at the bottom of thecylinder and dividing by Kj (recommendedvalue = 0.4)

For hopper geometries other than conical,numerical integration of the equations ofequilibrium is required.

As will be shown below, in the case of a massflow hopper the initial fill loads govern thestructural design of the hopper in roughly itsbottom two-thirds, whereas flow-induced loadsgovern in the upper third. See Fig.1. In mostfunnel flow hoppers, their structural design canbe based upon initial fill loads.

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Mass Flow – Single Outlet

Mass flow is a condition in which all of thematerial is in motion whenever any iswithdrawn. As indicated in the SILO DESIGNsection above, particles can be flowing atdifferent velocities and still satisfy therequirements for mass flow as long as they aremoving.

A mass flow bin or silo can still exhibit a no-flow condition of arching if the outlet is toosmall relative to the particle size (arching due tointerlocking) or if the outlet is too small relativeto the material’s cohesive strength. Mass flowsilos can also develop self-induced vibrations asmaterial discharges [5].

If we assume that the outlet size is large enoughto prevent the formation of a stable arch, andfurthermore that self-induced vibrations do notoccur upon discharge, the loads that develop onthe silo walls are fairly well defined. In thecylinder section, a good starting point is to usethe Janssen equation but with a range of Kj andwall friction values as follows:

0.25 £ Kj £ 0.6 (6)

f' calc. = f' meas. ± 5o (7)

The “plus” sign should only be used in thisequation when calculating maximum shear

stresses for cylinder buckling calculations.Otherwise the “minus” sign should be used.

If an applicable silo code predicts higherpressures, it should be used for the reasonsstated in the SILO DESIGN section above.

In the hopper section, we recommend the use ofthe following equation [8] to predict flow-induced loads in conical hoppers:

p = g Kfh - znf

+qg

-h

nf

Ê

Ë Á Á

ˆ

¯ ˜ ˜ 1 -

zh

Ê Ë Á

ˆ ¯ ˜

n f +1Í

Î Í Í

˙

˚ ˙ ˙ (8)

Kf =1

23

1 +tanf'tanqc

Ê

Ë Á Á

ˆ

¯ ˜ ˜ -

16(s' / gB)tanqc

È

Î Í Í

˘

˚ ˙ ˙

(9)

nf = 2Kf 1 +tanf'tanqc

Ê

Ë Á Á

ˆ

¯ ˜ ˜ - 3 (10)

The value of “z” in equation (8) starts at zero atthe top of the hopper, as in equation (4). Thevalue of q can be calculated by taking theJanssen horizontal pressure p at the bottom ofthe cylinder and dividing by Kj. To beconservative, a minimum value of Kj should beused for the calculation of p.

These equations result in higher pressures inroughly the upper third of the mass flow hopperthan occur during initial fill, but lower pressuresin the bottom two-thirds of the hopper section.See Fig. 1.

Because of the rapid switch in the state of stressthat occurs at the top of a mass flow hoppersection, some increase in wall pressure is oftenexperienced in the section of the cylinder justabove the top of the hopper. To account for thiscondition, we recommend that the peak pressurebe spread along the vertical wall as shown inFig. 2. First, draw a circular arc centered on thetheoretical apex of the conical hopper, and

Fig. 1: Mass flow hopper

t

Flow

Initial fill

P

t = m p

p

8

passing through the top of the cone. Theelevation of the highest point on the arc isapproximately the maximum elevation at whichthe increased peak pressure is experienced. Thewall pressure distribution below this elevation(down to the top of the cone) can be assumedlinear.

A silo in which the fill and withdrawal pointsare located along the vertical centerline, andwhich behaves in mass flow, will probablyexperience some non-uniformity of pressuresaround its circumference. This could be causedby the wall being out-of-round or out-of-plumb,the intrusion of construction joints, orsegregation of the contained bulk material. It iscommon practice, although by no means alwayscorrect, to compensate for these effects bymultiplying the calculated wall pressure p bysome “over pressure factor” for the purpose ofdesign. We recommend that this should be aminimum requirement, and that a designershould make a rational attempt to estimatepressure non-uniformities and their effects.

