og G2 He a r rt ty te (a THS & THESIS A STRESS ANALYSIS OF SILO CONSTRUCTION Pol 1 Mes Pe edd) SBE) This thesis was contributed by —~=&B. Giffels Ry -¥y--Gé6fots under the date indicated by the department stamp, to replace the original which was destroyed in the fire of March 5, 1916. A Stress Analysis of Silo Construction A Thesis Submitted to The Faculty of MICHIGAN AGRICULTURAL COLLEGE By , , oy y R°FSCGiffels B.Giffels Candidates for the Degree of Bachelor of Science June, 1915 THESIS SCOPM OF THESIS. in this thesis it hac been our purpose to first determine how, in general, stresses are developed insilos, due to all the destroying agencies that may act upon them. We next determined what the usual practise in silo desien is, by analyzing several of the modern types of silos. Analyses were made of wood stave, reinforced concrete, metal, and vitrified tile silos. Our: results enabled us to decide as to the rationality or irrationakity of the present accepted theory of ensilage pressures, and to rec- commend changes in the assumed pressures of the ensilare. We were also enabled to reccommend a method of determining by experiments what stresses actually occur in the silos, and from these results to determine the most probable theory for the amount and direction of the internal forces. 96398 FORE‘TORD. The original intention in taking up this thesis was to determine the amount of the internal forces acting in a silo, and the manner in which they act. The reason for doing this was the beleif that no very complete and accurate theory for these forces had ever been worked. out. Our intention was to apply Jansen's Theory for the press- ures in tall bins to this field. However a thorough study of this theory showed us that it could not be satisfactorily applied. Two reasons for this became apparent. In the first place, Jansen's Theory was worked out for granular substances, such a8 grain, coal, sand, and similar materials. Ensilage is a fibrous material, entireky unlike those just named. Hence the theory could not be used with any assurance that correct values would be determined. Secondly, if Jansen's theory weww to be used, extensive experiments would be required to work out the constants involved; namely, the ratio between the vertical and horizontal pressures in the substance, and its angle of repose. For these reasons this theory was abandoned. We next attempted to investigate the values for silo rressures devehoped experimentally by the late Prof. F.H.King, of the Wisconsin Agricultural Experiment Station. Considerable time was spent in trying to determine themethods used by Prof. King in working out his experiments. In this we were unsuccessful (See letter from Mr. F.M. White, Agricultural Ensineerin? Dept, Wisconsin University, in insert.) Prof. King determined the horizontal pressure increment to be eleven 1bs. rer square foot per foot in depth. This seems to be quite gen- erally accepted among the agricultural colleses, as it is used by Wisconsin Agricultural College, Iowa Agricultural College (Bulletin 141, Iowa Aer. Fxp. Station), and has been used in design by Prof. H.H. Musselman of the Farm Mech. Department of The Michigan Agricultural College. Tor investigation we selected rerresentative silos of each common typee In making this selection we took those for which we had the most complete details of construction. The silos investigated were: The Ros: Wood Stave Silo; the Ross In-De-Str-Uct-0 galvanized metal silo, both made by The E.W. Ross Co., Springfield, Ohio; the Zyro galvanized metal silo, made by the Canton Culvert & Silo Co., Canton, Ohio; The Guernsay vitrified glazed hollow tile silo, made by The Guernsey Clay Co., Indianapolis, Indiana; and the Hy=-Rib Concrete silo, made by the Trussed Concrete Steel Coe, Youngstown, Ohio. This thesis has been mad e pos-ib&e only by