janssens equation

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Experimental Determination of Janssen's Stress RatioK. By Four Methods

A.O. Atewologun, G.L. Riskowski,A.J. Muehling ll'ABSTRACTThe stress ratio (K) used in design formulas ofgrain storage bins was determined by four different

methods. Static stresses from soybeans weremeasured in a 0.91 m diameter x 274 m high modelgalvanized steel bin. For the first method, the vertical loads on the floor and the wall were deter-"mined separately and K-ratio calculated fromJanssen's equation. The second method involvedthe measurement of vertical and hoop strains in thewalls of the model bin. Six two-element rosettegages were spaced at equal distances around theouter circumference of the bin 8;t15.2 cm above thefloor. The strains were reduced to stresses usingHooke's law for biaxial stress and membranetheory for thin-walled cylindrical shells. The thirdmethod was the use of dynamometric ring loadcells to measure horizontal and shear loads at thebin wall, simultaneously. Three wall ring cells wereplaced at different heights on the model bin wall(15.2 cm, 61.0 cm, and 106.7 cm above the floor).The fourth method was by direct measurement ofvertical and horizontal stresses within the grainmass using in-mass transducers (IMTs). These IMTswere used at four different heights at the center ofthe bin (15.2 cm, 61.0 cm, 106.7 cm, and 152.4 cmabove the floor). A total of 18 runs was performed.The K-ratio decreased with increasing depth ofmaterial at shallow depths. At depths of three timesthe diameter of bin, K-ratio approached a constantvalue that may be approximated by-Ko = 1 - sinewhere is the angle of friction of grain to grain.RSUM

La rapport K utilis dans les formules de calculdes silos grain tait dtermine par quatremthodes diffrentes. Les chargements statiquesdu Soya tait mesurs dans un modle cylindriqueen mtal galvanis, 0,91 m de diamtre x 2,74 m dehauteur. Pour la premire mthode, le chargement1. The authors are: ADENUGA O. ATEWOLOGUN, GraduateResearch Assistant, GERALD L. RISKOWSKI, AssistantProfessor, and ARTHUR J. MUEHLlNG, Professor, Agricultural Engineering Dept., University of Illinois, Urbana, IL.

vertical sur l'aire et l'espalier tait dtermin sparment et le rapport K tait calcul d'quation deJanssen. La deuxime mthode a impliqu lamesure verticale et un cercle aux tensions del'entourage de l'aire et de l'espalier modle l'extrieur autour de la circonfrence du silo. Lessix deux-lments gage rosette taient espacs des distances gales 15,2 cm au-dessus de l'aire.Les tensions taient r'duites par la loi de Hookepour deux axes tension et membrane thorie d'unespalier mince corps cylindrique.La troisime mthode a us d'un dynamomtrique charge cellule pour mesurer la charge horizontale et la charge en cisailles du silo et l'espalier,simultanment. Trois cercles en cisailles taientplacs diffrente hauteur, sur le modle du silo(15,~ cm, 61,0 cm et 106,7 cm au-dessus ge l'air,,';Pour la quatrime mthode on a mesur directement la tension verticale et horizontale l'intrieurde la masse de grains avec masse transducer(IMTs). Les IMTs taient uss quatre hauteurs diffrentes au centre du silo (15,2 cm, 61,0 cm, 107,0cm et 152,4 cm au-dessus de l'aire). Un total dedix-huit rampes taient accomplies. Le rapport K adiminu quand la hauteur du grain a augment pourles petites hauteurs. Pour des hauteurs de trois foisle diamtre de silo, la proportion K s'tait approche une valeur constante Ko = 1 - sinapproximativement, o est l'angle de frottementinterne du grain.

INTRODUCTIONJanssen's equation (Janssen, 1895) is used

extensively for calculating grain loads. The accuracy of Janssen's equation is greatly dependent onthe accuracy of the K-ratio, However, currentK-ratio values are subject to controversy due to differences in definitions and questionable measurement methods (Sundaram and Cowin, 1979; Glastonbury and Bratel, 1966).