Funnel Flow – Single Outlet

As noted above, since there is no flow along thehopper walls in a funnel flow pattern (exceptperhaps when the hopper is being emptied at the

end of the discharge sequence), it is reasonablein most cases to consider that the designpressures acting normal to the hopper walls arethe same as those which occur during initial fill.Therefore no additional calculations are neededfor the hopper section. This presumes, of course,that the outlet size and feeder arrangements aresuch that no arching or ratholing can occur asmaterial is discharged. It is also important thatthere be no self-induced silo vibrations acting tomagnify pressures [5].

As far as the cylinder section is concerned, thereare two main conditions to consider. First, if theflow channel does not intersect the cylinderwall, it is safe and reasonable to assume that thepressures acting against the walls will be thesame as during initial fill. If, on the other hand,the flow channel does intersect the cylinderwall, one must consider whether or not the flowchannel is centered (i.e., intersects the cylinderwall at the same elevation around itscircumference). If the flow channel is centered,one can assume a Janssen stress field above theeffective transition (i.e., the elevation at whichthe flow channel intersects the cylinder walls).As with mass flow cylinder pressures, werecommend using a range of Kj and wall frictionvalues as described above.

At the effective transition where the flowchannel strikes the wall, there is a rapid increasein wall pressure due to the convergence whichthe material is undergoing. Within the flowchannel itself, it is reasonable to assume that thepressures will vary as if this were a mass flowhopper but with the hopper angle replaced bythe flow channel angle, and the wall frictionvalue replaced by the internal friction ofparticles sliding on each other. How thispressure distribution is transmitted to thevertical walls of the cylinder is not well-defined.It is safe, but probably somewhat conservative,to assume that the pressure which acts normal to

Fig. 2: Spreading of mass flow pressure peak into cylindersection

t

t

P

p

p

t = m pR

9

the cylinder walls is the same pressure whichacts normal to the flow channel.

As with the conditions which occur at thebottom of a cylinder just above a mass flowhopper, there is some progression of thispressure peak, which occurs just above theeffective transition in a funnel flow silo. For thiswe recommend that the total radial outwardforce given by the peak pressure, multiplied bythe effective area over which it acts, beconverted to a smaller uniform pressure spreadover a wall height equal to one vertical bendinghalf wave length. This should be centered at theelevation of the effective transition. See Fig. 3.

Since the side slope of the flow channel – andthus the elevation at which it intersects thecylinder wall – is variable, the above procedureshould be used to develop an envelope of peakpressures to be used in design of the cylinderwall.

If the flow channel is not symmetric but stillintersects some or all of the cylinder wall, theloading conditions become much more complex.The resulting eccentric flow channel can causenon-uniform pressures to act on the silo walls.In cylindrical reinforced concrete silos thiscauses horizontal and vertical bending momentswhich act in addition to the membrane forcesand can lead to serious cracking if the walls arenot designed to withstand such loading, as isoften the case with concrete silos constructedwith a single layer of reinforcing steel. Inaddition, there are many documented cases ofdented or collapsed steel bins and silos as aresult of eccentric flow channels. The shape ofthe flow channel, the locations at which the flowchannel intersects the silo walls, and thepressure within the flowing and non-flowingregions must all be estimated to permit thesebending moment calculations.

Several studies have been conducted in anattempt to predict the shape of flow channels infunnel flow bins. One of the older and betterknown of these studies is that which wasperformed by Giunta [9]. He postulated that fora silo having a circular outlet with a diameterlarge enough to prevent arching and ratholing,the flow channel shape would consist of a coneemanating from the outlet and flaring out tosome diameter. In the upper portion of the bin orsilo, he postulated that the flow channel shapewould be cylindrical with a diameter set by themaximum size of the conical flow channel.Giunta tested his hypothesis on an 18 in.diameter flat-bottom bin having a single, centraloutlet. Test materials included industrial starch,pulverized coal, and iron ore concentrate. Hefound reasonably good agreement between theactual flow channel shape and his theory.