the gener- osity of several manufacturers of silos. We especially wish to thank The E.W. Ross 60., The Canton Culvert & Silo Co., The Guernsey Clay Co., and The Trussed Concrete Steel Co. We also wish to thank Prof. C.A. Melick, and Prof. H.H.Mussel- ran for advice and sugcestions. We are indebted to "Walls, Bins, and Grain Elevators", by Ketchum, and"Modern Silo Construction", Bulletin 141, Iowa Experiment Station. Values for wind pressures were taken from the "American Civil Engineer's Pocketbook", TABL™ OF CONTENTS. Analysis of Ross Wood Stave Silo........eeeePave 2 Analysis OF Hetal SLlLOSeccccsccccevseess oosesssd 5 Ross In-De-Str-Uct-O Metal Silos. csccveesseee 9 ZDYLO Metal SLLOw.ccrccccescsccvecvesesessesece oe -13 Analysis of Guernsey Vitrified Tile Silo........19 Analysis of Hy-Rib Concrete Silo... ...ceececvveeend CONCLUSLONe ccccsvvnvcvecvesseseseseseseseeseser- een Pnotographs and Blueprints. ROSS Wood Stave Gildececccevcsvesvvsecsesesserace J Details of Joints of Zyro and Ross SiloSec.ceoee 5 ROSS Metal SilOc.ccccceccevecvvecsssvssecscsessesses & ZYLO Metal SLLOc.ccreccccccccrccccsvseccecevsersess la Guernsey Vitrified Tile Siloc..cccevvcevsvesevese L? Sectional View of Guernsey Tile Siloe....eceeee 18 Hy-Rib Concrete Silode cccvccccvsvccesessessesee oT Blue-print of Hy-Rib Concrete Silode.....cceeee-. 20 a ¢ 6 & & 4 # . ¢ ae - ° . < é oa ¢ #eg¢t¢ee# Vhorcughly Manutacturcd O ROSS ("wooo srave™ SIL 010 | * = ty ~ dae) | 7 - Us| wove) | | | ral) hha bad Ty , ah ty Lid] | : Ie P = Licensed under Harder Pat. No. 627752 Purnished in “LONGLEART YELLOW PINE, “OREGON” FIR . é ee ee oe oe i] POUT NUN eet ROSS WOOD STAVE SILO. ANATYSIS Of ROGS “OOD ETAVE FILO. This silo is 40 ft. high and 24 ft. in inside diameter. As shown by the photograph on the preceding pase, the con- struction consists of anx 4" set vertically and bound to- gether by round stecl hoopd@ threaded at each end, and malleable iron lugs. On page 9 of the manufacturers catalog included in the pocket is given a table of the number and size of hoops foe each size silo. This 40ft. silo has 6 #" hoops at the bottom and 10 5/8" hoops above. We assumed the hoops spaced 31" apart, leaving a distance of 7" from the top hoop to the top of the silo, and from the bottom hoop to the bottom of the silo. Inifiguring the pressure that comes on one hoop we assumed that the preszure that comes on that length of stave from a point half the distance to the next lower hoop, or to the bottom of the silo in the case of. the lowest hoop, to a point half the distance to the next higher hoop, is carried by each hoop. The numbering of the hoops in the following table of stresses is from the top down, the top hoop being number l. Areas of hoops given are areas at the root of a standard thread, as taken from the American Civil Engineer's Pocket-~ book. The unit stress necces-ary in all hoops to prevent defcrmation by shear between staves yvnen empty is computed, rather than full, becavse of the ad“itional resistance offered bv the ensilacre when tne silo is full. TABLT OF EOOP STRESSES DUE TO INVHNRNAT, PRESSURE. | Hoop. €tave length Mean Area Tension Unit Stress. : transmitting head. of in # pressure. hoop . "100De " ' Seine if 1bs/saein. 1 LO 1125 202 241.5 1195 2 31 38.5 202 1094.0 5410 3 a1 69.5 202 1975 9770 4 31 100.5 .202 2860 14200 5 31 131.5 .202 3740 18500 6) 37 162-5 .202 4620 22850 7 32 193.8 .202 5500 27200 8 31 22405 9 2OR 6380 31600 9 31 295.5 .202 7250 35900 10 31 £2625 202 8150 40300 11 31 317.5 .302 9020 29900 12 31 348.5 .302 9920 32850 13 31 379.25 2302 10800 35800 14 31. 