The experimental method of determiningK-ratio on storage bins can be subdivided into threeapproaches according to the location of pressuremeasurement sensors :

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on the bin wall on a separately supported floor in the mass of the granular materiaiWall pressure measurements have been takenusing strain gages on steel reinforcement in con

crete bins (Pieper, 1969). Pressure diaphragmsmounted flush to bin walls have also been used togive direct stress values (Williams et al. 1987), andoutward wall deflections have been measured withlinear variable differential transformers (LVDTs) ordial gages. Wall pressure measurements give directinformation about the response of the designedstructural member and the material and installationcosts for prototypes are reduced. However, theflexibility of the wall distorts the results of model bintests. There are also problems in dealing with wallfriction values that are not accurately kjnow andthere are problems with very small strain ranges.Erratic results are th us common.

Floor pressure measurements involve theweighing of a floor that is supported separatelyfrom the bin walls (Janssen, 1985; Reimbert andReimbert 1976; and Jamieson, 1903). Though thisprovides little information on the local response ofbin sections, it has the advantage of averaging outlocal irregularities for. determining the averageK-ratio of the grain mass. Material and installationcosts are reduced for model testing and there isless need for statistical evaluation.

Few investigators have taken pressu re measurements within the mass of a granular materiaifor many reasons :

design foc uses on bin walls introducing a foreign body within a granularmass may change the existing stress pettern special sensors are needed calibration of sensors is difficult the need for statistical evaluation increasesTerzaghi (1920) used three vertical steel tapesin sand and he pulled the middle sandwiched tape

out through a groove. The force to pull the centertape out was related ta the horizontal force on theouter tapes. Perry and Jangda (1970) used a cylindrical diaphragm sensor sensitive to radio waves tomonitor flow patterns of glass beads. Clower et al.(973) jnvestiQated the variation in K-ratio for sugarbeet pulp, cornmeal, wheat and soybean meal bydrawing horizontally nd vertically oriented bladesthrough the confined mass. Moysey (1983) useddiaphragm sensors in model bins and Nichols et al.(1987) designed and tested a six-faced transducerembedded in soil to measure normal stresses in sixpredetermined directions under tractor load. Lee(1987) pulled thin plates coated with a monolayer ofparticies out of a plexiglass model bin filled withsteel spheres to measure interior stresses.

EXPERIMENTAL PROCEDUREA model bin was constructed and instru

mented to measure the K-ratio by for methods.was an open-ended cylinder, 0.91 m in diameter b2.74 m high and was fabricated from 0.93 mm thicsmooth galvanized steel. The four methods were;bin floor method; 2) wall strain method; 3) rintransducer method; and 4) in-mass transducersmethod. The arrangement of ail the componentsthe apparatus is shown in figure 1. A dial gauge wamounted to measure the wall deflection at 38 cmfrom the bin floor to determine if the model bin wastiff enough to ensure at rest conditions.

Bin Floor MethodThe bin floor was supported separately frmthe wall so the weight carried by the floor aloncou Id be determined. A clearance of 3 mm betwee

the floor and the wall prevented load transfer fromwall to floor. The floor loads were measured witthree cantilever load cells spaced evenly arounthe floor circumference. These load cells wercalibrated on a Tinus Olsen universal testingmachine prior to the grain load tests. A 10 cm diameter opening was cut in the center of the wood~floor and equipped with a sliding gate for unloadingrain. The wall loads were transferred directlythe laboratory floor without being measured. Thgrain was weighed before it was loaded into thmodel bin. Wall loads were determined by subtracting the floor load from the total weight of the graiin the bin.

Wall Strain Method

Two-element strain-gage rosettes were fixeon the outside wall of the model bin at a height15.2 cm fram the bin floor. Six rosettes were evenspaced around the bin circumference at the samheight to get an average strain at that height. Eacrosette was bonded onto the bin so one strain gagwas oriented in the horizontal axis and the otherthe vertical axis of the bin to measure the hoop anmeridional strain, respectively. The rosette systemwas not calibrated prior to the test runs. The strainwere reduced to stresses using Hook's faw fobiaxial stress and membrane theory for thin wallecylindrical shells.

