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~~B:.4~.Z~~~tWil~~~ DESIGN.AND CONSTRUCTION ·. PF SILOS AND BU.NKERS
SargisS.Safa'rian . , SMH Engineering Lakewood,Colorado
Ernest C. Harris,Ph.D. University of Colorado !)enver, Colorado
~- fl{ /):- a] ~a-inhofu--~ribga ~011{; Qio.,
;Iltt'l.
Preface Storage silos and bunkers for bulk materials are in ever increasing demand, with the' newer ones often surpassing any built previously in both capacity and complexity. Industry is also developing new uses for silos; beyond mere storage. These trends point to the need for an up-to-date, comprehensive presentation of structural analysis and design information to aid the designers, builders, and users of modern storage silos and bunkers for industry and agriculture. This book is written to meet that need. The authors have drawn heavily on their own design and construction experience plus that of others in the United States and other countries. The book brings· together technical information from many sources: technical papers, design standards, and design and construction codes. In Chapter 2, "Stored Material Pressures," the classical methods for computing static pressures are presented first.Then a modern interpretation of material-flow characteristics is presented, followed by methods by Reimbert, Walker, Jenike, and others for computing total pressures, that is, static pressures plus overpressure. Requirements of various codes and standards are also discussed. Methods of including the pressure anomalies due to eccentric discharge are shown. Following Chapter 3, "Silo and Bunker Loads," there are chapters devoted to the design of silos and bunkers of reinforced concrete, posttensioned and precast concrete, steel, and less common materials such as wood and masonry. In most of these, design examples are presented to show methods that the authors have used successfully. Silo failures have been quite common, and the engineer cari learn much by studying them. The authors have been called to investigate many such cases. Chapter lO describes failures and findings of various· investigators and tells of the repair methods used. Since poor detail has been a frequent cause of distress, this chapter and the chapters on design give considerable attention to details. It is our hope that this compilation of up-to-date design and construction information will help designers and builders of modern silos and bunkers to produce structures that are reliably safe, yet reasonably economical. SARGIS S. SAFARIAN ERNEST
C.
HARRIS
Acknowledgments The authors owe their thanks to many individuals and organizations who have assisted by providing valuable information used in this book. The help and encouragement of the following have been particularly valuable: ABL Engineering, Ltd., Edmonton, Alberta, Canada American Concrete Institute, Detroit, Michigan Gernot Appelt, URS Company, Denver, Colorado Vahe Aprahamian, Consulting Engineer, Des Moines, Iowa Dr. Alex Aswad, Stanley Structures, Denver, Colorado BBR Prestressed Tanks, Inc., El Cajon, California Leon Bialkowski, Consultant, Arlington Heights, Illinois Brick Institute of America, McLean, Virginia G. Broersma, Consultant, The Hague, The Netherlands Cargill, Inc., Minneapolis, Minnesota George Carhart: NCI of Minnesota, Inc., Minneapolis, Minnesota CBI Industries, Inc., Oak Brook, Illinois Claudius Peters, Inc., Dallas, Texas Clayton & Lambert Mfg., Co., Buckner, Kentucky G. P. Deutsch, Hardcastle & Richards Prdprietary Lim., Parkville, Victoria, Australia The Dodson Manufacturing Co., Inc., Wichita, Kansas Dundee Cement Company, Dundee, Michigan Dynequip Inc. (Peabody TecTank), Material Handling Systems & Equipment; St. Paul, Minnesota Fuller Company, Bethlehem, Pennsylvania . Danilo Guevara, P. E., SMH Engineering, Inc., Lakewood, Colorado IBAU Hamburg, Hamburg, Germany Ideal Basic Industries, Cement Division, Denver, Colorado International SiloAssociation, Inc., West Des Moines, Iowa The James F. Lin~oln Arc Welding Foundation, Cleveland, Ohio Dorian Janson, URS Company, Denver, Colorado Dr. Andrew Jenike, Consulting Engineer, Billerica, Massachusetts K .. Ketchek, Consultant, Rochester, New York Marietta Concrete Company, Marietta, Ohio
Dr. P. Martens, Institut fiir Silotechnik, Braunschweig, Germany Masonry Institute of America, Los Angeles, California McGraw-Hill Book Company, New York National Concrete Masonry Association, Herndon, Virginia Peabody Coal Company, St. Louis, Missouri Dr: K. Pieper, Universitat Braunschweig, Germany Plan/ Engineering Magazine, Barrington, Illinois Post-tensioning Institute, Glenview, Illinois Powder Advisory Centre, London, England The Preload Co. Inc., Garderi City, New York Dr. J.C. Ravenel, Industrial Engineer, Barcelona, Spain M. L. Reimbert and A. M .. Reimbert, Consulting Engineers, Paris, France S. P. Sheng, Consulting Engineer, Williamstown, West Virginia Steel Structures, Inc., Madera, California Minoru Sugita, The Shimizu Construction Co., Ltd., Tokyo, Japan Dr. K. Stiglat, lngenieurgruppe Bauen, Karlsruhe, Germany K. H. Schmidt, Universitat Karlsruhe, Korlsruhe, Germany Taisei Corporation, Tokyo, Japan Dr. 0. F. Theimer, Consulting Engineer, Munich, Germany Trans Tech Publications, Clausthal-Zellerfeld, West Germany Unadilla Silo Company, Inc., Unadilla, New York VSL Corporation, Los Gatos, California Dr. F. Wenzel, Universitat Karlsruhe, Germany Western Wood Products Association, Portland, Oregon Wilhelm Ernst & Sohn, Berlin, West Germany Wydawnictwo Arkady, Warszawa, Poland Special thanks and sincere appreciation go to Mr. George Carhart, who has acted as co-author of'Chapter 11, "Construction of Rein-forced Concrete Silo and Bunker Walls." The he/p of Dr. Andrew Jenike, Dr. Otto Theimer, and Dr. Fritz Wenzel who have read and commented on chapters related to their work, and Alex Aswad, who translated the French silo codes, is also gratefully acknowledged. Thanks also to Kyra Hauser and John Rarick for all the inked sketches, and to Mrs. Pearl Safarian and Mrs. Claudia Harris (the authors' wives) for their patience and hard work in typing the manuscript.
