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I Q Agar Major profe% Date ”3- 26 o 1963 0-169 U ..-.-——-—..—-. ova—“VA. . _,-,_A_.,_. fi,..m-.-.‘on . ABSTRACT AN ANALYSIS OF SILAGE PRESSURES IN CYLINDRICAL TOWER SILOS by Wei Wen Yu Constant reports of silo structural failure called for an investigation into conditions within filled silos. Horizontal,vertical and frictional silage pressures were measured fromeSOft. silo 60 ft. high, for immediate ap- plication in silo design. In the past four years, strain-gage pressure cells, pressure panels, air pressure gages and two-way gages were used to measure the pressures in a 30 x 60 ft. silo. These pressures are affected by unit weight of silage, coefficient of friction between silage and silo walls, the ratio of horizontal to vertical pressures, moisture contents and method of handling. The variation of unit weight of silage, coefficient of friction and the ratio of horizontal to vertical pressure were measured and formulated in terms of depth of silage. Maximum horizontal pressure was observed at an elevation of 5 to 10 ft. from the bottom of the silo, each year. The frictional pressure on the silo wall remained almost constant when the silage depth exceeded 40.ft. Vertical pressure on the floor had several high Wei Wen Yu pressure zones. Empirical formlas were developed by least square curve fitting and may be used as a refer- ence for the design of 30 ft. diameter silos. An analytic investigation was made to find satis- factory formulas upon which to base silage pressure calculations. Horizontal,vertical and frictional pres- sures were analyzed with and without considering arch action in silage. The occurrence of maximum horizontal pressure before reaching the bottom of the silo is characteristic of the pressure distribution along the depth when considering arch action. No such occurrance is found when there is no arch action. More experimental data are needed on density, coef- ficient of friction between silage and silo walls, pres- sures and the ratio of horizontal to vertical pressure to verify the validity of the assumptions used.in this study. Approved/Qflpmg/ fi/fi’fl/QQZ AN ANALYSIS OF SILAGE PRESSURES IN CYLINDRICAL TOWER SILOS By Wei Wen Yu A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1963 VITA Wei Wen Yu candidate for the degree of Doctor of PhiloSOphy Final Examination: August 26, 1963, 10:00 A.M., Room 218 Agricultural Engineering Building Dissertation: An Analysis of Silage Pressures in Cylindrical Tower Silos Outline of studies: Major subject: Agricultural Engineering Minor subjects: Civil Engineering Mathematics Personal data: Date of birth: October 9, 1931 Place of birth: Ro-tong, Taiwan, China Education: National Taiwan University, B.S. 1954 Michigan State University, M.S. 1960 Michigan State University, 1960—1963 Experience: Junior engineer, Technical Division, Wu-sheh Dam Project, Taiwan Power 00., Taiwan, China. 1955-1957. Junior engineer, Design Division, Irrigation Section, Provincial Water Conservancy Bureau, Taipei, Taiwan, China. 1957-1959 Graduate research assistant, Agricultural Engineering Department Michigan State University, 1959-1963 Professional and honorary societies: The society of the Sigma Xi Chinese Society of Agricultural Engineers American Society of Agricultural Engineers ii ACKNOWLEDGEMENTS I would like to thank Dr. James S. Boyd for his support and counsel throughout the course of the project. Sincere thanks are extended to Drs. A. W. Farrall, F. H. Buelow and Mr. R. Baird for providing funds for an assistantship which made possible the completion of this work. Appreciation is expressed for the interest and sug— gestions concerning this program from the members of the guidance committee, Drs. C. P. Wells, C. A. Cutts, F. H. Buelow, Shosei Serata, R. H. Wasserman. I also owe a debt of gratitude to Ayako Susuki for help in preparation and typing of the manuscript. iii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . . . . . . . . Chapter I. INTRODUCTION . . . . . . . . . . . . . . . Objective II. REVIEW OF LITERATURE Silage Density Friction Coefficient Pressure Pressure Formulas III. INVESTIGATION. . . . . . . . . . . . . . Silage Density Friction Coefficient Ratio k Experimental Study of Silage Pressure IV. ANALYTICAL INVESTIGATION . . . . . . . . . Solution without Arch Action in Silage Solution Considering Arch Action in Silage V. RESULTS AND DISCUSSION . . . . . . . . . VI. SUMMARY AND CONCLUSIONS. REFERENCES . . . . . . . . . . . . . . . . . . iv Page iv 13 38 1+6 55 57 Table LIST OF TABLES Densities of corn silage . . . . . . . . . Coefficient of second and third degree poly- nomials for densities of corn silage by least square curve fitting . . . . . . . . Coefficient of polynomial equations for horizontal pressure. . . . . . . . . Coefficient of polynomial equations for frictional pressure. . . . . . Page 17 18 36 37 Figure 1. IO. 11. 12. 13. 