There are a number of limitations in applyingGiunta’s work as pointed out by Carson et al[11]. Unfortunately, as the work of these authorsillustrates, there is no straightforward anduniversal method by which the shape of a funnelflow channel can be predicted.

With non-free flowing bulk solids, relativelysteep flow channels form which tend to becomemore or less circular in cross-section some

Fig. 3: Funnel flow hopper – flow channel intersectingcylinder wall

t

P

p

t p

Pressurepeak

Distributedpressure peak

t = m p

Effectivetransition

Vertical bending halfwave length of cylinder

10

distance above the outlet. If the outlet is circularand its diameter is less than the bulk solid’scritical rathole diameter, a stable rathole willform whose diameter is approximately the sameas that of the outlet. With elongated outlets, thediameter of the flow channel will beapproximately equal to the length of thediagonal of the outlet. Again, if this diameter isless than the bulk solid’s critical ratholediameter, the flow channel will empty out whenthe silo level is lowered. The diameter of theresulting rathole will be approximately equal tothe diameter of the flow channel.

In both of the above cases, the wall pressure willbe essentially constant at any elevation unlessthe outlet is near the wall. Only then will thesteep flow channel intersect the wall. However,if this occurs, the resulting horizontal bendingmoments can be very large because of thehighly non-uniform wall pressures.

The other extreme is with free flowingmaterials. As shown by Carson et al, the steadystate flow channel angle with such materials isconsiderably less steep than the anglespostulated by Giunta. Furthermore, the authorsfound that with eccentric outlets, the resultingflow channel expanded at roughly the sameangle as in a bin with a centered outlet, and theeccentric flow channel’s axis of symmetry wasapproximately vertical. See Fig. 4.Unfortunately, this study failed to identify anycorrelation between steady state flow channelangle and material flow properties such aseffective angle of internal friction or angle ofrepose. Clearly, much more work needs to bedone with larger models, more bulk solids, andfull scale silos before any definitive conclusionscan be reached. In the meantime, the authors ofsilo design codes should write silo designrequirements to reflect a high degree ofuncertainty, not only about actual pressures, butalso about the angle of convergence of flowchannels and their boundaries.

Bulk solids that fall in between the extremes ofthose that are free flowing and those whichrathole, produce flow channels which fallbetween the extremes described above. Eachcase needs to be studied closely so as to avoidproblems with the design.

Expanded Flow – Single Outlet

An expanded flow silo is defined as one inwhich the lower hopper section has walls whichare steep enough and smooth enough for flow tooccur along them, whereas in the upper sectionof the hopper the walls are either too shallow ortoo rough for this to occur. Provided that theflow channel in the lower hopper sectionexpands sufficiently to prevent ratholing at thetop of this section (i.e., the diameter of the flowchannel exceeds the critical rathole diameter ofthe material), ratholing will not occur within thesilo. Furthermore if one assumes that the outletis sufficiently large such that arching does notoccur, and that no self-induced vibration occursduring discharge, then the followingcombination of loads can be considered. (SeeFig. 5) In the cylinder section and in the upperportion of the hopper where flow does not occuralong the hopper walls, the bin loads will be thesame as those which would occur in a funnelflow silo of the corresponding dimensions. The

Fig. 4: Flow channels with centered and eccentric outletsin a funnel flow bin or silo

a) Centered outlet b) Eccentric outlet

Flowchannelangles

11

lower hopper section where flow does occuralong the hopper walls, can be designed as ifthis were a mass flow hopper. However, sincesome convergence of the flow channel willoccur above this section, there will be no peakpressure at the top of this hopper section asoccurs at the top of a mass flow hopper where itintersects the cylinder. Therefore, the governingloading condition is usually that of initial fillpressures.