Ring Transducer MethodRing load cells were developed for the simutaneous measurement of normal and shea

stresses which were based on the principles suggested by Smid and Novosad (1971). Each circular- 136 -


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ring was designed as a thin curved bar, having aradius of curvature at least ten times the thicknessof the ring. This constraint ensured that linear distribution of bending stresses cou Id be assumed inthe perpendicular cross section of the bar. Appliednormal and shear stresses cause bending stressesin the ring which, in turn, cause deformations on theouter and inner periphery of the ring. These deformations are combined in pairs of equal positive andnegative values by special wiring in a wheatstonefull bridge circuit. This corresponds to the stressesxerted on the outer fibers of bent beams on opposite sides of the neutral axis. The sensitivity isamplified due to larger relative deformations. Adetailed description of the design is given in Atewologun (1990). Normal and shear loads were transmitted to the ring by a 64 mm sensing plate. It wasdesirable to have a pressure sensing area of atleast twenty times the maximum dimension of thegrains (Perry and Jangda, 1967).On one side of the model bin, three 6.4 cmdiameter holes were cut out along the same verticalaxis at 15.2 cm, 61.0 cm, and 106.6 cm heightsabove the bin floor to fit the sensing plates of thethree wall ring load cells. A steel post held the threewall ring load cells in place. The wall ring load cells .were mounted to the post with a bracker that couldbe adjusted in three directions. The sensing plateswere adjusted to be flush with the inside of the walland so they were free to deflect without touchingthe wall.

Each ring Joad cell was calibrated in radial andtangential directions using known weights. Therewas a small gravit y effect, wich was subtractedfrom strain readings to obtain the actual strainvalues that correspond to applied loads. The performance of each transducer circuit was very gooqbecause the calibration curves were linear andInterference between the tangential circuit and theradial circuit was negligible.

InMass Transducers

Two in-mass transducers (IMTs) were designed to measure pressures within the soybeanmass. Each IMT had three diaphragm sensorsarranged to measure normal stresses in threeplanes (Figure 2). The three sensors were held inthe desired orientation by a rigid wire frame. Eachdiaphragm sensor was designed as a circular thinplate wilh fixed all-a round support. A detailed description of the diaphragm sensor design is in Atewologun (1990) Grains were glued to cloth whichwas fixed to the diaphragm of each sensor, whichgreatly reduced variation in data due to orientationof grains in contact with the diaphragm

On the opposite side of the bin from the ring load,four 12.7 cm diameter hales were cut to allow theplacement of the in-mass tra:lsducers. These fouropening, located at 15.2 cm, 106.7 cm, and 152.4cm from the bin floor were covered with plates afterthe IMTs were put in place.

~he IMTs were calibrated in a special bin withan air inflatable diaphragm on top of a soybeanmass which exerted uniform overburden pressureson the grain mass. This calibration bin was made ofthe same steel and diameter as the model test bin.The IMTs were embedded in the grain mass at thecentral axis of the bin.

A Measurement Group Inc. P-3500 strain indicator and two 8B-10 switch and balancing unitswere used to measure strains of ail cells, transducers, and strain gages. A Hamilton Baldwin 8T-340strain indicator and its accessory switch andbalancing unit were used for measuring the strainreadings from the cantilever load cells and thehopper weighing load cell.