14. LIST OF FIGURES Unit weight of corn silage from least square curve fitting . . . . . . . . . . . . . . Coefficient of friction between corn silage and stave silo walls by curve fitting . Ratio of horizontal to vertical pressure from two—way pressure transducer . . . . . . . Horizontal pressure measured by cells . . . . Vertical pressure measured by cells . . . . . Silage pressures measured by panels in 30 ft. silo, 1960. . . . . . . . . . . . . . . . . Horizontal pressure measured by panels and and air gages, 30 x 60 ft. silo, corn silage. . . . . . . . . . . . . . . . . . . Horizontal pressure during filling and empty- by panels 1, 2, 3 and A. 1960-1961 . . . Silage pressure measured by panels in 30 ft. silo, 1961.. . . . . . . . . . . . . . . Average pressures measured by panels from 1960 to 1962, 30 ft. silo, corn silage. . Horizontal pressure measured by panels and air gages, 20 x 60 ft. silo, corn silage. Horizontal pressure and vertical pressure measured from two—way pressure transducer . Estimated horizontal pressure at 90% normal distribution in 30 ft. silo from panel meas— urements, 1960-1962 . . . . . . . . Silage pressures measured by panels in 30 ft. silo, corn silage, from 1960-1962 vi Page 19 l9 23 26 26 28 28 3O 30 32 32 35 35 Al Figure Page 15. Horizontal pressure calculated from para-. meters 2,,» and k varying with depth of silage, 30 ft. silo . . . . . . . . 41 16. Pressures calculated from successive super- position, 30 ft. silo, without considera- tion of arch action in the silage . . . . . . A5 17. Pressures calculated with consideration of arch action of silage, 30 ft. silo. . . . . . A5 18. Horizontal pressure by successive super- position for silos of different diameters . . A9 19. Horizontal pressure considering arch action of silage, varying parameter c9 in k-function. . 51 20. Horizontal pressure considering arch action of silage, for silos of different dia- meters. . . . . . . . . . . . . . . . . . . . 52 21. Vertical pressures, with and without con— sideration of arch action in the silage . . . 53 22. Frictional pressures on the silo wall, with and without consideration of arch action in the silage . . . . . . . . . . . . . . . . 5A vii CHAPTER I INTRODUCTION For over 80 years, silos have played an important and necessary part in livestock farming. In earlier days horizontal pits were used for feed storage. Grad- ually, cylindrical tower silos became more common. The number of silos made of wood and blocks decreased with the increase in the size of silos required on farms. In addition to monolithic concrete silos, stave silos have become widely accepted. During the period 1940-1945, a study of silage pressure was made by the United States Department of Agriculture. The pressure was measured in full scale farm silos of sizes up to 18 ft. diameter, 45 ft. high. Empirical formulas for silage pressure were the results of this investigation. These formulas have been used commonly since then for calculating silo pressures. Recently, following the advance and development of field machines for harvesting, transportation of silage, and mechanization of feed handling, large silos have become more and more desirable. However, the knowledge of silage pressures in large silos,unfortunately,still was very limited. Builders designed silos according to their own experiences or by the extrapolation of existing 1 information on silage pressure. Numerous structural failures of large silos have demonstrated the need for information on which to base designs. Objective The objective of this study was to develop formulas for computing silage pressure in cylindrical tower silos. CHAPTER II REVIEW OF LITERATURE Silage Silage has been defined in the dictionary as fodder, either green or mature, converted into succurent winter feed for livestock through the process of fermentation. Silage which has been most common in livestock farming is as follows: 1. Corn silage: The corn crOp is harvested and fed in a wide variety of ways. The three most common methods of harvesting corn silage are (a) the whole- plant, (b) high moisture shelled corn, (c) high moisture ground ear corn. Sometimes the stalk is ensiled after the ears have been picked. A farm operator can use all three types of corn silage and adjust the rations as necessary because of changing needs in his livestock program. 2. Grass silage: Alfalfa, legume, and clover are very common. It is defined as silage made of uncured hay or forage crOps. Usually moisture contents of grass silage are very high, at 75% Or more. Excessive leakage of soluble nutrient in the juice is found as a result of high moisture contents of silage ensiled in the silo. 3 3. Grass haylage: To reduce the loss in nutrients, forage crops are wilted before ensiling. This process results in higher storage capacity and less loss in nutrient. Density Silage pressure was indirectly obtained from density by Otis and Pomroy (1957). They measured densities of corn silage by the layer method, the surface sampling method and the horizontal core sampling method at various elevations. The samples used for the density measurement were placed in airtight plastic bags and reused in the laboratory in pressure measurement. A portion of each sample was placed in a cylinder and compressed to the density in the silo at the time the core sample was taken. Comparison of the pressure obtained in the laboratory and density measured at sampling showed, good agreement with high density material located in high pressure area. Perkins et_al, (1953) found that both the stage of growth of the ensiled material and the depth of silage affect the silage density. They thought fineness of cut was an important factor affecting the density of silage, for both corn and alfalfa. James §t_a1, (1962) used a technique of passing gamma rays through the silage and measured densities by a gamma spectrometer, in a silo 12 ft. in diameter and 25 ft. high. They