Multiple Outlets

If more than one outlet is present in a silo, it isessential to design the silo structurally towithstand the worst possible loading condition[12]. This usually occurs when one or more ofthe outlets is active while the rest are inactive.Even if all of the outlets are active but aredischarging at different rates, preferential flowchannels can develop even though functionallythe silo is designed for mass flow.

To account for these various design conditions,the silo should be designed for funnel flowloading conditions with an off-centered flowchannel occurring above one or more of theactive outlets. The most severe combination offlow channels must be considered whencalculating the eccentric loads.

MATERIAL FLOW PROPERTIES

Most silo design codes include, either in thecode itself or in the commentary section, atabulation of “typical” properties of a number ofbulk materials. One should approach the data insuch tables very cautiously. Interpolatingproperties or guessing properties on the basis ofsuperficial similarities in the description ofmaterials should be vigorously avoided. It isimportant to remember that it is not possible toknow, or to look up, the required flow propertiesof a granular material from its generic namealone. This is true not only of the bulk materialby itself, but also of the surface on which it issliding. For example, providing values, or arange of values, for wall friction of “coal onsteel” sounds simple but can be very misleading.Before using such data, one should consider thefollowing questions:

• What type of coal (e.g., bituminous, lignite,anthracite) was used in developing the datain this table?

• What was the particle size, moisture content,ash content, etc. of the coal which is beingdescribed?

• What type of steel and what surface finishwere used for the tests? If carbon steel wasused, was the variation from a smooth,polished surface to a rough surface (e.g., dueto corrosion) considered? If stainless steelwas used, was the surface rough (mill finishplate) or smooth (2B finish sheet or polishedplate)? If the steel was mechanicallypolished, was the direction of polish linestaken into account?

In our opinion, most such tabulations provide adisservice to design engineers in that they temptthe engineer to use them in spite of the warningswhich are given either within the table or inaccompanying text. An engineer can be lulled

Fig. 5: Expanded flow silo

pt

t p

t

Pp

Mass flowinitial pressuredistribution

Funnel flowdistribution(see Fig. 3 ifflow channelintersectscylinder wall)

t = m p

12

into a sense that he or she has some quantitativedata that is useful for design, whereas in fact, nosuch assumption is valid.

Material flow tests should be run wheneverpossible to accurately quantify the flowproperties (and range of flow properties) of thebulk material to be handled. This is particularlyimportant when the bulk material being handledis not free flowing, or when its flow propertiesare unknown, uncertain, or variable. Definingwhether or not a material is “free flowing” issomewhat subjective and a matter of debate. Inour opinion, the best way to define this is tobase it on the flow properties of the bulkmaterial and how those flow properties dictatethe type of flow which will occur in a given binor silo. For example, if it is known (eitherthrough experience or through flow propertiestests) that a given bulk material will not form astable arch or rathole in a given bin or silo, onemight reasonably conclude that this material inthis silo is “free flowing.” This same material inanother silo having a different flow pattern orsilo dimensions might no longer be considered“free flowing.”

If tests are to be done, we recommend thefollowing [13]:

• Flow function and effective angle of internalfriction. Measurements of a material’scohesive strength and internal friction anglesshould generally be run on the fine fractionof the bulk material, since it is the fineswhich exhibit most strength. Furthermore,concentrations of fines are usuallyunavoidable because of particle segregation[14]. Once these parameters have beenmeasured, it is possible to follow designprocedures to calculate minimum outletdimensions to prevent arching as well ascritical rathole diameters.

• Bulk density. Generally this is measured byconsolidating the bulk material to variouspressures and then measuring the resultingbulk density at those pressures. Such testsshould be run both on the fine fraction (inorder to use the resulting values to calculatearching and ratholing dimensions) as well ason the full particle size range. The largervalue should be used when calculating binloads.

• Wall friction. Generally it is easier to runthis test on the fine fraction of the material,and the resulting values typically don’t varysignificantly with particle size. It isimportant to run this test on both thematerial of construction of the cylindersection as well as that of the hopper.Consideration should be given to variationsin the initial condition of the silo walls aswell as conditions that can occur after usagedue to abrasive wear, corrosion, etc. Ingeneral, the smoother the wall surface, thehigher the wall pressure acting against it.