410.5 .302 11700 -38800 15 31 441.5 .3@2 12550 41600 16 Lo 468.5 .302 9880 32700 WIND STRESCES WHEN EMPTY. On cylindrical surfaces a wind velocity of 120 mi/hr. gives a pressure of 20 lbs. per square foot of section nor- mal to the direction of the wind. (A.C.E.Handbook, paze493) Moment of wind on staves= 24 x 40 x 20'x 20:" =384000 ft elbDSe Assuming an additional height of 4 ft. for roof, Moment of wind on roof = 4x24x20:!x42' = 80600 ft.lbs. Total moment = 3840C0O + 80600 = 464600 ft. lbs. This moment produces shear between the different staves, this snear boing greatest in a plane through the center of the sil0, perpendicular to the direction of the wind, Let §& Total shear in section through the center, "MN Moment in the silo walls (Treatine whole structure as a beam fixed at one end) Let Y = Distance from centre of stress in half-section to neutral axis of section. Assuming unit stress at unit distance from neutral axis: M= f(y”) or iM =2(dley*)= 2a1(R sin ®)° (see Fic) Let F =.Total stress in half-section. F =2(y a1) =2(d1-R sin 9) Y=M =/4R°(1- cos 2@) do B ( dl = R ao) fFR sind 4o , %, #p (9 = + sin 20) < . = J——- -- - -- —-------- = WR/4 = .7854 R cos © Oo But S= u/ Y = 664600 = 24600 lbs. 07254 x 24 Assuming coefficient of friction of wood on wood to be e25, Total stress neccessary in hoops = 24600 = 49200 (lbs) 2X 25 Total area of hoors = 3.832 sq. in. Unit stress in hoops = 49200 # 3.832 = 12800 lbs. per sqein.e ce 3 Wh tee ee ti «aca | moe tHe “WHE bolts vi i oa J fill ey throvghe ty rf / i i a) f ee | Wiens OUTSIDE VIEW: Ht | | iH - +E | ae i | | I ; Vane een tt | rT | | | ! if | ae Jes Me ri ZYFo Foss hh | ’ i ne Sy fT ra | + ny Si in on ) s it ; * it | pe , py aa | | wee a: Ht | pe et : yo i AS. ) —_] ran TS HW Se : ; marones a HA CROSS - SECTIONS ware | ae A 2ANg | VERTICAL JOINTS EY zyRo 24NG Ha | sai | DETAILS or JOINTS ' oF ZYrRO AnD FOSS ) METAL SILOS | SCALE---- FULL SIZE . | F ! } | | H ‘4 OUTSIDE VIE , om } WwW ECTION y p) hs ee 4 » HORIZONTAL JOINTS HORIZONTAL JOINTS ; > 4 oo = amecceeseoen ow emaeeaews ee = ee | Cn i renee ED ane — pele ni et =e FD es oe «ae emma | es SEs - : ET my Ee, vs i | : Ce da R 5 ee ee eH ea 4 re J “5 “G throvghout N \ ANALYSIE OF MUTAT SITOS. Both metal silos tested are made of sheets of gal- vanized iron of varying thicknesses, according to the posit- jon in the silo at which they are used. The ends of the curved sheets are fastened together with bolts thru the vertical-outstanding flanges, as shown by the blue-print _ of the jointa, to form a circular ring. The rings are bolted together thru horizontal outstanding flanges. The difference in the construction of the vertical joint caused us to analyze both silos. The stress in any one ring of the silo is figured for the head that acts on a point three inches above the bottom of that fing, except in the case of the bottom ring, which is set in concrete, in which case it is figured for one foot above the bottom of the silo. ‘The unit stress at the root of the thread of the bolts is figured. The horizontal tension and the combined vertical compressive stresses in the body of the walls were figured, and then combined according to the method given on page 2°5, American Civil Engineer's Handbook. For the ratio between vertical pressure and the increase in horizontal tension caused by that pressure, we used 3 3; l- Due to the special construction of the vertical flanges, a method of computing the stress in each bolt had to be devel- oped Development Of Formuka for Ctress per rolt in Vertical Joih* Due to Unit Eorizontal Tension. Assume the bolts in the vertical flange to be drawn up snugly so that that pofition of the flange outside of the gause line will remain fixed in position, even thousch that porition inside the gauge line is deformed by a horizon- tal tension in the body wall. Assume that there is the same bending in the section tnrough the corner of the angle that there is in tne section alons the vsauge line for the bolt holes. If this assumption is true the bending moments in the two sections mentioned are proportional to their