found that alfalfa silage density varied from 25 to 40 lbs. per cu. ft. and the density is not directly proportional to the depth of silage. Aldrich (1962) compiled apparent unit weight of corn or grass silage, with moisture contents of from 68 to 72% in tower silos. Data were obtained from silos up to 20 ft. in diameter and up to 40 ft. high. The curves were extrapolated beyond 40 ft. Friction Coefficient Kleis and Okamura (1962), using laboratory scale storage silos, measured friction of haylage on silos made of concrete, vitrified clay, Permaglass and wood staves. All test silos were 15 in. in inside dia- meter and 42 in. high, except the Permaglass units which were 16 in. in diameter. They were similar to conventional silos in effective cross section. Vertical forces were measured with predetermined silage weights and densities. Frictional forces were deter- mined by extruding the total haylage mass from the silo unit. Statical and dynamical friction were meas- ured. The results provide information on the magnitude of coefficient and forces as related to silo materials, surface treatment, densities, moisture content tempera— ture and crop type. As a by-product of panel measurements by Boyd and Yu (1963), frictional coefficient was obtained in conjunction with the measured horizontal and frictional forces. The frictional coefficient for corn silage was formulated in polynomial equation of silage depth. Pressure Silo deterioration and failures brought demands from farmers for assistance and to meet this demand an investigation was instigated at the New Jersey Agricul- tural Experiment Station in 1937 with the c00peration of the Bureau of Agricultural Chemistry and Engineering, USDA, to measure the pressures exerted on silo walls by grass silage. Pressure was found to be influenced by moisture content of silage, silo size and fineness of cut. Maximum values for grass silage varied from 159 lbs. per sq. ft. in a 12 ft. diameter silo with 64% moisture silage, wet basis, at 25 ft. head to 1189 lbs. per sq. ft. in an 18 ft. silo with 77% moisture silage at 40 ft. head. This was a range of from ap- proximately one-half to two and one-half times the pressure commonly considered in silo design which is 12 lbs. per sq. ft. per ft. of depth. The panel used for pressure measurement averaged about 4 sq. ft. in area. (Besley, 1941) Panels were developed by McCalmont (1946) to measure silage pressure. The pressure panel was built up of two layers of l by 6 in. lumber as in an ordinary silo door. To this were attached two vertical pieces of 3 in. T- section iron with 12 in. between the outside faces to transfer the load to the calibrated steel bars. The panel was supported on two 5/8 in. round alloy steel bars that passed through the holes in the T-section and rested in corresponding holes in the channels along each side of the doorway. The whole door panel was used as the sensing element to measure pressure. Test work began in 1936. During the following 6 years a total of 8 separate tests were made with corn silage and 17 with grass silage. The size of silos ranged from 14 to 20 ft. in diameter and 25 to 40 ft. in height. He found that corn silage exerted less hori- zontal pressure than grass silage under comparable moisture conditions, but high moisture corn silage caused much higher pressures than those for which silos had been designed. The increase in pressure due to the increase in moisture contents is greater than that due to increase in diameter. The frictional pressure, measured by vertical deflection of the rod in the pressure panel, was found not significant com- pared with the horizontal pressures. As the silage was fed out, the frictional pressure gradually decreased until they changed direction and actually exerted up- lifting pressure on the silo walls. One of the important develOpments associated with the mechanization of cattle feeding has been the use of larger diameter and higher silos. This increase in size presented a problem for the silo industry. Boyd and Yu (1960) developed a group of pressure cells, made of four A-l8 SR—4 strain gages attached to a stainless steel diaphragm. The cells were 2 in. in diameter and embedded in the concrete staves so the surface of the cell was flush with the wall. The staves were placed in 4 quadrants at 6 elevations, O, 2.5, 5, 10, 20, and 30 ft. from the ground in 60 ft. silo. Thirteen cells were placed on the floor in 4 radial directions. The highest horizontal pressure was found some distance above the bottom of the silo. During the summer of 1960,with the COOperation of the USDA,a 30 x 60 ft. silo was equipped with a column of pressure panels. These panels were similar to those used earlier in New Jersey and had an area of 5 sq. ft. per panel. Each panel was supported by two 1/2 in. heat treated steel rods mounted so that the rods were floating in a rigid support on the silo. The horizontal and frictional pressure was found from panel pressure measurement. Pressure Formulas In 1946, based on the panel pressure measurements by McCalmont (1946) in the previous 6 years, formulas for horizontal pressures were formulated by him. For silos 14 ft. and less in diameter D z1.195 2.65 and for silos 16 ft. and more in diameter 1.4 H = D z 5 (2) 5 where H = horizontal design pressure in psf z = depth of silage in ft. D = diameter of silo in ft. The formulas were recommended for the design of silos up to 20 :ft. x 45 ft. for both corn and grass silage with moisture contents below 74% wet basis. Gurrey, §t_a1, (1946) compiled the ACI standard for the construction of concrete farm silos in 1946. The horizontal pressure adOpted for the standard was obtained in a research study as described previously, by USDA, ACI, NSA, etc. Because silos are built with. heights greater than 40 ft. extrapolation became a lO practical necessity. Knowing the danger of extra- polation, Gurrey obtained the curve of best fit by least squares, disregarding moisture content. The ACI horizontal pressure formula then became, H = 3.3 2:1“ (3) in which H = horizontal pressure in 1b./ft.2 N H depth of silage in ft. The maximum moisture was specified as 75%. The vertical component, i. e. frictional load, was also evaluated. The curve of best fit for the data from the panel measure- ment was found to be, P: 5.5 731.08 (A) in which 2 F = frictional pressure in 1b./ft. z = depth of silage in ft. Newbauer (1960), using available data from ACI, formulated the pressure function in terms of depth of silage, diameter of silo, and moisture contents of stored material. Since the available data are limited to prac- tical existing conditions the suggested formula applies 11 only within certain ranges. He recommended that the following limits be used: 2 = 5 to 75 ft. d = 10 to 20 ft. m = 60% to 90% The proposed equation for the horizontal pressure was: H = 0.0133 2 (d - 6) (m - 50) (5) in which depth of silage in ft. N ll H = horizontal pressure in lb./ft.2 diameter of silo in ft. 0.» ll moisture contents in per cent 3 II The most pOpular formula being used by silo industries is the formula by Janssen (1895). The formula was derived under the assumption that the stored material is uniform along the depth of deep bins under consideration. Coefficient of friction, moisture content of material, and the ratio of hori- zontal to vertical pressure are independent of the depth. The first order differential equation was derived from the equilibrium of a thin layer of ma- terial in the silo. The solution was obtained as follows. l2 v _ W R (1 - exp (- kuh/R)) (6) kjl L = kV (7) in which V = vertical pressure of grain in lb./ft.2 L = horizontal pressure of grain in lb./ft.2 w = unit weight of grain lbs. per ft.3 U = circumference of bin in ft. R = A/U = hydraulic radius of bin in ft. ‘p = coefficient of friction between grain and bin wall k = ratio of L to V :3" ll depth of grain in ft. Janssen's formula is applicable when the material stored in the silo is uniform. He did not consider the variation of w,lp and k along the depth and possible arch action in bulk material. In silage pressure cal- culation, as the density, coefficient of friction be- tween silage and silo wall and the ratio k, vary with the change in depth of silage, Janssen's formula is no longer valid. A new formula is desired to include the variation of factors w,‘p.and k along the depth of silage and possible arch action. CHAPTER III INVESTIGATION As tools for investigation for silage pressures, direct and indirect methods have been used. The direct method includes panel, transducer, pressure strip and cell pressure measurements. The indirect method in- cludes density measurement and the pressure is found by reproducing the equivalent density with applied force. Most research workers found it extremely difficult to obtain the data on silage pressure for silo design. Silage pressure was affected by many factors such as density, friction coefficient between silage and silo wall, k, the ratio of horizontal to vertical pressure, maturity of silage, method of filling silos, and elapsed time after filling. Among those factors, density, coefficient of friction and ratio k are more signifi- cant and can be measured and controlled in the design of the silo. Silage Density An important factor causing pressure is silage density. In the process of ensiling, forage, grass and whole plant of corn are all chopped, and hauled by wagon to the blower. Silos are filled by blowing l3 l4 material to be ensiled in at the tOp of the silo. At the bottom of the silo, silage is compressed by the filled silage. Silage is usually cut 3/4 to 3/8 in. in length, but comparing with the fine grain material, it is irregular in size. The interlocking of leaves and stalks causes the mass of silage to become spongy. The additional load of silage causes the consolidation of material, similar to clayey soil in nature. Liquid in silage, then, is exuded and becomes free flowing liquid. From the observation of silo failures in recent years silos failed most often immediately after filling with excessively wet silage. When silage under the surcharge load arrives at the saturation limit, the excessive moisture will flow out from a drain or from Openings in silo walls. The density of saturated silage may become very high. Even at the saturation point, the density of silage may still be greater than that of water. In general, due to the cavity and air space in the silage mass, the upper limit of silage density may be considered as the unit weight of water. ’ We may assume that density is directly proportional to the increase in moisture content before saturation. Choppers now available all have adjustable length of cut. For forage crOps, leaves and stalks do not vary much in fineness of texture and relative structure and size. But 15 for corn silage, there are great variations. With