vii
Notations
A= area; interstice dimension (Fig. 4~19) A., Ab = bottom areas tributary to walls a and b, respectively Ag = total reinforcement area per unit width or per column AP = area of plate cross section AP• = area of prestressing steel per unit width A,= area of ring-beam cross section A,= area of stiffener, area of tensile reinforcement per unit width A;= area of compression reinforcement per unit width A,"= area ~f reinforcement in vertical direction per unit width B = hopper opening dimension; factor for Walker's method
C = Reimbert's characteristic _abscissa; silo capacity; coefficient C' = density coefficient for Platanov-Kovtunequations Cb, c., C9, CN, C, = overpressure coefficients (German Silo Code) Cd = overpressure coefficient C; = impact factor CP = factor for seismic force computation C, = multiplying factor for raft foundation design Ci, C3 = factors for ring-beam analysis D
= diameter; dead load
E = modulus of elasticity; earthquake load E' =' welded joint efficiency factor Em = modulus of elasticity of stored material in compressed
condition £1, £2 = pressure increase factors for eccentric discharge (Theimer)
I= moment of inertia I, = moment of inertia of stiffener
K = torsion factor; factor for crack-width in walls with bending; coefficient for stave silo tests; prestress wobble coefficient K., Kb, Kd = overpressure factors for Reimbert method for total pressures KL, Kg= load factors for dead and live loadi, K, = coefficient for wall temperature gradient Ki= factor for ring-beam analysis K, K1, Ki= constants for Ciesielski's method for nearly flat walls L = length; live load; subscript meaning "live" L, = stiffener length M ~ mass; moment; bending moment
MP= 10 kN (ten kilo Newtons) M' = moment applied to ring-beam by column M0 = overturning moment M, = radial bending moment per unit width; horizontal loading moment in ring-beam M,n = service load bending moment for flexural crack-width computation M, = tangential (circumferential) bending moment per unit width; applied distributed torque '. Mx, MY= bending moment (per unit width) in x- or j-directions Mx,u or My,u = ultimate bending moment in x- or j-direction due to temperaturegradient N = number (bolts, for example) Pn,w
F
= force; distribution factor for Walker's method
F;. = allowable horizontal inward force per unit length on ring-beam Fm = meridional force per unit width Fm•• Fmb = meridional force per unit width on walls a and b, respectively F, = allowable tensile stress; tangential force per unit width F,,., F,,b·= tangential force per unit width· on sides a and b, respectively · F.u = ultimate (factored) shear force per unit width
= nominal (theoretical) ultimate strength of wall per unit
width Pu = ultimate load Q = force Qc, = approximate section modulus of cracked section Qep = elastoplastic section modulus R = hydraulic radius; temperature change ratio (for stave silos) Rd = dome radius
S = section modulus; subcript for "secondary" G = shear modulus of elasticity , H= horizontal force; height of storage zone
T = tensile force; temperature; period of vibration Tb = anchor bolt tensile force ix
X
SILOS
AND
BUNKERS
T; = temperature of stored material 7~ = outside air temperature
/,; = average initial prestress in steer ./;' = ultimate tensile strength of concrete
h· = specified
U = cross-section perimeter
yield strength of steel
g = acceleration of gravity; subscript meaning "gravity": factor . V = shear:
seismic base shear; sum of vertical friction forces above point in question. V, = nominal shear strength of concrete alone per unit width V_. = total downward drag force
for Ciesielski's method for nearly flat walls h = wall thickness;
W = total
overall depth of beam or slab; effective thickness of stave wails: subscript indicating "hopper" It,= effective head '10 = heightof wall opening
Y = depth of stored material above point in.question
i = subscript meaning "imaginary" i"' = factor for Caquot's equations
Z = earthquake zone factor
j = subscript meaning "juice"
a= opening width; width of wall of rectangular or polygonal unit: coefficient for silage moisture a' = fictitious length for side of rectangular silo
k = ratio of horizontal to vertical pressure by stored material; stiffness k , = system stiffness
b = subscript meaning "bottom", wall width b,« =- effective width ',
I= length; distance along a tendon; subscript meaning "live" Ir= clear distance between supports
distance from neutral axis ( or centroid) to extreme fiber; subscript meaning "column" or "concrete"; hopper dimension (Fig. 4-57) c0, cb = coefficients for distributing bottom load to areas A0 and Ab er~ subscript meaning "crack" or "critical"
m
max= maximum; subscript meaning "maximum" med = subscript meaning "median" min= subscript meaning "minimum"
d = effective depth of flexural section, from compression face of
n = number (columns or welds,
weight of stored material; weight of designated structural element; distance between stiffeners
r: ,:
concrete to centroid of tensile reinforcing; subscript for "dead"; opening diameter d' = distance from compression face of concrete to centroid of compression reinforcing bars d" = distance, extreme fiber on tension face of. concrete to centroid of tensile reinforcing bars daN = decaNewton (10 N) des= subscript indicating "design" value
= concrete shrinkage coefficient; subscript meaning "meridional" or "mean"; hopper shape factor; ratio of increase in k due to unit lateral pressure
nr,
for example); ratio of unit weight increase due to unit vertical pressure, modular ratio (E.,/Ec) 11>, = factors for triangular and trapezoidal plate analysis
o = subscript indicating "initial" p = lateral pressure
q = vertical pressure by stored material e ==eccentricity; subscript meaning "emptying" or "earthquake" e 1 = slenderness ecc = subscript meaning "eccentric" or "eccentricity" eff = su bscript indicating "effective" eq = subscript meaning "equivalent"
f
r = radius; subscript meaning "ring-beam" rb = bolt circle radius s = subscript meaning "silage," "static," or "steel" s.; = crack spacing
= actual or computed stress; subscript meaning "filling" or
"noor" J; = compressive stress; compressive stress in concrete· J; = unit compressive strength of concrete 'i J;; = unit compressive strength of concrete at · time of wire wrapping fj = friction loss J~. = calculated stress in prestress steel at design load .IP"= ultimate unit strength of prestressing steel f, = computed tensile stress in reinforcing steel f; = computed compressive stress in reinforcing steel hr= effective stress in tendon steel (after losses)
l
= subscript meaning "tangential." "total," "top," "thermal," "tensile," or "thickness" (see also h)· ·
u
= subscript indicating "ultimate" (i·:e., factored)
-,
v ·=" subscript meaning "vertical" or "shear" verl = subscript meaning "vertical" w = weight per unit volume; radial displacement; load per unit area; fillet weld leg dimension; subscript meaning "wall" 11·_, = width of crack ·
NOTATIONS w1, w2, w3 = width of crack due to various loadings
x = "subscript meaning "x-direction" or x-distance" x, y, z = coefficients for curved interstice wall analysis (Timm and Windels) .\', Ji = coordinates of centroid
17
coefficient for Platanov-Kovtun interstice curved wall analysis
equations;
angle,
for
= angle between hopper plates; carrying capacity coefficient for grain arch (Platonov-Kovtun)
8 =.= angle of slope or rotation; angle around perimeter 01 = factor for computing shear due to tendon pressure
y = subscript meaning "j-direction" YL = limiting depth of compression block
.
( =
xi
i.
A = factor for cijcular slab analysis or ring-beam analysis
z = bracketed term on Janssen equation; abscissa for Reimbert's experimental curve 6 = displacement (linear); deflection t:.L = length of anchor set t:.T = temperature difference, outside and inside wall faces
11 = angle of friction (stored material against wall or hopper) 11' = coefficient of friction (tan 11) 111 = curvature friction coefficient
v = Poisson's ratio v,,, = Poisson's ratio for compressed stored material
LO= sum of rei_nforcing bar perimeters per unit width of wall
x = factor for flexural crack-width computation a.= angle of hopper slope; factor for circular slab analysis; subscript for forces or pressures on sloping surface; angle change along tendon a., = linear coefficient of thermal .expansion ff = factor for computing V and M due to tendon pressure; angle; factor for crack-width computation; factor for circular slab analysis
/l1
p = angle of internal friction for stored material, steel ratio = ratio of prestress steel area to gross concrete area
fip
a= stress
q, = strength-reduction
factor
1/1 = factor for computing vertical bending moment due to tendon pressure; factor for Gaquot's equations ij,1, 1/,2, 1/,3 = factors for crack-width computation
= ratio, depth of compression block to depth d t»
1· = weight per unit volume ~=angle, used in curved-wall analysis; friction (Jenike, Walker)
w1
effective angle of
= rotational frequency = angle, used in curved-wall analysis
Contents PREFACE/ v ACKNOWLEDGMENTS
2-12. 2-13. 2-14. 2-15.
vii
NOTATIONS t ix 2-16. 2-17. 2-18.
1. INfRODUCTION 1-1. 1-2:' 1-3. 1-4. 1-5. 1-6.
Recent Trends Failures / 3 Codes and Standards / 3 Storage Facilities / 3 Classifications and Definitions Stored Materials I 5 Bibliography / 5
2-19. 2-20.