sectional AYCAS « (See blue-print of flanges) Let a = distance from back of angle to gauge line. " At= section area of corner of angle for a length equal to spacing of bolt holes. Let A"= Section area of metal between two adjacent bolt holes alonse the cauce line. Let *'! = Moment in A* due to P " i" = Noment in A" due to P Pa = ]t' + M" and Tt! : 1" = At: Af Mio At / an " m"(1 + AN/A") and rm = BEB Let b = distance from gauge line to the center of Pa pres:uge of the pressure existing between the outer halves of the two flanres. Let R = The amount of this pressuree In order that the summation of moments about the gauge line snall equal 0, Reb must equal NM". Roe= ii At “hen R= 1" bo _ a (A" # At)b Totel pressurc on G@ bolt= Rh + ?P T=P(1+A%.a __ ) ( (A" + A')b ) Galvanized METAL OSS IN-DE-STR-UCGT-O SILO = Ay ral : \ ‘ee | Le Se | 1 AE ales AUNTS PV VAR TUS Sot GE VRANTE Es he Mbt et —-— ROSS METAL SILO. Ross In-DeeStr-Uct-0 Vet 1filoe It will be seen from the blue-prirt on the precedinc vase and the cuts in tre manufacturers catalog that an arron flance is used for the horizontal joints, but in the vertical joints a U-shaped reinforcing strin is put over the flanres and the bolts put throuch four thicknesses of metal. As noted on pase 23 of the cataloz, the svacins of the bolts is 3 inches and their diameter is 5/16". On pase 44 of the catalog is a table of the sires, weights, caracities, anc the number of circles of the diff- erent cauces of material used. For the silo,4¢6' hich and £3! 105" inside diameter, and capacity of 42° tons” 14,565 1>s;3; there arc 7 circles of 14 saute, 12 circles of 16 sauge, and 3 circles of 1& Thickness of 14 gauge metal is 0.078125", of 16 sauce is 0.0625", of 18 sauge is 0.05" (Pace 394, Am. C.eE.Eandbook) As we were unable to obtain suffident data from the ranufacturer regarding dimensions of the vertical joints, (See letter in insert) -e were obliged to make assurptions as to the vosition of the gavrte line on the flange. We there- fore assumed that the pnorition of the flange outside the gauge line is the same width as the distance from th: gauge line to the back of the angle. The assumption that the pressure between the backs of the outer poition s of the flanges varies directly as the distance from the muge line 10 gives tne followinz formulas: b= 2/3 a T= P(1 + Ata ) ( (A" 4°A')b) Assuming thickness of reinforcins strip to be same as thickness of body wall, (Thickness = t) A' = 3.t sqe ine A" = Qoe (2t) = Se t T = 1.946 P The-area at the root of the thread of a 5/16" bolt is 0045 Sqeine In the fohlowins tanle of circles and stre: 3es the > Gircles are numbered consecutively from the bottom, the lowest circle beings Noe le TABLE OF MAX STRESES COMING IN THE LOWEST CIRCLE OF EACH GAUGT OF METAL. 23' 103" x 46' Silo. Noe of Thick- Eff. Tens.eper Tension Unit Unit Tens. rim ness. head 3"of ht. in bolt strees in body (Inches) (ft.) (lbs) (lbs) in bolt wall (#/sq.in) (#sq.in.) L 0078125 45.00 1343 2618 58100 5740 8 00625 51.75 949 1843 41000 5060 OL 095 5.75 172 334 7420 1145 COMPRESC IVE STRESSES Assuming a coefficient of friction of 0.35 Yor ensilazge on galvanized iron, the total dovmward force exerted b: the ensilace on the silo wall for any heignt H on a linear foot of horizomtal section is equal to ay” x 0.35 = 1.925 He Since weight of silo equals 14565:" and height is gt assure weight per foot equal to 3174. Effective perimeter is 3.1416 x 23' 103" = 75'. Averase weight per aquare fort is 3174/75 = 4.225lbs. 11 Compressive Stress Tue to Vind. Max. vertical commrescsive stress at any section, due to a moment 71, equals Me/I ES An) U/4n et wnere t = thickness of metal in inches, R = radius of silo in inches, and Mis in inch pounds. Assume effective height of roof to be 4 ft. Then moment in any ame section in inch pounds ig equal to: (Hd. of silace + 