a proper combination of sizes extremely high density is possible. On the contrary, extremely low density is also possible if only the light leaves accumulate at the down wind side Of the blower pipe. The fineneSs Of chopped silage thus may affect density. During the filling Operation, interruptions are very common. The filling operation may stop for several hours or several days and this unsteady rate Of weight increase affects the density increase. Research workers have found it extremely difficult to estimate density specifically from one silage to another. Several compilations of silage density were found, in Table l. (Otis and Pomroy, 1957). For calculating pressure by formula it is desirable to express density as a function Of depth, which can be specified definitely. Density can be defined as a function of depth Of silage, moisture content, length of cut, method Of handling, rate Of filling, maturity Of silage crops and weather condition during the en- siling Operation. Depth of silage and moisture con- tent can be expressed in numbers while the other fac- tors are qualitative and not controllable. Experience and investigation have shown that to avoid spoilage and keep the juice loss at the minimum the moisture content Of the silage should be held between 50 and” 16 85%. When the moisture content is low, due to its spongy property,the storage capacity is reduced. At the same time, silage spoilage may increase. If the moisture content Of silage is kept below 85% and above 50%, density can be specified in terms Of depth of silage only as shown in Figure 1. Polynomial equations are derived by means Of least square curve fitting. Sets of points from Table l were fitted into least square polynomials Of second and third degree. Coefficients Of the least squares polynomials are tabulated in Table 2. The second degree polynomial from data A in Table 2 is most desirable in relating density and depth for actual application. The equations recommended by author for use are as follows: £11 (2) = w = 40.519 + 0.434 2 , (8) £12 (2) = w = 34.779 + 1.121 2 - 0.0104 22 f13 (z) = w = 30.051 + 2.076 2 -(L045A-z2 + 0.000332 23 Friction Coefficient Two types Of coefficient of friction arise in tower silos, coefficient Of internal friction and coefficient Of friction between silage and silo walls. Coefficient Of internal friction is defined as tan— gent Of the angle Of repose of silage. From 1959 to 1962, the angle Of repose for corn silage was Observed by author l7 I I I I I mo cs I I I I I m.:w me I I I I I so om I I I I I m.mw mm I I I I I mm on I I I I I S m: I I I I I Ho o: oo mo m.m: mm we m.mm mm mm mm m: m.:m s: m.mm om mm :m m: :m we em mm on m: H: mm s: m.mm om o: m: o: Hm m: mm ma mm mm mm >2 mm me oh mm mm mm on em on m smwa mmma mama Head memHIoemH xoom .pm .mpm .axm omwa .mem .axm moo .ccaz saws moms .sm< .omaz Imm ammo .sma .cmm .osao some so .>Hcp spam meme meaflm MO m m Q o m < gamma .Bm .Do\.wmq ZH mwmDo mm 5 P- pf' —” _ 0 I ! l 0 200 400 600 Pressure in psf Figure 7. Horizontal Pressure Measured by Panels and Air Gages; 30 x 60 ft. Silo, Corn Silage 29 ft. above the measuring point, from then until the silage was removed the pressure dropped Off to zero. The vertical pressure, for the same 4 panels during filling increased to 125 psf at 40 ft. depth, and did not increase appreciably from 40 ft. to 60 ft. During emptying the vertical pressure did follow very closely the loading curve. When the silage was 10 ft. deep and 1ess,a negative pressure Of 30 to 40 psf was re- corded. This may be due to the spongy action Of the silage. In Octoben 1961, panel measurements were again made in the %)x 60fiu silo. Figure 9 shows the results Of horizontal and frictional pressures with average M.C. of 67.7%. During filling the silo distributor did not Operate which caused the silage to pile up on the silo wall Opposite the panels. This caused a loose fluffy filling against the pressure panels. The distributor was readjusted to correct its distribution when the silage was 25 ft. deep. The maximum horizontal pres- sure measured was 400 psf at 50 ft. depth and 300 psf at 60 ft. depth at the end Of filling. This pressure is much lower than that recorded in 1960, which was Obtained under good distribution during filling. This is an indication that distribution had an influence on silage pressure in tower silos. The distribution Of frictional pressure Obtained in 1961 was similar to . T ‘ l r ".00; a“. . . ' 10 L ":v.I".o.° .. cooo“.. ’ q s . . .. ' 20 - o ,. .- - - +2 °° ' ° . m *. . . a 30 - '. 2-. 2 - I 4% 00.0.0... .2. . 8‘ Ll’o _ moo ..° 0 o. q o °Loading . . “a.” . -Unloading ‘° 3, é,‘:; f3: 50 P 2' ‘27 . $0 . o 0 ..° , 0, 6O ! l “0 l O O 200 400 000 Pressure in psf Figure 8. Horizontal Pressure during Filling and Emptying by Panels 1, 2, 3, and4 ; 30' 0' Silo, Corn Silage .S m c _ .,—( 3‘3 3 -——-Avg. horiz. pressure Q -—n—-Avg. frict. pressure W . . . 