Test Runs

Soybeans were used as the test grain in thisstudy. Their average water content was 9,2 % (wetbasis) and the average density was 7 KN/ma Atriaxial test done at Iowa State University gave aninternai friction angle of 32 for the soybeans,

Soybeans were loaded into two hoppers andweighed with a 22,000 N ring load cell. After fillingthe bin, the hoppers were weighed again to determine the weight of grain in the bin, The hopper waslifted with a forklift to a height of 15.2 cm above themodel bin and agate was opened allowing the grainta empty into the bin, The hopper gate was locatedover the center of the bin for axisymmetric loading,Loading was stopped intermittently as required toplace IMTs,There were a total of eighteen runs. Grain was

removed and reloaded for each experimental run.The same soybeans were used for ail the runs.Readings were taken for the floor, wall rosette, andwall ring load cell methods for each of the eighteenruns with the bin full of soybeans which providedeighteen replicates for each of these threemethods, Readings were taken immediately afterfilling the bin, one hour later, and again four hoursafter the original filling. The one-hour readings wereused for analysis because they were essentially thesame as those of the four-hour readings.For the first twelve runs, the two IMTs werealways placed in the concentric center of the binand the heights of the IMTs varied randomly amongthe four given heights from run to run. The order ofruns and the location of the IMTs was randomizedfor the test runs. This provided six replicates for the

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IMT reading for each of the four heights. The finalsix runs were done exactly as the first twelve,except the IMTs were located only at the twobottom heights and on the bin floor. This set of runswas performed to investigate the radial variation ofthe horizontal and vertical stresses within the grainmass fram the center to the bin wall. Readings weretaken at grain height intervals of around 55 cmwhile loading and after the bin was full.'

RESULTS AND DISCUSSIONBin floor methodBulk density was determined throughout the

study by using total grain weight loaded into the binand the known bin volume. The bulk densitiesremained essentially constant at around 7 KN/m3The vertical stress. S. at the bottom of the bin wascalculated by dividing the grain weight carried bythe floor by the floor area. This value was substituted into Janssen's equation to solve for K. A valuefor of 0.25 was assumed (which corresponds to afriction angle u of 14) which is for soybeans at9.2 % moisture content on galvanized steel (Mohsenin, 1986; Sitkei, 1986). The average K-ratio fromthe eighteen runs of the floor method was 0.55 witha standard deviation of 0.05, Table 1.

Wall strain method

8train data were reduced to horizontal andvertical stresses by

averaging the six strains in each direction calculating the magnitudes of the hoop (cir

cumferential) stress and the meridional stress inthe bin wall from the average strains, using Hooke'slaw for biaxial stress (Young, 1989).

Calculating horizontal and vertical stressesusing the membrane theory for thin circular shells(Billington, 1982).

The average K-ratio from the rosette straingage method was 0.40 with a standard deviation of0.08, Ta.ble 1. This K-ratio was omputed without aneed ta assume any value for the coefficient of wallfriction.

Ring transducer methodThe horizontal stress at each load cell location

was calculated using a sensing plate diamter of 64mm. The resulting horizontal stresses were substituted into into Janssen's equation to solve forK-ratio. A value of 0.25 was assumed for. TheK-ratio a the bin wall was found to increase withheight above the bin floor which means that itdecreased as grain depth increased, figure 3. The

average K-ratio at the 15.2;:- ~~ ;:~: :=.:: -= :~e binfloor was 0.44 with a stanaa'c cs. :=.: :~ :' = . J: forthe 61.0 cm height, the average -(-'El:;: .'.as 0.69with a standard deviation of 0.15 a~c a: :~e 106.7cm height, the K-ratio average 'lcreaseo :0 0.80with a standard deviation of 0.23 (Table'

!nmass transducer (IMT) methodThe IMT method was a direct measurement

procedure of obtaining K-ratio values. The observedstrains were converted to pressures using theln-grain calibration curves for the IMTs which wereobtained in a previous study (Atewologun, 1990)The results at each of the four heights are in Table1. The average vertical (8z) and horizontal (8)stresses both increased with grain depth. The vertical stress increased more rapidly than the horizontal stress. Figure 4. Therefore, the K-ratio at thecenter of the bin also decreased as grain depthincreased, Figure 3.ln this study, three normal stresses weremeasured on different planes with the IMTs (horizontal, plane, 45 angle to the horizontal plane, andvertical plane). The 45 angle diphragm was usedas a check for the readings fram vertical and horizontal planes. The vertical shear stress. Srz istheoretically zero at the center of the bin andmaximum at the wall because when grain is-Ioadedinto a bill, the vertical stress, 8z, tends inltially to bethe major principal stress. The shear stress 8rz wascomputed from :8rz = 845 - 0.5SM, - 0.58z