I
4
2. STORED MATERIAL PRESSURES / 10 2-1. 2-2. 2-3. 2-4. 2-5. 2-6. 2- 7.
2-8.
2-9. 2-10. 2-11.
Methods of Computing Static Pressures Due to Granular Material / 10 The Janssen Method for Computing Static Pressure I 10 The Airy Method for Computing Static Pressure l 11 The Reimbert Method for Computing Static Pressure / 12 Pressure Normal to Inclined Surfaces / 14 Comparison of Methods for Computing Static Pressure / 14 Flow Patterns / 18 Mass-Flow Silos / 18 Funnel-Flow Silos / 19 Expanded-Flow I 20 Eccentric Flow and Cohesion Effects / 20 Flow Irregularities I 21 Pulsation / 21 Shocks / 23 Effect of Very Cohesive Solids / 24 Total Pressures -r- Static Plus Overpressure / 24 Caquot's Method for Computing Total Pressures / 24 Total Pressures by the Pieper-Wenzel Method / 25
2-21. 2-22. 2-23.
2-24.
~· Geniev's Analytical Solution / 25 Platanov's and Kovtun's Solution / 25 Theimer's Approach I 26 Walker's Method for Computing Total Pressures I 27 Design Pressures by M. and A. Reimbert I 28 Safarian's Approach / 28 Jenike's Approach for Computing Total Pressure / 29 German-Silo Code J 39 Soviet Silo Code J 48 Quality of Materials (Uniformity Factors) J 48 Load Factors / 49 Service Condition / 49 Silo Code, CH302-65 / 49 U.S. Silo Standard I 52 French Silo Regulations / 54 Effect of Eccentric Discharge and Nonsyrnrnetrical Flow I 57 ACI 313-83 Approach / 58 Safarian's Method / 59 Theimer's Approach / 60 A More Nearly Rational Procedure 60 Pressures in Bunkers f 62 Rankine Method / 62 Reimberts' Method / 63 References I 63
3. SILO AND BUNKER LOADS
65 .
3-1. 3-2. 3-3. 3-4. 3-5. 3-6.
Load Combinations / 65 Dead Loads / 65 Live Loads / 65 Wind Loads / 66 Equipment Loads· / 67 Thermal Effects / 67 Reinforcement for Temperature Gradient Due to Hot Stored Material / 67 3-7. Loads from External Restraint / 70 3-8. Loads at Hopper Feeders.or Gates / 71 3-9. Seismic Loading I 74 Other Loading Considerations I 76 References / 77 xiii
xiv
CONTENTS
4. CONCRETE SILOS AND BUNKERS
/ 78
4-J. Introduction / 78 4-2. Shapes of Concrete Silos and Bunkers / 78 Conventionally Reinforced Silos and Bunkers I 79 4-3. Wall Reinforcement / 79 Vertical Steel / 80 Horizontal Reinforcement / 81 Steel for Rectangular Silos / 81 Top Edge Reinforcement / 81 Intersection Columns / 81 Ties. I 82 Soviet Code Requirement for Vertical Steel and Ties t 83 -'l-4. Splices of Reinforcement / 83 4-5. Reinforcement Around Wall Openings / 84 4-6. RoofBeamPockets / 87 4-7. Fillets / 87 4-8. Dowels / 87 · 4 -9. Design Procedures - Conventionally Reinforced Silos or Bunkers / 90 4-10. Design of Circular Silos / 90 4-11. Grouped Circular Silos or Bunkers I 104 4-12. lntersticeWalls I 106 Interstice Loadings I l 06 Arch Computation ./ 107 Interstice Reinforcement for Pressure / 107 Shrinkage of Interstice Wall / 107 Thermal Stresses in Interstice Wall / 107 Simplified Method of Timm and Windels for Curved Interstice Wall·s I 108 4-13. Ciesi~lski's Method for Interstice Walls / 108 4-14. Pocket Bins / 113 Nearly Flat Enclosure Walls by the Ciesielski Method / 113 4-15. Circular Silos with Internal Cross-Walls / 115 Subdivided Circular Silos- Other Methods / 117 4-16. Details, Circular Silos and Silo Groups l ' 119 4-17. DesignofRectangularSilos / 121 4-18. USD Approach for Combined Tension and Bending / 125 · 4-19. Crack Width in Rectangular Silos / · 128 4-20. Other Forces and Bending Moments Rectangular Silos and Bunkers · I 130 4-21. Rectangular Silo Groups / 130 4-22. Details for Rectangular Silo Groups / 131 Reinforcing Steel. / 133 4-23. Shortening the Work -- Rectangular Silo Groups / 136 4-24 -. Regular Polygonal Silos I 137 Bottoms for Concrete Silos / 139 4-25. Bottoms General / 139 4-26. Bottom Loads / 140 Eccentric Discharge / 140 Earthquake Forces on Silo Bottoms / _ 140 v-
Flat Bottoms I 140 Loads / 140 4-28. Flat Circular Bottoms / 141 4-29. Rectangular Flat Bottoms / 153 4-30. Conical Concrete Hoppers / 154 4-31. Pyramidal Concrete Hoppers / 158 Geometry of Pyramidal Hoppers / 158 Pyramidal Hopper Loads / 160 Analysis of Symmetrical Pyramidal Hoppers / 160 Wall Design -- Pyramidal Concrete Hoppers / 160 Pyramidal Hopper Wall Thickness / 162 Pyramidal Hopper Details / 163 4-32. Circular Concrete Ring-Beam and Column Supporting a Conical Steel Hopper / 168 4-33. Buckling of Edge-Beams and Circular Ring-Beams / 174 4-34. Columns Supporting Silos or Silo Bottoms 174 4-35. Other Silo Bottoms / 178 Concrete Bunkers / 179 4-36. Bunker Loads and Forces / 179 4-37. In-Plane Bending and Wall Forces - Bunker with Pyramidal Hopper / 179 4-38. Suggested Procedure, Concrete Bunker Design l 181 4-39. Details for Reinforced Concrete Bunkers / 181 4-40. Roofs / 182 Roof Structures / 183 References / 187 4-27.
5. POST-TENSIONED AND PRECAST SILOS AND BUNKERS / 188 Post-Tensioned Silos and Bunkers / 188 5-1. Advantages of Post-Tensioned Walls /. 188 5-2. Typ5s of Post-Tensioning System for Silos I 188 5-3. Wire Wrapping / 190 Wall Thickness / 190 Nonprestressed Reinforcing / 190 Placing Prestress Wires / 191Prestressing / 191 Stresses and Wall Design / 192 5-4. Protective Cover. for Wound Post-Tension Wire / 192 5-5. Post-Tensioning with -i;endons / 193 StressingPoints / 193'· Ducts / 194 5-6. Stresses and Wall Design / 195 Concrete Stresses / 196 Stresses in Wire and Tendons / 196 Loss of Prestress I 196 Prestressing Steel Area Required / 198 5-7. Nonprestressed Reinforcing I 198 Stressing of Tendons I 201
CONTENTS
5-8.
Suggested Procedure for Design of Post-Tensioned Silo Walls / 204 Precast Concrete Silos I 214 5-9. Use and Advantages / 214 5-IO. Grouped Precast Rectangular Silos / 215 5-11. Circular Precast Silos / 218 5-12. Precast Stave. Silos / 221 References /. 222 \
7-4. 7-5. 7-6.
6. STEEL SILOS AND BUNKERS / 224 6-1. 6-2. 6-3. 6-4. 6-5. 6-6. 6- 7.
6-8. 6-9. 6-IO. 6-11.