1 I 0 200 400 600 800 Pressure in psf Figure 9. Silage Pressure Measured by Panels in 30 ft. Silo, 1961 31 that measured in 1960. The maximum frictional pressure was 150 lb./ft.2; however, a curve through those points would be close to 100 1b./ft.2 from 40 ft. to 60 ft., which is slightly higher than that in 1960. This small increase in frictional pressure being associated with a large decrease in horizontal pressure. Following the procedure Of the previous years' work, pressure panels were used again in measuring pressures, in October, 1962. The average moisture contents Of corn silage filled this year was 64.9% with a maximum 71.7% and minimum 53.0%. Due to the improper alignment Of the distributor, the silage was piled up on the side Opposite to the panels up to about 20 ft. Manual leveling was required, at the latter part of filling. The final maxi- mum pressure distribution was very similar to the past 3 years' results. At the depth Of 58 ft., maximum horizontal pressure was 640 lb./ft.2. The frictional pressure also was slightly lower than the past 3 years‘ results, but the distribution pattern was almost identi- cal. A summary Of panel pressure measurement from 1960 to 1962 are shown in Figure 10. Twelve air gages were built and installed during the summer Of 1961. TO supply air pressure, the air in the supply line was allOwed to react on the inside Of the shimstock diaphragm to balance the pressure exerted by the silage. As soon as the balance is correct air will by-pass the gage and cause bubbles to appear in the 32 60 j \I ,. / 1 a, ,0 ‘v/ 6” 94: J 0 . N N 95 a. 0.. I3 / solutions to the problem of calculating pressures in tower silos are pr0posed: 1. Solution without considering arch action in the silage. 2. Solution considering arch action in silage. Solution Without Considering Arch Action of Silage From the previous investigation, factors such as unit weight, coefficient of friction between silage and silo wall, and the ratio of horizontal to vertical pres- sure, were not constant along the depth of silage although 38 39 Janssen assumed constant values throughout the silo. When factors are assumed constant over a small increment of the depth of silage, say 5 ft., then the following derivation will be valid over£15ff, interval. In cylindrical tower silos, using assumptions similar to Janssen's,the equations for the vertical and horizontal pressures were derived as follows. Assume the equilibrium of the shown free body L D #1 I l VA N ‘I' HUdZ AWdZ I JdZ HUtangdzI' IHUtanadz (V + dV)A VA - (v + dV) A + Awdz - HUtan 0 dz = 0 ~ (15) and dV ( Ht 0U )d = W - Jan — Z A (16) assuming H = kV, the solution is found equal to V=wR(l-exp(-k}lz/R))/(k,ll) (17) Using the functions obtained from previous studies for w, p.and k, let 34.779 + 1.121 2 - 0.0104 22 f12(z) = w f22(z) =,u 0.698 - 0.00876 2 + 0.0000706 22 f32(z) = k 0.641 - 0.0149 2 + 0.000238 22 40 then H = f12‘Z’ R <1 - exp<-r32 r22 z/R) > (18) f22(z) and v = H/f32(z) (l9) and F = f22(z) H (20) can be obtained. In studying the variation in horizontal pressure along the silo wall the calculation was made in two dif- ferent ways. First, assume a variable w, p, k at each depth. The calculated pressure is approximated by least square curve fitting, and Figure 15 shows the results. Secondly by using the variable w,‘p, k at each depth, calculate the difference in successive two pressures of a 5 ft. interval. Then, the difference of pressures is successively accumulated. The results are shown in Figure 16. Solution Considering Arch Action in Silage Wet silage tends to settle faster than drier silage. When the silo is relatively tall compared to its diameter, the silage may not settle at a certain depth. At this Figure 14. 60 41 40L ) l 30 - Depth in Ft. 20 - 10 . Fric. Pr . O—4L Est. Fric. PrgE. 90% —-—- Avg. Horiz. Pr s. O—o-Est. Horiz. Pnns. 90% Interval of Grouping 5' L 0 200 l I .1 400 600 800 Pressure in psf Silage Pressures Measured by Panels in 30 ft. Silo Corn Silage, from 1960 to 1962 70 l I I I 60 - +; 50 r- a. c «4 4O ._ g 4..) 3 c: 30 '- 20 +_ = First degree polynomial_‘ 2 = 2nd degree polynomial 3 = 3rd degree polynomial 10 - _ O I J l l 0 200 #00 600 800 1000 Pressure in psf Figure 15. Horizontal Pressure Calculated from Parameters w, p, and k Varying with Depth of Silage, 30 ft. Silo 42 point the weight of silage is not directly transmitted to adjacent silage but to silo walls. The silage tends to form an arch which will hold the total or partial weight of the surcharge of silage. The detailed varia— tion of pressure in the silo is yet unknown. The ratio of horizontal to vertical pressure, k, is no longer a constant. Modification should be made in the k—function which will satisfy thetmundary condition. When the arch action occurs, the vertical pressure decreases to zero at the lower boundary of the arch. The load on the arch will be taken by the resisting pressure of silo walls. Consequently,the ratio of horizontal to vertical pressure becomes very great near the bottom level of arch action. At the top surface of the silage, neither vertical nor horizontal pressure exists. Therefore, the value of k at the upper boundary where depth equals zero may be assumed equal to zero. Let the ratio of depth z to the hydraulic radius of silo R equal n then, n = z/R or z = nR (21) Assume n = 10. Knowing that the ratio R varies from zero at zero depth to infinity at the depth of arch action, a function of n can be assigned to the ratio k then, k(n) = 10 n/(100 — n2) (22) 43 From the differential relation derived in the previous section, we have dV = (w - k(n) V,» ) Rd“ 3 (23) R By the change of variable the equation becomes dV = (w - ) dz R dV +11 k(n)V = wR (24) dn Solving for a particular case assuming dV/V = -k(n) )1 dn (25) Assume F(n) ‘Jn k(n) dn has been solved, then an= -}1F(n) +01 V = Cg exp (-»F(n)) (26) In order to find a proper value for the constant C2 to satisfy the boundary