4')£.3.20(23.875 X 12) O(mff. Hd. + 4')f TAB. OF COMPRESCIV' STRESCES DUN TO WeIGit OF MUTAL AMD FeICTION OF BNSILAGH. No. of Thickness Zffective Comp.stress Comp. stres- rim. of metal. head. due to due to : wte of metal friction (inches) (feet) (#/sqe in.) (/sq. in.) 1 0078125 45 Qe 4160 8 00625 31275 179 2580 21 005 5.75 106 ABLE OF COMPRESSIV=S STRESSES DUE TO WIND. No.of Thickness “ffective Wind moment Comp.stress rim of metal head. in eection due to wind (inches) (feet) (inch lbs) (¢/sq. in.) 1 6078125 45 6,860,000 1070 8 00525 31.75 3,650,000 215 21 005 5.75 272,000 1202 TABLE OF COMBINED STRES:'SS. No. of Direct Total Cor-bined tensile rim. tonsile comoressive stress (Due to stres:; stress. direct tension ae compression) (!/sqein.) (!/sqein.) (f¢/sa. in.) 1 5740 5458 7560 8 5060 3469 G21L5 ol 1145 171 1202 ZYRO METAL SILO. 12 13 Tis 2% RO TVTAL ILO. From tie bluc-prinf shown precedins tc discussion ts of tre Ross silo, it will be seen that the norizontal joint of the Zyro silo is the same as that of the Ross. The vertical joint, however, is different, and in the Zyro silo consists of an "L" flanse and an anvron flanrte. Standard 5/16" bolts spaced 3" apart, center to center, are used in the outstanding flanzes. (See paso 13 of catalog) Tor table of weights and sizes of silos see pages 2 and 23 of catalog. In the 19'-9" x 50'-0" silo(The size anvlyzed); 18070 los. withse$ the roof and 14299 lbs. wit tne roof. There are three rims of 12 gause, 8 rims of 14 cauge, and 13 rims of 16 gauge. In the analysis of tne flanged vertical joint it is neccessary that one should have certain dimensions. “nen we wrote to the manufacturer for this data we received no reply. Hence we assumed that the widtn of that porztion of the flance outside of the gause line is tne same as that por#tion inside of it. Then assuming, as in the analy- sis of the Ross silo, that the pressure between tne backs of the outstanding flances varies as tne distance from the gauze line, wederive the following formulae: p=e23a T=P( 1+ Aba )) ( (A"+A') b) A'® 3 t sae in. 9 : 5 A"= 2 —%.t Sdeine = med SAeine 16 q 5 q 14 P(1l + 2.562 ta ) ( t(2.505 4+ 32)(273 a) ) T= 1.692 P HI tl (Tor derivation of above formulae and meanins: of letters used see discus:ion of Ross metal silo.) In tne following table of rims and stresses the rims are numbered consecutively from tne bottom, the lowest rim being Humber 1. TABULATION O° TENSILE STRESSES IT BOLTS AND VALLS OF ZYRO METAL SILO}; 19'-9" x 50!'-0", No. Tnickness "ff. Tens. Tension Unit stress Unit tens of head ver 3" in bolt inbolt at in wall. cim. of nt. root of thd (incnes) (ft) (lbs) (lbs) (1bs/sqein.) (lbs/sq.in) 1 0109375 AQ 1329 2246 50 ,000 4,055 4 0078125 43.5 1182 2000 44 500 5,040 lé 0050000 25.8 954 1610 35 ,800 6,360 Comoressive Stresses. As deyeloped in the discussion of the Ross metal silo, the compressive stress, due to friction of ensilae, in one foot of norizontal section is 1.925 He. where I is the effective head of ensilazte on the section. The total weight of the silo, with the roof, is 16070 lbs. (Sec catalog.) Wt. of silo without roof is 14299 lbs. Wt. of roof is 1761 lbs. If the>weisht were evenly distributed over the whole silo the averaze wei¢cnt per square-foot of surface of wall would be equal to: 14299/(50 XT X 1975) = 4.61 lbs. per sq. in. 15 As the weight of the roof is carried by (3.1416 X 19.75)f: the adiitional stress on each foot of norizontal section is 1761/(3.1416 x 19.75) #@% = 28.4 (lbs. per foot) Wind Stresses. Assuming the effective diameter of silo, inc]ludin: 40" fordeptn of feeding cmte, is 23', and the effective heignt of the ~oof is 3!, the moment in acy section due to a wind load of 20 lbs. per sq. ft. of cross section is equal to IM. (41 is in inch pounds) Mo= $.20(23 K 12)(Erf. hd. + 3)” = 2760(Eff.hi.