As expected, the IMT placed at the center ofthe bin gave shear stresses nearly equal to zero forail experimental runs. The readings from thediaphram a a 45 plane thus confirmed the dependability of the readings fram the vertially and horizontally oriented diaphrams Future measurements01' K-ratio in a grain mass with ln IMT would onlyneed the vertical and horizontal diaphrams.Comparaison of Kratio ValuesFrom Ali Four MethodsAverage K-ratio values obtained for the different load measuremnt methods and at the various

heights is summarized in Table 1. There was closeagreement between the Rosette strain gagemethod, the wall ring cell method at the 15.2 cmheight, and the IMT method at the 15.2 cm height(0.40 to 0.46). An unpaired t test for thesemethods at the 15.2 cm height showed no difference in the K-ratio mean values (P 005)However, as the height from the bin floor increased,

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the agreement between the wall ring cell methodand the IMT method diverged, Figure 3. Althoughthe K-ratio increased with height from the bottom ofthe bin in both cases, the shapes of the curves differed.

An unpaired t test showed the means for ailheights other than 15.2 cm to be statistically different (P 005). The IMTs measured K-ratio at thecenter of the bin and the ring load cells measured itat the walls, so K-ratio may vary radially from thecenter of the bin at shallow grain depths.For both the wall ring and IMT methods, the theK-ratio was found to decrease with depth. Regression analysis of the wall ring and IMT data showed astrong variation with height (P 0.01) in both cases.This trend corresponds with the results of Caugheyet AL. (1951), Reimbert and Reimbert (1976) andPleissner (1906). Amundson (1945), Clower et al.(1973) and Pleissner (1906). Amundson (1945),Clower et al. (1973) and Lenczner (1963) foundK-ratio to be constant with depth of grain whileKetchum ans Williams (Ketchum, 1919) and Kramer(1944) reported that K-ratio increases with depth ofgrain ln a storage bin.The floor-Ioad method gave an average K-ratiofor the entire grain mass of 0.55. Interestingly, the

CONCLUSIONS1. The floor method gave an average of the

K-ratio for the entire height of grain above the floorat the bin center. Reproducibility of the results wasvery good. The main objection to using the floorload method is that the K-ratio values depend on thechoice of the coefficient of friction (u'). Thus, unless'u' is known accurately, the K-ratio values obtainedfrom the floor method may be erroneous.2. Wailload meassurements obtained with wallload cells are good when combined with othermethods. Improper alignement of the ring sensingplates with respect to the bin wall would alter thereadings of the wall ring load cells substantially. It isrecommended that spl3cial care be exercised in thealignment of wall diaphragms so that they arecompletely free from and flush with the wall of thegrain bin. An accu rate value for u' is needed for thew8~1load cell method.

3. The rosette strain gage method is good ifseveral measurements are taken around the circumference of the bin. There was a wide variationof readings from one gage to another. Therefore anaverage of at least six measurements must beconsidered. Another limitation of the rosette straingage method is that if the strain levels are small, the

average K-ratio for the four heights of IMTs was0.53. An unpaired t test showed that the difference between these two means was not statistically different (P 005). This suggests that thefloor method corresponds to the average K-ratiowith height along the central axis of the binln the shallow bin range, wall ring cells gavehigher'K-ratio than the IMTs which suggests thatthe measurement of K-ratio values at the wall by thepiston-type sensor mounted flush to the wall willconsistently yield higher K-ratio values than the 1MTmethod.