6-12. 6-13. 6-14.
6-15. 6.:.16.
General / 224 Loads I 224 Circular Silos and Bunkers 226 Conical Hoppers / 229 Temperature Effects / 231 Reinforcement at Openings and Concentrated Loads I 232 Circular Silo and Bunker Supports / 233 Column Supports / 234 Wind or Earthquake Load Distribution in Columns I 234 Silos or Bunkers Without Columns / 234 Roofs for Circular Metal Silos or Bunkers / 237 Roof Loading I 239 Other Late;al Loads / 239 Tolerances / 239 Rectangular, Square, and Polygonal Silos and Bunkers / 243 Vertical Loads on Wall I 243 Bottoms for Rectangular or Polygonal Silos or Bunkers / 243 Hopper Walls / 244 Edge-Beams / 244 Hopper Plate Stiffeners / 245 Protective Lining for Steel Silos, Bunkers, or Hoppers / 247 Painting I 248 Sheet Metal Silos and Bunkers I 249 Circular Sheet Metal Silos and Bunkers / 249 Noncircular Sheet Metal Silos and Bunkers / 251 Stiffeners for Sheet Metal Panels / 253 Brackets and Hangersfor Steel Silos and Bunkers / 256 Materials / 257 References I 258
7- 7.
7-8. 7-9.
7-10.
7-11. 7-12. 7-13. 7-14.
7-15. 7-16. 7-17.
7. SPECIAL SILOS
259
7-1. Homogenizing or Blending Silos / 259 7-2. Pressures in Homogenizing Silos / 259 7-3. Claudius Peters Blending Silo I 260 Bottom Slab Alternatives. / 261 Bottom Slab Support I 261 Slipforming I 261 Structural Design - General / 262
Fuller Blending Silos / 264 Design Loads / 264 IBA U Hamburg Blending Silos / 265 Material Pressures / 266 Coal Silos / 270 Designing to Minimize Danger of Fire or Explosion / 270 Providing Smooth Flow / 271 Preventing Dust Explosions / 271 Other Problems in Coal Storage Structures / 272 Grain Silos I 272 Location of Explosions in Grain Storage Facilities I 272 Preventing Grain Dust or Flour Explosions / 273 Dust Control I 273 Venting / 273 Grain Damage or Deterioration / 273 Ducts / 274 General Guide for Ventilation / 274 Preventing Damage from Molds, Fungi, Insects, and Germination / 275 Flour Silos / 275 Silos for Raw Cocoa Beans I 275 Filling Silos with Cocoa Beans / 276 Withdrawal of Cocoa Beans from Silos 278 Moisture and Aeration of Cocoa Bean Silos I 278 Temperature Control / 279 Dust Control / 280 Dust Explosions / 280 Ignition Causes / 282 Ignition Temperature / 282 Protection from Explosion Damage 283 Venting / 284 Other Devices for Protection from Explosion / 284 Explosion-Relieving Roofs / 284 Concentric Silos / 287 Silos with Flow-Improving Devices / 287 Silos with Inverted Concrete Cone Bottom / 290 Loading / 293 Construction of the Inverted Concrete Cone / 295 Precast Cone / 295 Styrofoam Mold / 297 Sloping Bin Grain Elevator / 298 Radiation Hazards to Stored Food in Silos and Bunkers / 298 Silos for Storing PVC Powders / 300 Bibliography / 303
8. SILAGE OR FARM SILOS / 305 8-1. 8-2. 8-3.
xv
General I 305 Physical Characteristics of Silage / 305 Filling and Unloading Silage or Forage / 306 Top-Unloading Silos / 306 Bottom-Unloading Silos I 306
xvi
CONTENTS
8-4. Pressures Due to Stored Silage / 307
8-5. 8-6.
8-7.
8-8.
8-9, 8-10. 8-11. 8-12.
8-1'3. 8-14.
German Code for Silage Silo Design / 307 Farm Silo Standards inthe United States / 308 Overpressure Factors / 310 Bishara's Approach for Computing Pressures in Silage Silos / 311 Evaluation of Silo Capacities / 311 Other Loads. I 312 Other Methods of Load Determination / 312 Wall.Design for Cast-in-Place Concrete Farm Silos / 312 Stave Silos I 312 Stave Silo Wall Design / 31~ Stave Silo Wall Thickness / 3'14 Wall Design for Hoop Tension / 314 Hoops and Hoop Tensioning / 315 WallOpenings / 317 Vertical Loads and Stresses in Stave Silos / 317 Vertical Tensile Stress / 319 Wall Bending in Stave Silos / 320 Circular Bending / 320 Vertical Bending I 321 Stave Silo Foundations / 322 Stave Silo Joints / 322 Stave Testing / 323 Strength Tests of Individual Staves / 324 Tests of Stave Assemblies / 324 Joint Shear Strength / 325 VertlcalCornpressive Strength / 325 Vertical Stiffness Test . I 325 Horizontal Stiffness Test I 326 Stave Absorption Test / 326 Stave Silo Wall Finish and Grouting / 326 Stave Silo Construction and Maintenance / 327 Construction Tolerances I 327 Maintenance / 327 Monolithic Concrete Farm Silos 327 Metal Farm Silos / 328 Wood Farrn.Silos / 329
8-15 -. 8-16. 8-17. 8-18. MasonryFarm Silos / 330 Concrete Block Silos / , 330 Brick Farm Silos / 331 Tile Farm Silos . / · 333 References I 333
9. SILOAND BUNKERFOUNDATIONS / 340 9-1. 9-2. 9-3. 9-4.
Selection of Foundation Type / 340 Loads and Load Combinations / 340 Raft or Mat Foundation I 340 Continuous or Strip Footings / 345 References / 345
10. FAILURESAND REPAIRSOF SILOS AND BUNKERS / 346 10-1. Introduction / 346 10-2. Inadequate Design / 346 10-3. Faulty Construction / 348 10-4. Misuse by Owner or Operator / 348 10-5. Explosions / 349 10-6. Types of Structural Failure / 349 10-7. Foundation Failures / 350 10-8. Wall Failures / 353 Failures of Concrete Silo Walls / 353 Coal Silo Distress / 358 Distressed Twin Cement Silos I 358 Repairs to Coal Silo / 360 Grain Terminal Collapse / 360 Failure of Pocket Bin Wall / 361 Failure Reported by J. Sadler / 365 Wyoming Coal Silo Cr.acking / 366 Failures Due to Flow-Improving Device / 367 10-9. Repairs to Concrete Silos / 370 10-10. CausesofStaveSiloFailure / 372 Problems from Stored Material (Silage) / 372 Wind Problems / 373 Problems from Deterioration / 374 Construction Problems / 374 Stave Silo Failure Examples / 374 10.:11. SteelSiloWalls I 371 10-12. Roof Failures / 381 10-13. Silo and Bunker Bottom Failures / 382 References I 383
11. CONSTRUCTIONOF REINFORCEDCONCRETE SILO AND BUNKERWALLS / 387 l J -1. Historical Background / 387 11-2. Slipform Construction Method / · 387 Limitations and Guidelines / 388 Description of Slipform Fabrication and Erection I 389 11-3. Description of Slip form Operation I 395 Jacking Operation. / 397 Concrete Placement / 398 Wall Finishing· / 399 Placing Reinforcing Bars / 400 Placing Post-Tensioning Ducts f 401 Openings and Insert'~ j 401 Wall Openings / 401, Inserts I 402 Reduction in Wall Thickness / 403 Changes in Silo Configuration / 404 Stripping Slipforms / 404
CONTENTS
11-4.