+ 3) Stress due to Mis S. S =1/(4 R°t) where R is radius of silo and t is tnickness of wall. TABLE? OF COMPRESSIVE STRES "ES DUE TO HIGHT O* METAL AID FRICTION OF WNSILAGH. No. Thickness Eff. Comp.stress Comp. stres: of of head due to wt. due to friction. rir metal of metal. (inches) (ft) (:!/sqe in.) (#/sq. in.) 1 0109375 49.0 194 37580 4 0078125 43.5 244, 3280 12 «950000 268 630 2405 TABLE OF COMPRUSCIVE STRMSSFRS DUE TO WIND. No. Thickness Eff. Wind moment Comp. stress of of metal head in section due’ to wind rim (inches) (ft.) (inch lbs) (1bs@sq.in.) 1 .109378 49.0 17,455,000 1210 4, 0078125 43.5 5,974,000 1353 12 .050000 26.8 2,450,000 868 TABTZ® OF COMOLITE No. of Direct Total Combimed tensile rim. tensile compressive stress (Due to dir- stress stress ect tension and effect of comoress.) (los. /sq.in) (1bs./aq.in.) (lbs. /sq.in.) 1 4055 4988 — 6336 4 5040 4877 + 6566 Le 6360 3893 + 7658 Cucensey Twin Silos of Ponting Bros., Stonington, Ill. Two of the largest Silos in Mlinois, Diameter 20 ft.; height 50 ft GUERNSEY VITRIFIED TILE SILO. Li 18 a ‘ TWISTED TEEL KOD wo f ee ae i \ ae & 7 1) | } Sectional View showing Construction of the Guernsey Suo SECTIONAL VEIW OF GUERNSEY VITRIFIED. TILE SILO. 19 AUATMGIS OF CUEPIISNY VITRI-LISD TIL? SILO. This silo is 60! hien and 20' in inside diameter. The photogravnd on the preceding page snow the construct- ion. The walls are made of hollow vitrificd tile, one foot in heisnt, fastened tovetner with mortar joints and tile clamps, and reinforced with 7/16" square steel bands, twisted cold. (See c&balog in pocket, pages 4, 10, 13, and 15.) In this size silo the bands are laid in every course of tile for the first ten courses, and every second course from the tenth to the top of the silo. (See letter in pocket) In the first ten courses every second band crosses tne door opvening, under the ladder step, which is a steel angle. This angle also carries tension, and thus makes this part of the cir- cumference a3 strons as the rest. The entire burstins pressure was assumed to be taken by the bands, though the tile clamos and mortar joints really take part of tne tension. Since the sane size bands are used throughout, it was only neccessary to compute the stresses in the lowest band, and in the lowest one of the bands wnach are scaced two courses apart. That is, the stresses were fissured in the No.l band and in the No. 1]. hand, numberins from the bottom upward. “We also tested this silo for overturnins, due to wind load, when empty. The weight of the silo was 0 sonroximately determined by weighing a 15" by 15" 20 tile, made by anotnrer manufacturer, and assuming trat tne weiernt ver unit of surface was tne same for tnis silo. TABLE OF STRESSES IN RYINIFORCING BANDS. Guernsey Vitrfied Tile Silo. 20' x 60'. Unit No. of Area of Spacing Head. Pressure Tension Stress bande band. of bands. in band in band. (sq. in.) (ft) (ft) (#/sy.ft.) (lbs) (#/sa.in) 1 01907 1 59 649 6490 33000 11 21907 2 48 528 10560 35900 Overturning Moment Due to Wind. 12' x 50' Silo. In testing for overturning a different size silo was used tnan in testine for burstinz pressure. In each case the aim was to test that size silo which was most likely to fail from the action of the forces for whicn it was tested. Allowins 6" for thickness of wall, area of cross- section is 13 e« 60 + (6 . 