The K-ratio values that have been obtained bysome past investigators for soybean range from0.38 to 0.54 (Table 2). The K-ratio values measuredin this work by the floor method (K' = 0.55) and theaverage of the IMTs over ail heights (K = 0.53)were similar to Ir'e value of 0.543 reported by Sundaram and Cowin (1979) who used the floor method.The K-ratio value of 0.43 from wall pressure diaphragms (Sundaram and Cowin, 1979) agreed closelywith the values from the rosette method and thewall ring cell method (K = 0.40 and K = 0.44, respectively) of the present study. Consistent differences in K-ratio therefore exist because of different measuremnt methods.

readings are subject to external interference fromtemperature, humidity, or vibration.4. In-mass measurements revealed a definitedecrease in the K-ratio as the depth of grainincreased. ln the shallow bin range, K-ratio as highas 0.67 was obtained. At depths greater than twice

the diameter of the bin, the K-ratio approached thevalue 0,47. The measurements of the K-ratio at thedeep bin range (15.2 cm and 61 cm above the floor)of the bin were not statistically different.The IMT method of measurement was successful. It has the advantage that measurementsmade away from the wall of the bin were notdependent on a choice of coefficient of friction ofgrain on the wall (u'). It compared favorably to thefloor load method if averaged over the height of thebin.

5. Of ail the four methods, only the floormethod gave a different K-ratio at deep bin range.The floor method K-ratio corresponded to the average of K-ratios at ail heights of the IMT method atthe center of the bin. Regression analysis of datafrom the wall ring and IMT methods showed astrong variation with depth (P 0.01) in the shallowbin depths. Although K-ratio decreased with

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increassing depth of material for methods, the walfring method gave higher K-ratios than the IMTmethod.6. It can be concluded from the results of thisstudy that the K-ratio is not a material property,because a true materiai property will not beaffected by depth of material (or overburden pressure) or diameter of the bin. Therefore the use ofthe Rankine coefficient

Ka = (1 - sin p)/(1 + sin p)for the design of grain storage bins cannot bejustified. Using an angle s = 32 in the above equation for the soybean material of the present study

gave Ka = 0.307, a value much below the K-ratvalues obtained at deep bin depths from ail fomeasurement methods. However the static earpressure coefficient commonly used in' smechanics (Ko = 1 - sin p) applied. to the temateriel used for this research becomes Ko0.470, which coincides with the K-ratio resultsthe IMT measurement method at deep bin depthsgrain. The use of the Rankine active coefficient fdesign in the case of the storage of the materiaused in the present study would underestimate th;vertical compression in the bin wall.

REFERENCES1. Amundson, L.R. 1945. Determination of bandstresses and lateral wheat pressures for a cylindrical grain bin. Agricultural Engineering26:321-345. ASAE, St. Joseph. MI.2. Atewologun, A.O.. 1990, Static stress distributionln tall cylindrical bins filled witl'l pseudosolid grains.Unpublished Ph. D. Thesis. Library. University ofIllinois, U rbana-Champaign.3. Billington, D.P. 1982. Thin shell concrete structures. Second Edition. Mc Graw-Hill Book CompanyInc., New York.4. Caughey, RA, C,w Tooles and A.C. ScheeL1951. Lateral and vertical pressure of granularmate rial in deep bins. Bulletin 173, EngineeringExperiment Station, Iowa State College, Ames.5. Clower, R.E, I.J. Ross and G.M. White, 1973.Properties of compressible granular materials asrelated to forces in bulk storage structures. Transactions of the American Society of AgriculturalEngineers 16:478-481.6. Glastonbury, BE and P.G. Bratel. 1966. Pressures in contained particle beds from a twodimmensional model. Transactions, Institution ofChemical Engineers 44:T128-T135.7. Jamieson, JA 1903 Grain pressures in deepbins. Transactions, Canadian Society of Civil Engineers 17:554-654.8. Janssen, H. A. 1885. Versuche uber getreidedruck ln sllozellen. VDI Zeitschrlft 39:1045-1049.'9. Ketchum, M.S. 1919. The design of walls, binsand grain elevators. Mc Graw-Hill Book CompanyInc., New York.