Jump-Form
Construction
Limitations Description
and Guidelines / 405 of Jump-form System I
Method
/
404
12-17.
Tests by Ichikawa, Isobata, Mitani, and Sugita (Japan) / 442 Recycling / 443 Tests by Wenzel and Oertling on Silage Pressures (Germany) / 444 Results of Measurements / 445 Observations and Conclusions J 446 Experiments of Jenike, Johanson, and l{\ssocia t es / 44 7 Conclusions / 450 References / 450
405
Form Panels / 406 Placing Reinforcing Bars / 406 Concrete Placement / 406 Openings and Inserts / 407 Reduction in Wall Thickness / 407 References /'• 407
12-18.
12-19. 12-20.
12. EXPERIMENTAL STUDIES 12-1. 12-2. 12-3.
12-4: 12-5.
12-6, 12-7.
12-8.
12-9.
12-10. 12-11. 12-12. 12-13. 12-14.
12-1 S. 12-16.
/ 408
Historical Background I 408 Tachtainishev's Experiments (USSR) / 408 Experiments by Marcel and Andre Reimbert (France) / 409 Tests of the Chateau-Landon Silos / 409 Depression Column I 410 'Experiments of Kim (USSR) J 410 Experiments of Petrov and His Associates (USSR) / 412 Akmiansk Test Silo / 413 Oktiabr Test Silo / 414 Platonov and Kovtun's Experiments (USSR) I 414 Pieper and Wenzel's Experiments J 415 Effect of Wall Roughness / 416 Effect of Coefficient k / 416 Effect of Filling and Emptying Speeds I 417 Load Tests on Bunkers (Shallow Silos) I 420 Effect of Eccentric Discharge / .421 Martens's Tests (Germany) / 425 Horizontal Pressures, p / 425 Wall Friction, V / 428 Vertical Pressure, q I 428 Bottom Pressure, a» / 428 Joachim Hierlein 's Tests (Germany) 428 The Switch I 428 Safety of the Double Concentric Silos / 435 Experiments by G. P. Deutsch and.Associates (Australia) / 436 Kvapil's Studies (Sweden) I 436 Lenczrier Flow Tests I 437 Kotchanova Material Flow Experiments (USSR} / 437 Sugita's Tests / 438 Determination of Wall Pressures J 438 rests for Determining Flow Pattern /'. 440 For a High Initial Density I 440 McCabe's Flow Tests / 441 Sugden's Tests on Material Flow (South Africa) t · 442
xvii
APPENDIX A / 455 Table A-1. Values of Z ::: (1-e -x) in which x (tor.use in Jaussen's Table A-2. Values of function
=
µ'k Y
R
equations)
s = [I
-{ ~-· + 1 )-2J
(for use in solving Reimbert's equations) Fig. A-3.
Graphs showing comparisons·of design pressures in a circular silo, computed by various methods.
Fig. A-A.
Comparison of code flow pressure (overpressure) for H/D = 4 (Ref. Deutsch, G .P., Structural Design Criteria Codes and Specifications) - Symposium - Steel Bins. Australia Institute of Steel 'construction/ Australian Welding Research Association, 1983
Fig. A-5.
Comparison of code flow pressure ( overpressure) for H/D = 2 (Ref. Deutsch,G.P., Structural Design Criteria Codes and Specifications) - Symposium - Steel Bins. Australia Institute of Steel Construction/ Australian Welding Research Association, 1983.
APPENDIX B (Examples refer to Chapter 2) J 461 Example B'7l. Example B-2. Example B-3. Table Table Table Example B-4, Table Example B-5.
INDEX
/ 465
B-1. B-2. B-3. B-4.
Chapter 1 INTRODUCTION The custom of storing grain in upright containers is centuries old. Not until the mid 1800s, however, were relatively large storage containers built for commercial purposes. Since then, silos and bunkers have come into extensive use-not for storing grain alone, but for storing a wide variety of granular materials. In agriculture arid industry alike, improved production methods and mechanization 'of handling have opened the way for large storage complexes, with sophisticated filling, unloading, and handling systems.
1-1.
RECENTTRENDS
While earlier silos were only for more-or-less sedentary storage, the silo of today often plays an active role in the manufacturing and distribution process. Mixing. blend-
ing, proportioning-all are done using the silo as a vital part of the process system. Recently, the desire to withdraw stored material faster has led to a demand for larger-capacity silos, having either greater height or greater diameter, or both. To be functional and economical, these larger-diameter silos generally have several discharge openings. Each new trend brings new challenges to silo designers and builders. Frequently, meeting the challenge effectively has required research and experimentation. Although extensive research is done in Europe and Japan, the necessary research still lags behind the need, espe~ cially in e~e United States, where not much activity is reported in this field, except the work of Jenike19-21 and Johanson.P'(/) a.
~] LJ
a.
Cl>
~
Effective transition
Stagnant solid
(a) Moss flow
(bl Funnel flow (or core flow) Fig. 2-13. Mass flow and funnel flow.
than Y = 4D, the Reimbert and Janssen curves will intersect, as they do in Figs. 2-8 and 2-12. Figures 2-7 through 2-12 compare computed static values with each other. Perhaps·a more meaningful comparison would be that of computed static pressures to measured pressures. Static lateral pressure measurements generally support the use of Janssen's method, whereas vertical static pressures are generally better predicted by the Reimbert method. Differences between computed static pressure values, however, are far exceeded by differences between static pressure and actual total pressures occurring during emptying or during simultaneous filling and emptying of the silo. These pressure differences are usually referred to as "overpressures." Total pressures be called "design pressures" in this book. Other names used are "operational pressures" and "flow pressures." Whatever their name, design pressures are the subject of the rest of this chapter.
will
2-7.
Mass-Flow
Silos9-12.3s.36.4o.41
In mass-flow silos· the hopper is sufficiently steep and smooth to cause flow of all the solids-without stagnant regions-whenever any solid is withdrawn. Mass-flow silos are usually recommended for cohesive materials (coal, for example), materials that degrade with time, powders (unless means of withdrawal such as aeration are used), and materials in which segregation needs to be minimized: Fig. 2-14(a) shows typical mass-flow silo shapes. Mass flow will occur if three conditions are met: I . The outlet must be large enough for the material to flow without arching. 2. The flow-control device must permit material to flow through the entire opening area. . 3. The hopper walls must be smooth enough and steep enough to allow the material to slide, thus expanding the flow channel upward until it meets the vertical walls of the silo.
FLOW PATTERNS
Advantages of mass-flow silos are :41 Flow or stored material from silos is of two main pat- . terns, funnel flow (core flow) and mass flow. In mass flow, all of the stored material is in motion during discharge. In funnel flow, movement occurs only .in a· channel within the· stored material, and this channel is surrounded. by non flowing material. The two. types are illustrated by Fig. 2-13. Because loads and stresses are related to flow pattern, the structural engineer should consider the effect of flow pattern when designing silos or bunkers. .