13) = 728 sq. ft. (Assuning 6' additional height for roof) Moment of wind M' = 728 x 20 x 28 = 408000 ft. lbs. Weignt of 15"x 15" tile = 50lbs. Tnerefore assume weient of wall per square foot of surface equal to: 50(52)” = 32 Ibs. Weight of total surface = 12 x 3.1416 x 50 x 32 = 60,400 lbs. Using an effective lever arm of 5 fest, the resisting moment M", of this weight =5 x 60400 = 302000 ft. lbs. “This would not resist a wind pressure of 30 lns. per square foot on a flat surface , or 20 pounds on a cylindrical surface, but would just resist a pressure of 22.2 pounds per square foot on a flat surface, which would be produced by a wind velocity of 86 mi. ver hour. (p=a v when a = 2.003. Sec A.C.E. Handbook. ) 9 HY-RIB CONCRETE SILO. HY-RIB CONCRETE SILO. wo ANALYSIS OF HY=RIB CONCRETE CIT,0. A silo 50' hisn and 20! in inside diameter, of this make, was analysed. The walls are 34" thick in the lower half of tne silo, and 3" thick in th upver half. The walls are mide by plastering concrete on Hy-Rib, which is expanded steel. The construction is shown by the accompanying blue-prints and tne catalog in the pocket. T-e cross-sectional areas of tne strivs of Hy-Rib were determined from a Hy-Rib handbook. We assumed tnrat £2 gauge Hy-Rib was used for the lower one-third of the walls, 24 sause for tne next one-third, and 26 gauge for the top one-third. (See letter in pocket.) The steel was assumed to carry all the bursting pressure. The compressive stress in the concrete was com- puted, taking into consideration the weight of the structure, the weignt of the ensilage, and the wind stresses. The unit weight of concrete was taken to be 155 lbs. per cubic foot. The coefficient of friction of the ensilage on the silo walls was taken to be .40. The wind pressure was taken, as with tne other silos, to be 20 lbs. per sq. ft. of cross section. The bands referred to in the tabulations of stresses are numbered from the top downward. Each bend is a strip of Hy-Rib 2 fect wide, except between the doors, where the strips are 1'-5" wide, and are rein- forced with 3/8" Rib bars 10! long. TeNEION IN EY-RIB. 20' x 50! SILO. 0 iS No. of Mean Head Mean Head Total Tens. Tot. Tens. pande on band. vbetween doors in band. between Do. ft. ft. lbs. 1bd8. 1 1 Qe 2 G 660 3 5 4.71 1100 2070 4 7 1540 5 9 | 8.71 1980 230 6 11 2420 7 13 12.71 2860 5600 8 15 3031 9 17 16-71 3740 7360 1c 19 4180 11 PAl 20.71 4620 9110 2 Ro 5060 13 25 24.71 5500 10870 14. 27 5940 15 29 28.71 63 80 12630 15 31 6820 17 53 32071 7260 14400 18 35 7700 19 37 36071 8140 #8150 20 39 8580 OL 41 40.71 9020 17900 22 43 9460 23 45 44,71 9900 19600 24 47 10340 25 49 10780 AREAS AND STRESSES IN BANDS BETWEEN DOORS. Band No.of Area Gauze Area Total Total Unit No. Rib bars Rib of of area stress stress . bars Hvy-Rib. Hy-Rib. band. eqein. Sqeine Sqeine lbs. #/sqeine 3 1 1406 28 0246 03866 2070 5350 5 1 01406 28 0246 09866 3830 9900 ? 1 1406 28 0246 3866 5600 14500 9 1 ~1406 26 0246 03866 7360 19000 11 1 o1406 24 0328 04686 9110 19500 13 2 e2812 24 0328 ~6092 10870 17850 15 a 02812 24 0328 6092 2530 20800 17 3 e4218 24 0328 27498 14400 19200 19 | 3 04218 22 0387 86066 16150 20000 21 3 04218 22 0387 e8088 17900 22200 20 3 04218 22 0387 -8088 19600 24300 ARMAG AND STRESSES IN BAIS. (In vertical sections which do not pass throusn tN Ol doors) No. of Gaure. Area. Total stress. Unit stress. band. sqeine Los. Lhs./eqein. 1. 26 ed28 220 7 2 26 0328 660 2010 3 26 0328 1100 3750 4 26 6-6 528 1540 4700 5 26 > e328 1980 6040 6 26 ' 6328 2420 7400 7 26 0328 2860 8600 8 26 / 6328 3031 9250 9 26 0328 3740 11400 LO 24 0438 4180 9340 12 24 0438 4320 10550 12 24 0438 5060 11550 13 24 0438 5500 12550 14 24 0438 5940 13550 15 a4 0438 6380 14550 16 a4. 0438 6320 15550 17 24 0438 7260 16000 18 ae 0438 7700 14100 19 Qe 0546 8140 14900 20 20 0546 8580 15700 a1 22 0546 9020 16500 2:! De 0546 9460 17300 Qe De 0546 9900 18100 24 OA 0546 10340 18900 25 22 0546 10780 19700 COMPRESSIVE S233=STRESSES. The moment of inertia of a section of a thin eylinder = I = + A.R?, where A = area of section and R = radius of section. I x 3 x 3.1416 x 2434 x 34 x 122° Unit stress S§ = M.c (Due to moment of wind, 1) I = 52 x 20 x 20 x 246 x 12 x = 39.1 lbs/sca.in. =x 3.1416 x2434 x 34+ x 122 Assume weisht of concrete = 155 lbs. per cue ft. Volume of roof per inch of circumference = V' tO Ov Vi=ietxtx12 x 34 = 242.5 cue ine Volume of wall ver inch of circunference = V" vu = (12 x 25 x 3+) + (12 x 25 2 3) =1°950 cu. in. 26200 + 1950 = 2212.5 cue ine = 1.28 cu. ft. 1.28 x 155 = 198.5 = Weisht of wall and roof in pounds cer inch of circumference. 