• Abrasive wear. A tester is available [15]which can quantitatively predict the actuallife of a bin or silo wall material due to abulk material sliding across it. This testercan also be used to determine the change inwall friction due to wear.

Each of the above parameters can vary with thesame bulk solid if any one or more of thefollowing conditions change:

• Moisture content• Time of storage at rest• Particle size distribution• Temperature• Chemical changes

Note that we have not included in the abovelisting the measurement of the value of Kj. Inour opinion, this parameter is more silo-

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dependent than material-dependent. Therefore,attempts to measure its value for a given bulksolid are inappropriate.

FORCE RESULTANTS

Tension

In a circular bin or hopper wall with uniformpressure on the circumference, the onlyhorizontal force resultant is ring tension. This iseasy to calculate and accommodate in design.

If the hopper bottom is supported at its top edge(i.e., the junction with the vertical wall), it willbe loaded in tension along the line of slope, aswell as ring tension. This too is easy to calculateand design for, but it is important to check formeridional bending.

Vertical Force, Upper Section

There is a vertical compression force in thewalls of the upper silo section due to theaccumulation of wall friction effects from thetop surface down to the level of the support.This is the sum of the horizontal outwardpressures at each increment of depth, multipliedby the depth increment and the wall frictioncoefficient. Add to this any loads from the roofclosure and self weight.

The critical buckling stress in the wall is thecriterion governing the thickness required tocarry this vertical compression. This conditionseldom dictates the thickness of reinforcedconcrete walls, but is a major consideration indesigning thin-walled steel or aluminum silos.

Bending in Flat Walls

Flat walls appear in rectangular bins or hoppers,or in a chisel-shaped hopper between a circularupper section and a slotted outlet. This bendingis always combined with tension in the plane of

the wall. In the upper section of a bin, verticalcompression may also be present. A flatreinforced concrete wall in bending must havetwo layers of reinforcing steel, adequatelyanchored at the ends by lap splices running intothe adjoining walls. In a steel design it is usuallyassumed that the tension or compression iscarried by the wall plate, and the bending iscarried by the external stiffeners.

The flat walls of a rectangular or chisel-shapedhopper, operating in mass flow, must remain asnearly flat as possible, or the mass flow patternmay be lost.

Horizontal Bending of a Circular Wall

This is the major resultant of a funnel flow,single eccentric flow channel reaching the upperbin wall. The horizontal radial outward pressureof the material on the wall is not uniform on thecircumference, so out-of-round bending isinduced. Non-uniform pressures insymmetrically filled and emptied silos can alsoresult in bending which needs to be evaluated.

Combined bending and tension effects can bestbe calculated using a finite element model of thebin wall loaded by the internal pressurescalculated over the whole circumference andheight. Alternatively, a hand calculation ofbending and tension in a ring can be performed.

The most important effect on a steel plate shellis the reduction in vertical buckling strengthresulting from an increase in the radius ofcurvature when the shell deflects out-of-round.If the construction is of reinforced concrete, thereinforcing steel must be provided in two layers,with adequate capacity for the bending and ringtension at any point.

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Vertical Bending of Upper Wall

In mass flow, as well as in a case of funnel flowat the point that the flow channel strikes thewall, a peak pressure develops at the effectivetransition. This may be on the full perimeter oran isolated patch, and is also transient. In funnelflow this peak pressure may be several timesgreater than the pressures above and below, andoccurs on a very shallow band. The forceresultant is bending in the vertical direction. In aconcrete wall the result may be the developmentof horizontal cracks.

Vertical Force on a Flat Bottom

This is calculated using a value of Kj which willmaximize the vertical pressure. One mustremember that a large portion of the grossweight of contained material is carried by thebottom when the height-to-diameter ratio issmall. This portion decreases rapidly as theheight-to-diameter ratio increases.