1. Material flow is · uniform, and feed density is practically independent df the depth of material in the silo. This often permits using volumetric feeders for feed-rate control. ' 2. Low-level indicators work reliably. 3. Segregation of the discharging shear is minimized. While the material may segregate as it is placed into the silo, the first-in/first-out flow sequence causes the same particle-size distribution at. dis-
STORED MATERIAL PRESSURES
19
J~ I)J~ Trortsilion hopper
Conical hopper
(al.Mass-flow
{t1
silos
(d) (ff) Contours for conical channels, &=50°
steep
~
enough for mass flow
Conicol hopper
Pyramidal hopper
(blFunn_el-flow silos
(el (ff) Contours for symmetric wedge channels, ti= 50° (cl Expanded- flaw silos Fig. 2-14. Various flow silos and the respective flow factor (ff) charts (after Jenike).
charge as existed at filling. This flow sequence also ensures uniform time in storage and deaeration of a fine powder. Hence, air locks can often be dispensed with, provided the critical inflow and outflow rates are not exceeded. Valleys are usually not permitted in mass-flow hoppers, nor are ledges or protrusions into the hopper. · The discharge opening must be fully effective; that is, if the hopper is equipped with a shut-off gate, the gate must be fully open. If it is equipped with a feeder, the feeder must simultaneously draw material across the full outlet area.
Funnel-Flow
Silos9-12·36·36
Funnel flow occurs when the hopper is not sufficiently steep and smooth to force material to slide along the walls, or when the outlet of a mass-flow bin is not fully effective. In a funnel-flow silo, solid flows toward the outlet through a channel that forms within stagnant material. Usually, funnel-flow bins are suitable only for coarse, free-flowing or slightly cohesive, nondegrading solids in which segregation is unimportant. Yet, at the time of this writing, funnel-flow silos are the more prevalent type. Funnel-flow silos or bins· are illustrated by Figs. 2-14(b) and 2-18. With a non-free-flowing solid, the
20
SILOS'AND"BUNKERS,:
·' '
1"'
•
flow channel expands upward from the outlet.to a.diame- . ter that approximates the largest dimens'ion of th~ effecs tive outlet. Wh~n t~e outlet: is full~ . effective, this dimension is the diameter of the outlet -if it. is circular or the diagonal if it is square or slotted {rectangular). Higher within the mass, the flow channel remain vertical, forming a pipe, if its diameter :is less· than the' critical "rathole": diameter. With a free-flowing solid, the flow channel expands at an angle that depends on the effective angle' of friction of the material. the results ing flow channel is · generally circular.. its diameter exceeding the outiet diamete~ or diagonal dimensi~n .. • When the bin discharge rate is greater than the filling rate, the level of material within the flow channel drops, causing layers to slough off from the top of the stagnant mass and fall into the channel. This spasmodic behavior is detrimental with cohesive solids, since the falling material becomes compacted on impact, thereby increasing the chance of arching. With sufficient cohesion, sloughing may cease, allowing the channel to empty out completely and form a stable rathole. Material charged into-this empty rathole may overflow the feeder. When a fluidized (aerated) powder is charged directly into a funnel-flow.channel at a sufficiently high rate and is withdrawn at· the fame time, · it has no· chance to deaerate. Therefore,it' remains fluidized irr the channel and "flushes" at exit from the bin. A rotary valve is. often used under these conditions to contain the material, but even so, uniform flow cannot be ensured b~cause flow into the valve. is erratic. Figure 2-15 shows charts by Jenike that may be used to predict (for two shapes of hopper) whether mass flow or funnel flow will.occur. The regions marked "uncertain" indicate conditions under iwhich flowtype may change abruptly.These conditions should preferably be avoided, ,since they =may . lead "to nonsymmetricflow patterns and frequent vibration ind'shcfok loads, which can seriously damage the silo.
will
Cone
(al
1
ExpandedFlow9-1·2·35
'"
:>·
Besides the two main Ilowpattems.ithere.is: anintermediate type called "expanded flow." Expanded flow is a combination of mass flow and funnel 'flow,' Figures · ·2-14(c) and 2~19 show expanded-flow silos, The lower portion of the hopper operates in mass. flow and.the upper in funnelflow, To prevent •ratholing in the upper, funnel-flow 'portion' of the mass-flow hopper; the flow channel should expand to a diagonal or diameter equal to or greater than the critical ta thole diameter· determined for the material to be stored. . Expanded-flow silos are· usually recommended · for storing large quantities of nondegrading material. Often an expanded-flow hopper design is used· to' modify an
10° Slotted opening
20•
30•
40•
50•
eo-
0p ( b)
Fig. 2-15. Mass-flow/funnel-flow
bounds (after Jenike-Johanson).
existingfunnel-flow hopper, correcting flowability problems such as arching, ratholing, and flushing. This concept can also be used with multiple outlets, where simultaneously flowing mass-flow hoppers are placed so close together as. to cause a combined flow channel of size larger than the critical rathole diameter. Eccentric flow and Cohesionlgffects,,.
,
The structural design problem is easier if the silo or bunker is axi-symrnetrical, and both charging-and discharge, are central. However, process layout, site details, and the like frequently make non-axi-symmetric arrangements., necessary.: Silos often .have offset outlets, or multiple discharge openings such that non-axi-symmetric flow will occur whenever all outlets: do, not .generate simultaneously,and in the same manner, These nonsymmetrical silos; bunkers, or. hoppers and multiple outlets and side outlets including eccentric filling create' flow-channel -pattems that· in turn could cause severe structurai problems by introducing unsymmetrical loading on wails. If these loading conditions are not. properly evaluated · and · considered by . the structural designer; serious structural problems may develop. It should also be realized that even symmetrical silos
STORf:D MATERIAL PRESSURES
21
instantaneous span
next failure plane 'free
surface of the arch
E
\--------I.
void
Fig. 2-17. Silo with a circumferential shelf (after Jenike).
------~-
velocity profile
Fig. 2-16. Suggested mechanism of pulsation (after Jenike),
and bunkers with symmetrical concentric discharge points are not always free from flow problems. These silos or bunkers could develop eccentric flow channels or eccentric withdrawal patterns. This could occur if a feeder were improperly designed or selected, or in use if cut-off gates were left partially closed. Such eccentric withdrawal patterns could _ also be caused by partially frozen stored material in the silos, nonsymmetrical falling, and so on. Such problems should be foreseen by the structural designer and considered in the design. There are frequent reports of structural distress or failure of funnel-flow silos that contain cohesive materials such as certain raw coals. In many cases it has been concluded that such failures have occurred largely because the behavior of the stored· material during withdrawal was not properly considered in the design. For this reason, structural designers today are giving greater attention to flow pattern. The most reliable means to ensure flow of cohesive materials (where withdrawal is by gravity only) is considered to be to use mass-flow silos, or at least expandedflow silos. Unfortunately, however, cost and geometric requirements often preclude such a choice. 2-8.
FLOW IRREGULARITIES
Certain combinations of material properties and silo and hopper geometry may cause harmful flow irregularities such as arching, pulsation, or shock. Jenike40•41 has discussed their origin and ways to reduce or eliminate their harmful effects. His articles are the source of the information that follows regarding pulsation,
Pulsation
Pulsing occurs when the slope of the hopper wall (or of a part of the hopper wall) plots in the "uncertain" boundary region between mass flow and funnel flow, as shown in Fig. 2° 15. Pulsations result. from repetitive formation and collapse of an obstruction to flow. The frequency of pulsation, which is usually between l /5 and 10 Hz, is directly proportional to the rate of outflow, while the amplitude tends to be higher at low flow rates than at high. A sufficient head of stored material above the location of the pulsation source is required; when the head becomes low enough, pulsation ceases. Outflow from a bin during pulsation is uniform. This means that material flow below the pulsation source is continuous, while above, it is "stick-slip." Each slip causes a pulse. Objectionable pulsations occur only with materials containing at least a fraction .of coarse particles, say greater than 0.2 in. (5 mm). Fines inhibit pulsation. When the voids between coarse particles are completely filled with impermeable fines, pulsation does not occur. Less coarse materials (such as sand) may pulsate', but at a fairly low amplitude. Powders do not pulsate. Jenike proposes the following mechanism of pulsation. Pulsation is generated at a transition or at an effective transition in cylinder diameter. High pressures, due to head h, compact the solid flowing down the cylinder into a firm plug. At the transition, a large part of the pressure due to head h, is transferred to the abutments, The highly consolidated material. there is capable of forming a stable arch of some span. The arch does not break up and flow until that span has been exposed through outflow of material from beneath the arch. The velocity profile of a solid flowing in the converging part of a channel is shown in Fig. 2-16. Material flows fastest at the center where it forms a void and exposes a stable arch. The void and the span of the arch increase, gradually increasing the stresses in the arch. When the strength of the material is exceeded, the arch collapses,
'
'22
,· ....