conditions, differentiate eq. (26) with respect to n, by considering C2 as a function of n. av/an = do? exp(-pF(n) ) - 02,1 k(n)exp(-p F(n) ) d“ (27) Using equation (24), (26), (27) dCe/dn = w R.exp(p F(n) ) (28) 44 By solving equation (28) c2 = w R G(n) + 03 (29) where G(n) =‘én exp(p F(n) ) dn (30) The solution of the vertical pressure becomes v = (w R G(n) + c3) exp< -p F(n) > (31) Apply the boundary condition n = 0, w = 0 C3 = 0 (32) Hence, the solution of differential equation becomes V = w R G(n) exp(1p F(n) ) H = k(n) V F =,u H where k(n) = 10 n/(100 - n2) (33) F(n) = 5 ln(100/(100 - n2) ) G(n) = G(n-l) + expguF(n{D)+ l/2[exp(7uF(n)) -exp(pF(n-l))] This gives the pressure under the arch action. In this derivation the unit weight of material and coefficient of friction are considered constant. Superim- posing the effect of variations of unit weight and coef— ficient of friction is done by using the functions as pre- viously defined. The resultson2130 ft. silo are shown in Figure 17. 7O 45 +—. rictional 50 __ Pressure 50 — 4., .5 Horizontal m Pressure C 40 - .4 .c 30 . .— Q Vertical Pressure 20 - 10 - 0 400 800 1200 1600 2000 Pressure in psf Figure 16. Pressures Calculated from Successive Superposition, 30 ft. Silo; without Considering Arch Action of Silage 70 6o — 50 -' , Frictional 5 Horizontal ” E 1K)«— Pressure Pressure c H .c 30 " -—-—» ‘3. Vertical m Pressur' c: 20 _. R = 7.5 _ lOn 10 k ‘ '1""‘00—'"- n2 n = i R 0 400 800 1200 1600 2000 Pressure in psf Figure 17. Pressures Calculated with Consideration of Arch Action of Silage, 30 ft. Silo CHAPTER V RESULTS AND DISCUSSION The experimental study of silage pressure in full— scale silos shows that the nature of the pressures is much more complicated than has been anticipated. The least square approximation of the various factors was obtained from data collected over a period of 4 years. Care, however, should be exercised in the general ap- plication of these results. Under normal conditions, unit weight of silage, frictional coefficient between silage and concrete silo wall are readily applicable. Equation (8) may be used both for grass and corn silage. The coefficient of friction given by equation (9) is only applicable to corn silage. The ratio of horizontal to vertical pressure was obtained from one year's experi- mental results. The mode of variation may be correct but further experimental evidence is needed to qualify these results. At this stage, the exact quantitative function for factors w,‘p.and k have not been formed, this experimental study offers additional information in an attempt to modify the existing formulas for the calculation of silage pres— sures in tower silos. 46 17 Figure 10 summarized the results of average hori- zontal and frictional pressure measured from 1960 to 1962. Grouping the data in 10 ft. intervals the hori- zontal pressure appears to be a linear increase with the increase in depth. The bulging of horizontal pres- sure was observed at the lower part of the silo when grouped in 5 ft. intervals. This bulging phenomenon has been observed each year in the panel pressure meas- urements. This bulging phenomenon may explain many past silo failures. In an analytic study of silage pressures, two hypothesis were made: first, the factors w, p, k vary according to the observed results without arch action of silage in the silo, and second, arch action does exist which affects these factors. Figure 16 shows hori— zontal, vertical and frictional pressure vs depth of silage when arch action is excluded in pressure cal- culation. The distribution of horizontal pressure is very similar to the pressure measured by panels but the magnitude is nearly 200 lbs. greater, at the depth of 60 ft. it will be inadequate and dangerous to con- clude that the empirical formulas from experimental data are the final result. 0bservations and experiments should be carried out over much longer periods of time to include possible extreme cases of pressure develOped in tower silos under different ensiling conditions. 48 Figure 18 shows the horizontal pressure calculated when disregarding the arch action of silage in different diameters, and may be recommended as the pressure on which farm silos should be designed. When the arch action of silage is considered, the horizontal and vertical pressure were derived.and cal- culated by assuming the ratio R as a function of n, where n equals the ratio of depth of silage to hydraulic radius of the silo. For function of k = 10n/(100 - n2), the pressure distribution is shown in Figure 17. The horizontal pressure, calculated considering arch action in silage, is almost three times as large in magnitude as that obtained from the panel pressure measurement but is identical in distribution pattern. The maximum pres- sure is found about l.0 R to 2.0 R from the bottom of the silo. In studying the pressure distribution corresponding to the change in k-function, let k = s}_n/( 100 - n2) and vary the parametercg. The horizontal pressure calculated by varying d from 6 to 20 was shown in Figure 19. The increase in parameter*:% causes a decrease in maximum horizontal pressure and a rise in the position of the action of maximum pressure. When 2% is less than 6, horizontal pressure increases with the depth having no bulging effect. When cA equals 20 the bulging effect of horizontal pressure is only half what it is when‘cfi = 6. Depth in Ft. 49 70 I | I I I D: ' D =.18' .