198.5 /33 = 56.7 = Unit stress at base of wall due to weight of silo. (lbs. per sq. in.) Mean head on wall = 25 fee t. 25 x 11 = 275 = Mean pressure on wall in lbs/sq.ft. Assume coefficient of friction of ensilate on concrete equals 40%. 408 of 275 = 110 = Mean vertical pressure in lbs. per square foot of wall. A FeO KI e = 131 =Unit stress in lbs. per sq. in. due to friction of ensilase on walls. 131 + 39.1 + 56.7 = 206.8 = Total unit edmpress- ive stress in walls at base of silo, in lbs. per sq. ine Resistance to Overturning. It will be seen from the computation of compressive stresses that tne tensile stress at tne bottom of the walls due to wind load is 39.1 lbs./sq. im. But the weight of the silo causes a compressive stress of 56-7 lbs. per sqe in. Hence at no time is there any tension developed in the vertical rods in the walls. For the game reason the silo will not overturn from wind load. CONCLUSION. It will]. be noticed tnat in all the silos analyzed very high unit stresses are found, by using Prof. Kine's value of eleven lbs. for the horizontal pressure incre- ment per foot in depth. Tensile stresses as high as 58000 lbs. per sqe ine were found in wrought iron bolts. In several cases the tensile stress in steel reached a point above the elastic limit of the metal. Since none of these silos are failures, the only logical conclusion is that the pressure increment of eleven lbs. per sq. ft. perfoot in depth is much to high. Since the elastic limit of wrougnt iron is about 25000 lbs. per sqe inch, tne actual unit tension in the W.I. bolts of the metal silos probably did not exceed this value, instead of being 58000 lbs. per sq. in. » as we found it to be. Therefore tne horizontal pressure increment did not exceed 25/58 of eleven, or 4.75 lbs. per sqe ft. per foot of depthe This value of 4.75 then seems to be a conservative value to use in design. The horizontal pressure on tne walls probably does not vary directly as the depth. The ratio between tne horixontal pressures is probably smaller at the bottom than at the top of the silo. Also the ensilage would seem to be held up by friction to a greater degree than at th= top. However, a study of the 28 eapacities, in tone, of various heights of silos of the same diamdter, shows us that tne density of tne ensilase is much greater at the bottom than at the top of the silo.(See page 22 of Zyro catalog in pocket.) This increase in density is offset by the decrease in the ratio of the horizontal to the vertical pressures. Therefore a reasonable working theory is that the horizontal pressures very directly as the depth of the ensilage. Probably the best method of determining these pressures would be to take extensometer measurements on the hoops of a stave silo while the silo was being fi filled, and after the ensilage had had time to settle. In doing this it would be neccessary to have the hoops loose enough at all times so that no stress would be developed due to the swelling of the wood staves. In this way the actual tension in the hoops due to the internal pressure could be found, and from tnese values the internal pressures at all heights could be computed. Another thing which will be noticed is that some of the silos examined would not withstand a wind press- ure of 20 lbs per sq. ft. of cross-section. However this pressure is given by a wind velocity of 120 mi. per hour. This velocity is attained only about once in @ life-time, and it would hardly be economy to design for this velocity with such small structures. This is especially true of the wood silo, the life of which is only about fiften or twenty years. 29 TUNA 3 1293 hI 4147