-
SILOS AND BUNKERS
and the plug slips and fills the. void. The process is then repeated. The tendency to. pulsate is inherent in materials of certain properties and occurs at a transition or an effective transition. Since the designer cannot select the material and transitions are required in most silos, the designer can only attempt to minimize the amplitude of pulsations. He may do this by reducing the effective head of solid, he, at the transition and by selecting hopper conditions to produce a large ratio kmax, thus preventing the development of large arches. The following factors decrease head h,: 1. 2. 3. 4.
Low ratio of H/D Rough cylinder walls Convergent cylinder Sloppily constructed silo containing a variety. of convergence, divergence, and rough ledges 5. Circumferential shelf, as shown by Fig. 2-17. A single shelf level appears to suffice. The surface of I Ihe shelf should be hard and smooth.
Pressure on the shelf is computed as if the shelf were the upper part of a hopper. While it may appear that the · shelf itself could generate pulsation, it actually does not because the velocity profile in the cylinder below the shelf is uniform. The entire arch is being continuously exposed and collapses before a void can develop. Effective head he on the hopper is limited to less than diameter D. The ranges of angle () and angle µ (µ = tan - i µ') that lead to large values of kmax are evident from Figs. 2-34 and 2-35; large kmax occurs for steep hopper walls with smooth surfaces. A steep conical ring can be used for that purpose. The material of the ring should be sufficiently hard to prevent scoring; it will then polish under the pressures of the sliding solid, and pulsations, if present; will abate with time. '. Jenike further explains the m.echanism of pulsation as follows: For repetitive arching and collapse to occur, it is necessary that the failure plane of one arch become the free surface of the next arch. Thus the failure plane must be parallel to the free surface of the arch. A failure plane is inclined at an angle ~ = (45° - p/2) to the major
e 11 70 60 D
Cl)
50
,:,
.s
%
40
effective transition
30 20 1·
10
I
I
0
10
20
30
40
50
I -
Fig. 2-18~ Included angle ofchan~el in funnel-flow silos (after Jenike).
60"'
11. 70
cf
STORED MATERIAL PRESSURES
i
23
t 0j'
a co.lumn
made of cubes
t e,
4)
-0
c
I
~ effective tronsition
+ \
I
I I
I
Fig. 2-20. Model of pulsating material (after Jenike).
form within the arching material, adding to gravity and collapsing the arch. In consequence, fine . solids now uniformly. · · Shocks
"'"' E
Fig. 2-19. Expanded-flow silo (after Jenike).
pressure. In an arch with a free surface, the major pressure is aligned with the surface. Hence the failure plane, being parallel to the free surface, forms an angle a= 0. This implies p = 90°, or a yield locus of the type shown in Fig. 2-20. Here p indeed equals 90~ for the loading at a free surface, indicated by the Mohr circle. A material of this type has compressive strength fc but zero tensile strength. (An example of such a material is a column made of cubes.) This appears to explain why only materials containing coarse particles pulsate. The higher Jc, the larger is the span at failure, the larger the void under the arch, and the stronger the pulse. Stress j, · increases with compacting head he; that· is why a sufficient level of material above a transition is required before pulsation is observed. While lc can be large in very fine materials, these materials do not pulsate because they have tensile strength. The yield locus does not pass through (0, 0), p < 90° at a free surface, and the failure plane penetrates deep into the arch. Thus, the high-frequency repetitive mechanism is not available. In addition, enclosed voids cannot form rapidly in materials of low permeability. Any tendency to form an enclosed void reduces air pressure in the incipient void, and air pressure gradients
Jenike's explanation of shocks is as follows: Periodic shocks are experienced in funnel-flow bins containing coarse solids with little fines. Such materials would inclµde cement clinker, coarse coal, and corn. In large silos these shocks can be destructive. The · interval between shocks is irregular, lasting from several seconds to a few. minutes. At a constant outflow rate, shock severity increases with the length of the . preceding interval. Uniformity of feed· rate is not affected PX. the shocks, but the top level of material in the bin. usually remains stationary during the interval, dropping abruptly during the shock. As the top level in the bin descends, the shocks diminish in strength and then vanish. Shocks appear to be caused by a recurring instability of the stagnant material around the flow channel.. The stagnant material slides inward into the channel, forming a secondary channel. This densifies the material in the flow channel, which re-forms with higher wall pressures, capable of stabilizing the material. around it. As material discharges, it dilates, wall pressures decrease, and a new collapse occurs.45 This mechanism -appears to be substantiated by wall pressure measurements,42 which at upper levels show ii drop of pressure during the quiet interval (corresponding to dilation), followedby a sharp increase of wall pressure . (corresponding to the collapse and contraction)'. M a . lower .level; pressure is essentially constant during the interval, indicating a narrow. channelsdistant from the· wans. ". . .,. ' • . ,.,.·,,,:,". . . Shocks can be eliminated or at least · minimized- by
24
SILOS
AND
BUNKERS
expanding· the flow channel to a base diameter of some 8 ft. Above that diameter the flow channel usually assumes a stable conical shape. Such an expansion can be obtained either by providing an 8-ft-long, rectangular, live outlet or by expanding the flow .channel with a mass-flow hopper to an .8-ft base diameter. The latter.is relatively easy to do in existing bins. Shocks of this type do not occur in cohesive materials that develop stable stagnant channels. Neither do they occur with fine material, probably because fine material always has some cohesion, and resists rapid dilation and contraction through counteraeting void air pressure gradients. In coarse materials, having high permeability, significant air pressure gradients do not arise. Severe shocks can originate within a flowing material . when the hopper slope and friction are on the boundary between mass flow and funnel flow. Such might be the · case, for example, with a conical hopper for a material with p·= 50°, a hopper with()= 30°, andµ= 16°. If the wallfrictionincreases a little, perhaps owing to corrosion of the walls during storage with the materialat rest, then mass flow will not occur on start-up. Rather, flow will proceed in a central channel. If the material in the region of the transition has sufficient strength to arch across that channel, the channel will tend to empty, gradually exposing the walls. At some exposed height, the stable material in the hopper will fail, and all the silo contents will drop into the void, producing a shock. These shocks may be recurring. To prevent these shocks, hopper slopes should be steep enough so that O andµ plot continuously in the mass-flow region. Also, wall frictional properties should not deteriorate with time. A stainless steel liner, or sometimes an epoxy coating, or special plastic lining, may provide a solution in an existing hopper that is not quite steep enough for continuous mass flow. Effect of Very Cohesive Solids
If the critical arching diameter of a material approaches or exceeds the diameter of the cylinder, then stable arches will tend.to develop throughout the bin. Such a materiai will not discharge by gravity alone. Vibration, aeration, or air cannons may be needed :10 initiate flow from -the hopper. However, after the hopper has emptied.there may still be a cylinder full of material.held .back by an arch at the transition. This is a dangerous condition because of the possibility that a large mass may drop into the hopper all at once, either tearing the hopper off its supports or breaking through the silo wall. Under these· conditions the head of material in the cylinder shoui'd not exceed one diameter, and the hopper should have the strength to withstand the impact of a dropping mass.