=26I “23—9 D=22' ‘14 “La ‘5‘ 6O " 132.34Pl 50 - .. 40 h- _ 3o - - 20 - - 10 ~— 1 n O l I 1 l I 0 200 400 600 800 1000 Pressure in psf Figure 18. Horizontal Pressure by Successive Superposition for Silos of Different Diameters 50 Since the variation of arch action of silage in silos has not been well established, no criterion is given at present as to which <fi to use, but for s% = 10, the results seem reasonably reliable and are similar to the results actually measured. The horizontal pressures were calculated for silos of diameter 14, 18, 22, 26 and 30 ft. as shown in Figure 20. The vertical and frictional pressure were cal- culated together with the horizontal pressure and are shown in Figure 21 and Figure 22. Depth in Ft. 70 60 51 1 l 1 J, l I 400 800 1200 1600 2000 2400 Pressure in psf Figure 19. Horizontal Pressure Considering Arch Action of Silage, Varying Parameter a} in 1'C-Function Depth in Ft. 70 60 50 40 20 10 52 ‘ I l T D = 30' D — 26' D = 22' L. — D — 18' _ ////// 3 D=l4' / k = 10 n 100 — n2 Z n =‘TT— l 1 1 l l 400 800 1200 1600 2000 2400 Pressure in psf Figure 20. Horizontal Pressure Considering Arch Action of Silage for Silos of Different Diameters 53 70 I I D=30' 50' n'lo'o [at] 1' 21' iii/i” 60- 13:26' I l I i I _ I I I l / ' , / // 50_ 13:22 / l / _ D=18’ I / // / 32' no ‘ / /// I :3 / / f; D=l4' // /// §30- / w — / W W 20 _ ‘/ _ ///// //// lo /” - / —-— Without arch act-ion / With arch action 0 l l l J O 400 800 1200 1600 2000 Pressure in psf Figure 21. Vertical Pressures, With and Without Consideration of Arch Action in Silage 70 I I. ijj/ I I (\H , is" 433' /0/ $7 D=30' c: 609/ / / // 6O - PI ' - ég/ ’l/l/U/ D=26 //// 50 D=22' _ E 210 D=18' / _ 5. 3‘5 / 8 3o / _ / ---- Without arch action 10 With arch action ‘ O _ l l l l O 200 400 600 800 1000 Pressure in psf Figure 22. Frictional Pressures on the Silo Walls, With and Without Consideration of Arch Action in Silage CHAPTER VI SUMMARY AND CONCLUSIONS 1. The factors affecting silage pressure were evaluated. Variation of the density of silage, coef- ficient of friction and the ratio of horizontal to vertical pressure affect the pressure in silos. 2. The density, coefficient of friction, and ratio R were formulated as a function of a single vari- able under the assumption that the moisture contents of the silage lies between 50 and 80%. 3. Pressure measured in a 30 x 60 ft. silo for corn silage over 4 years was analyzed. The bulging of pressure near the bottom of the silo was observed. The accumulated pressure data from 1960 to 1962 were grouped. The average and standard deviation was cal- culated and empirical formula for the 30 x 60 ft. silo for corn silage was formulated by estimating the pres- sure at 90% normal distribution. Simple polynomial equation of a single variable was obtained by least square curve fitting. 4. Horizontal, vertical and frictional pressures were analyzed with and without considering arch action in silage.“ Assuming the arch action exists, the pressure 55 56 distribution is shown in Figure 17. The bulging of maximum horizontal pressure characterizes the pressure distribution with arch action. If there is no arch action of silage, pressure distribution is shown in Figure 16. No bulging of maximum horizontal pressure is found. 5. The formulas in equations (l8, 19, 20) can be used when the arch action of ensiled material may be neglected. The formulas in equations (33) should be used when possible arch action may occur. 10. 11. 12. REFERENCES Aldrich, R. A. 1963 Tower silos: unit weight of silage and silo capacities. ASAE Data, agr. eng. Yearbook, 1963. Besley, H. E. and McCalmont, J. R. 1941 Observations on the storage of grass silage. Agr. Eng. Vol. 22 No. 2. Boyd, J. 8., Yu, W. W. and McCalmont, J. R. 1960 Silo pressures in tower silos from two years test. ASAE Paper No. 60-911. Gurney, W. W. et a1. 1946 Recommended practice for the construction of concrete farm silos. Jour. Am. Conc. Inst. Vol. 13, No. 2./ Ketchum, M. S. 1919 The design of walls, bins, and grain elevators. McGraw-Hill Co., New York. Kleis, R. W. and Okamura, T. 1962 Haylage friction on various types of silo wall surfaces. ASAE Paper No. 62- 419. McCalmont, J. R. 1948 Silos: Types and construction. Farmers' Bul. No. 1820. USDA. MtCalmont, J. R., Krueger, W. C. and Eby, Claude 1946 Pressures and other factors affecting silo construction. New Jersey Agr. Exp. Sta. Bul. 731. Neubauer, L. W. 1960 A simplified equation for silage pressures with moisture variation. ASAE Paper No. 60-912. Otis, C. K. and Pomroy, J. H. 1957 Density: A tool in silo research. Agr. Eng. 806-863. Perkins, A. E., Pratt, A. D. and Rogers, C. F. 1953 Silage densities and losses as found in laboratory silos. Ohio Agr. Exp. Sta. Res. Cir. 18. Saunders-Roe Foil Strain Gauges 1960 Diaphragm gauges. FS, 6.4, Iss. 1. 57 13. 14. 15. l6. 17. 58 Taylor, D. W. 1960 Soil mechanics. John Wiley & Sons, Inc., New York, p. 488. Yu, W. W., Boyd, J. S. and Menear J. R. 1963 Silage pressure in large diameter silos. ASAE Paper No. 62—419. Boyd, J. S. and Yu, W. W. 1960 Progress report on the use of pressure cells for measuring silage pressure. Proc. Nat. Silo Assoc. Boyd, J. S. and Yu, W. W. 1961 Progress report of three years work to determine pressure in tower silos. Proc. Nat. Silo Assoc. Boyd, J. S. and Yu, W. W. 1962 Change in silo design from the period 1912 to 1962. Proc. Nat. Silo Assoc. 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