Forces at Ring Beam

Perhaps the most common, even typical, designof a steel storage silo is circular, with a verticalupper section and a conical bottom hopper,supported at discrete points around thecircumference of a ring beam at the junctionbetween the two parts. A concrete silo willcommonly have a steel bottom hopper supportedfrom a ring beam which is either separate fromthe vertical wall, or built into the wall. This ringbeam accumulates the meridional tension fromthe hopper shell, and possibly the gross weightof the bin by vertical friction load from theupper wall. The tension from the hoppercontributes a horizontal and vertical component.The horizontal component from the hoppercreates compression in the ring beam.

The sum of the vertical forces creates bending,shear, and torsion in the ring beam. The bending

moments are negative (tension top) over thesupport points, and positive at mid-span. Shearoccurs at the supports. Torsion develops due tothe curvature of the beam, and is at a maximumat the points of contraflexure of the spans.

An additional force resultant is the rollingmoment. The line of action of the vector sum ofthe forces applied to the ring beam is unlikely topass through the shear center of the beam crosssection. The beam therefore tends to be rolledinside out. The net effect of rolling is anadditional vertical moment, applied at all pointson the circumference.

The ring beam must be designed toaccommodate all these forces in combination.

OTHER CONSIDERATIONS

Feeder Design

In addition to the geometry and materials ofconstruction of the silo, equally important is thetype of feeder which is used, as well as detailsof the interface between the hopper and thefeeder. This is particularly important if a massflow design is to be used in which case thefeeder must ensure that the outlet area is fully“live” [16, 17]. Feeder design is also importantwith funnel flow or expanded flow silos since,depending upon the details of the interface, theflow channel may either be centered oreccentric. Also important is the operation of agate at the outlet. If such a gate is used inanything but a full open or full closed position,it may upset the development of mass flow orthe type of flow channel which develops infunnel flow or expanded flow. A partially closedgate – even if only just projecting into flowingmaterial – can prevent flow along significantportions of the hopper wall.

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Thermal Loading

Many bulk solids are fed into silos at atemperature significantly different from that ofthe surroundings. In such cases, calculationshave to be made to estimate values for rate ofheat flow out of, or into, the silo, temperaturegradients through the wall, and change oftemperatures in the silo contents. From this,design can proceed to such things as heatinginput, selection of insulation, (e.g., to maintainthe contents at a carefully controlledtemperature, to prevent freezing) orstrengthening the walls to safely resist thermalstresses.

There are two distinct and different conditionsto be analyzed [18]. The worst thermal effectsare usually found in the walls of a silo above ahot material surface. Here the temperature ismaintained at a high level while fresh materialcontinues to be fed into the silo. As hot materialcontinues to be fed into the silo, the surfacerises. Material already in place, and successivelevels of wall, are buried. Material at a hightemperature comes in contact with the wall at alower temperature. This causes a brieftemperature excursion affecting a narrow bandof the wall, following which all the temperatureswill start to fall as heat flows through the wall tothe outside, and a zone of cooled materialdevelops against the wall.

The other condition to be considered in designexists below the material surface, wheretemperatures fall as heat flows to the outside. Atemperature gradient develops through somethickness of the granular material, from the hotinterior to the cooler wall. Gravity loads willtherefore co-exist only with reduced thermalloads. It is of interest to know the time taken forthis temperature gradient to develop to somecritical point, such as temperature falling belowfreezing at the inside face of the wall.

NOMENCLATURE

D = cylinder diameterh = hopper height

Kf = defined by equation (9)Kj = Janssen ratio of horizontal to vertical

pressureni = defined by equation (5)nf = defined by equation (10)p =pressure acting normal (i . e . ,

perpendicular) to a silo or hopper wallq = vertical pressure acting at top of hopperz = vertical coordinatez1 = vertical distance along cylinder wall

starting at point of intersection of toppile

z2 = additional vertical height added to z1 toaccount for pile height

g = bulk densityqc = conical hopper angle (measured from

vertical)m = coefficient of sliding friction between

bulk solid and wall surfaces¢/gB = see Fig. 58 to 62 of ref. [1]

t = shear stress acting along wall surface indirection of flow

f¢= wall friction angle between bulk solidand wall surface

REFERENCES

[1] Jenike, A.W.: Storage and Flow Solids,University of Utah EngineeringExperiment Station, Bulletin No. 123,Nov. 1964.