10. Kramer, HA 1944. Factors influencing tdesign of bulk bins for rough rice. AgriculturaEngineering 25:463-466. ASAE. Joseph, MI.11. Lee, W. 1987. The rheological nature of sopressures of granular media. Powder Technolog51:261-266.12. Lenczner, D. 1963 An investigation into thbehavior of sand in a model silo. The StructuraEngineer 41 :389-398.13. Mohsenin, N.N. 1986. Physical propertiesplant and animal mate rials. Gordon and BreacScience Publishers, New York.14. Moysey, E.B. 1983, Static and dynamic presures in grain storages. Phase III Report. DSS Cotract No. OSG83-00004. Scientific Authority, Wetern Regional Headquarters Agriculture CanadaSaskatoon, Sask.15. Nichols, TA, A.C. Bailey, C. Johnson and R.Grisso. 987. The stress state transducer for soTransactions of the American Society of Agricutural Engineers 30: 1237-1241.16. Perry, M.G. and H.A.S. Jangda. 970. Pressurein flowing and static sand in model bunkers. PowdeTechnology 4:89.96.17. Pieper, K. 1969. Investigation of silo loadsmeasuring models. Journal of EngineeringIndustry, Transactions of the American SocietyMechanical Engineers 91:365-372.18. Pleissner, J. 1906, Versuche zur ermittlung dboden and seiten wan ddrucke in getreidesil,o

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Zeitscrift des Vereines Deutscer Ingenieure30.976-98819. Reimbert. M.L and A.M Reimbert. 1976 Silostheory and pratice Series on Bulk Materials Handling. Vol. 1. No. 3. Translation Technical Publications. Clausthal. Germany.20. Sitkei. Gy. 1986 Developments in agriculturalengineering 8. mechanics of agricultural materials.Eisevi'er Science Publishing Company Inc NewYork..21. Smid. J. and J Novosad. 1971. Pressure cell formeasuring normal and shear stresses. PowderTechnology 4 322-327~2 Sundaram, V and SC Cowin 1979 A reas-

sessment of static bin pressure experiments.Powder Technology 2223-32.23. Terzaghi. K 1920. Old earth-pressure theoriesand new test results. Engineering News-Record 85(14) . 632-63724. Terzaghi. K 1943. Theoretical soil mechanicsJohn Wiley and Sons. Inc, New York.25. Williams. JC .. D. AI-Salman and A.H. Birks.1987. Measurement of static stresses on the wall ofa cylindrical container for particulate solids .Powder Technology 50163-175.26 Young. Warren C 1989, Roark's for stress andstrain, sixth edition. Mc Graw-Hill Book Company,Ine, New York.

Table 1. Average K-ratio values from all four measurement methods.Heights from bin floor (cm)

Method Replicates5.2 18.55(0.05)

646(013)

1840 1844(0.10)

610

047(007)*0.69(015)

106.7 15240

0052

0.67(007)

(0.15)**

0.80 (023)

* Height irrelevant to method' ..

(standard deviation in parentheses)

Table 2. K ratio for soybeans as reported by sorne past investigators.

Reference MethodsratioCaughey et al (1951) Floor load.383diaphragmsWall pressure430

iaphragms aloneFloor load alone.543

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45.7 IMT LOCATION

BIN

71.1

I-BEAM

PLYWOOC FLOORBINWALl- SUPPORTOCTAGONAL RING

1l!I1

1

1

l!I

STEELPOST

45.7

M...:t 45.7r-N

Figure 1. Mode1 grain bin (ail dimensions in cm)


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DIAPHRAGMSEHSOA

In-mass cransducar

~ ,6.35

o 56

50.80

-1

1

~ ,.6.35

D1aphragm sensor

Figure 2. In-mass transducer and its diaphragm sensor detail(aIl dimensions in mm)

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oo 0.4 . o.~K- ratio0.6 0.7 0.8

CDCo) 90cs-::sCftEcs~-.;:.-.CD~ 180ccs~C)

270

o 1MT s atcenter (method 4)X Rin9TransduClrw (method ~)

on the wall

Figure 3. K-r~tio variation with depth of grain at full load

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janssens equation

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