[2] Samuels, B.: Silo Design: Setting theStandard. Presented at a meeting ofAmerican Concrete Institute Committee313, Vancouver, March 31, 1993.

[3] Boaz, I. B., Private communication.

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[4] Jenkyn, R. T. and Goodwill, D. J.: SiloFailures: Lessons to be Learned.Engineering Digest, September 1987.

[5] Purutyan, H., Bengtson, K. E., and Carson,J. W.: Flow-Induced Silo Vibrations.Proceedings, Powder & Bulk SolidsConference/Exhibition, Chicago, May1993.

[6] Carson, J. W., Jenkyn, R.T., and Sowizal,J. C.: Reliable and Economical Handlingof Bulk Solids at Coal-Fired Power Plants.Bulk Solids Handling, Vol. 12, No. 1, pp.11-16, Feb. 1992.

[7] Carson, J. W. and Jenkyn, R. T.: How toPrevent Silo Failure with RoutineInspections and Proper Repair. Powderand Bulk Engineering, Vol. 4, No. 1,pp. 18-23, January 1990.

[8] Jenike, A. W.: Effect of Solids FlowProperties and Hopper Configuration onSilo Loads. Unit and Bulk MaterialsHandling (Loeffler, F.J., and C.R. Proctor,eds.), 1980, ASME, pp. 97-106.

[9] Giunta, J.S.: Flow Patterns of GranularMaterials in Flat-bottom Bins.Transactions of the ASME, Journal ofEngineering for Industry, 91, Ser. B,No.!2, pp. 406-413.

[10] Carson, J.W. and Johanson, J.R.:Vibrations Caused by Solids Flow inStorage Bins. Proceedings, InternationalPowder and Bulk Solids Handling &Processing Conference, Rosemont, IL,May 1977.

[11] Carson, J.W., Goodwill, D.J., andBengtson, K.E.: Predicting the Shape ofFlow Channels in Funnel Flow Bins andSilos. Presented at the American ConcreteInstitute 1991 Spring Convention, Boston,March 17-21, 1991.

[12] Carson, J.W. and Goodwill, D.J.: TheDesign of Large Coal Silos for Safety,Reliability and Economy. Bulk SolidsHandling Vol. 4, No. 1, pp. 173-177,1984.

[13] Marinelli, J. and Carson, J.W.: SolveSolids Flow Problems in Bins, Hoppers,and Feeders. Chemical EngineeringProgess, pp. 22-28, May 1992.

[14] Carson, J.W., Royal, T.A., and Goodwill,D.J.: Understanding and EliminatingParticle Segregation Problems. BulkSolids Handling, Vol. 6, No. 1, pp. 139-144, February 1986.

[15] Johanson, J.R. and Royal, T.A.: Measuringand Use of Wear Properties for PredictingLife of Bulk Materials HandlingEquipment. Bulk Solids Handling, Vol. 2,No. 3, pp. 517-523, 1982.

[16] Bridge, D.T. and Carson, J.W.: How toDesign Efficient Screw and Belt Feedersfor Bulk Solids. Proceedings. Powder andBulk Solids 12trh Annual Conference,Rosemont, IL, May 1987.

[17] Marinelli, J. and Carson, J.W.: Use ScrewFeeders Effec t ive ly . ChemicalEngineering Progress, pp. 47-51,December 1992.

[18] Jenkyn, R.T.: How to Calculate ThermalLoadings in Silos, Bulk Solids Handling,Vol. 14, No. 2, pp. 345-349, April/June1994.