2-9.
TOTAL PRESSURES-STATIC OVERPRESSURE
PLUS
Totai pressures (both lateral and vertical) can exceed computed static pressures by a wide margin. (These total pressures may be 'called "operation," or "flow" pressures.) In earlier silo designs overpressures were not considered, even though as early as the 1950s, it was fairly well recognized· that overpressures occur during emptying. The result of ignoring overpressure is to reduce the overall. factor of safety. A marginal structure is produced, with increased probability of bulging walls, damaging cracks, or even collapse. Overpressures are due to various causes, including arching of the stored material; collapse of material arches; sudden change of flow channels, velocities, and directions; and changes between funnel flow and mass flow. There are two general approaches to determining total pressures. One is to modify the computed static pressure using "overpressure factors"; the second is to compute total pressures directly. In their present stages of development, neither approach is completely satisfactory. In the following sections of this chapter various methods, codes, and standards for computing design pressures in silos are introduced. Also see Appendix A, for comparison of the various methods. 2-10.
CAQUOT'S METHOD FOR COMPUTING TOTAL PRESSURES
Developed in 1956 by A. Caquot and J. Kerisel, 13 this is one of two methods approved by the present French silo design code14 (the Reimbert method being the other). Caquot's method provides separate formulas for pressures during filling and pressures during emptying. It is 'based on the. relationship of horizontal and vertical stresses on an eiemental prism within the' noncohesive stored material, assuming that the relationship has the forin of Rankine's active pressure equation during filling, and the form of Rankine's passive pressure equation during emptying. The final equations.ofCaquot's method are as follows: Lateral. total pressure, Pdes• at depth Y is: (2-26) -in which b, = 2R/(i"' sin 21/1)) R is similar to hydraulic radius (see Table 2-1); ljJ = tan~1(0.866 tan p); it/I for the first case (filling) is (I - 0.6sinp)/(1·+ 0.6sinp); and it/I_· for the second case (emptying) is (I - 0.5 sin p)/ (I+ 0.5.sinp). Vertical total pressure, qdes• at depth Y is: (2°27)
STORED MATERIAL
PRESSURES
~5
Table 2-1. Values of R for Use in Caquot's Equation. R
SILO SHAPE
Rectangular, long side a, short side b Circular,.diameter =D Hexagonal, side =.a Square, side = a·
\,
0.5b for pressure on long side 0.285b for pressure on short side 0.5D 0.455a 0.385a I
2-11.
TOTAL PRESSURES BY THE PIEPER-WENZEL METHOD15
Presented in 1962,this method of solving for operational pressures is recognized by the German Silo Code, 6• 16 but later was modified based on more recent experimental studies. Pieper and Wenzel proposed twoseparateequations for determining pressures in silos: one for calculating pressure during filling, which gives large vertical pressures; and the other for calculating pressures during emptying, which gives large lateral pressure (both compared with values obtained by Janssen's method). A complete presentation of the Pieper-Wenzel approach (with recent revisions) is given below in Section 2-19 on the German Silo Code. 2-12.
GENIEV'S ANALYTICAL SOLUTION17
In 1958, G. A. Geniev published an analysis aiming to explain the phenomenon of pressure increase due to a granular mass in motion. Geniev claims that Janssen's theory is incorrect because it does not satisfy boundary conditions at the silo walls, and because it neglects the pressure variation across a horizontal section. Geniev assumed this variation to be parabolic. The behavior of the granular mass in a silo is a special case of Geniev's general theory of dynamics ofa granular mass. It is based on the theory of plasticity. Geniev derives the general equations for art incompressible mass and for a compressible granular mass in both steady-state and turbulent motion. His general equations are a combination of partial differential and algebraic equations, which may be found in reference i 7.
Fig. i-21. Formation of granular domes in deep bins (afterPlatanov and Kovtun), .
Upper zone: In the upper zone, of height H1, the pressure during emptying follows the Rankine theory; H1
== Dtanp
(2-28) (2-29) (2-30)
Middle zone: In the middle portion of the silo height, classified as the zone of arch or dome formatiea.. the transfer of forces is similar to that in, an arch-shaped structure, Therefore, following the equilibrium of aq arch structure of grain flows, the lateral and vertical unit pressures in this zone are, (2-31)
p2
= 0.5yD
tan.o,
(2-32) (2-33)
2-13.
PLATANOV'S' AND KOVTUN'S SOLUTION18
Analyzing their experimental results, Platanov . and Kovtun concluded that, for the purpose of obtaining actual lateral and vertical pressures in silos during emptying, the silo storage height should. be divided into the three zones shown. in Fig.· 2-21. · The height and equations.for.each zone are given below:
Lower zone: In the Jower zone, behavior pf the grain mass changes because of a flow funnel forming at the dischargeopening. This causes a change in the mechanics of force transfer in the flowing .grain, 'Platonov and Kovtun believe that the behavior in this lower zone is quite similar to that of the upper zone. Therefore; they suggest calculating pressures in this zone using-the same
. 26 ';SILOS'AND;BUNKERS
n
l; 1·
!, ~
.5 0 . I5
,:" \ -,
:c
. 67
\ \
. 25
I1
c.
32.83 c ,39.35 ~ ,·46._0 ~-
"ii, s:
52.5
5:.
65.61 72 25
\
__
;;:::
~ ci
-~ . ''\ .
\--,--~---t
\
\\ I•
\'\a-3
2-.\ \
59. I
:1 .:;~ - · en
-~,
·
\\
I
'\ \
o
~
:~_::j"
___..
:c
\,3 \ l
N
I
__)
----·
r
Bl
82
YQQY YOOQ O Q y cp 83
84
85
86
Cl
C2
C3
C4
C5
DI
02
EI
E5
OY~,
E9
E2
E6
E3
E7
E4
EB
discharge be considered by adding a correction, Pecc, to the .lateral desiqn pressure, Pdes- Safarian's method · for. computing Pecc, introduced later in this chapter (Section 2-23), or another reliable method may be used. For mass-flow pressures (if not determined by other . means) Safarian's method suggests an increase of the Cd factor given in Table 2-4 by IO to 25 %, Silos containing hot granular materials are subject to temperature stresses, which may be too high to be ignored. In that case, thermal stresses and the corresponding required additional hoop reinforcement should, be calculated'.2°·22 The reinforcement so computed should be added to that calculated for material pressures alone. (SeeChapter 3 for thermal stress computations in concrete walls and Chapter 6·for those.in steel silo walls.) , Figure 2-27 shows the resulting curve of lateral design pressures given by Safarian's method. Note that pressure increases," pecc, due to eccentric discharge; (if any) are added to the product Cdp. (See Chapter 4 .. for pressure computations using Safarian's approach.)
2-18.
~OYY
Fig. 2-26. Discharge opening arrangements for use with Reimbert's method for computing total pressures.
Table 2-4 shows values of the overpressure factor, Cd, recommended by Safarian. The factors for use with Janssen's method are from the Soviet Silo Code, but with some modification. Those for use with the Reimbert method are computed from those · for the Janssen method. To provide better flow of material, designers sometimes use a flow-improving device (such as the Buehler Nose), usually located directly above the hopper. Tests show that such devices may cause large additional local overpressures, beyond the normal overpressures without the device. Local overpressures caused by such devices may be determined by the method introduced. in Chapter 7. When the device is used and its effect is not determined experimentally, then it is suggested that the normal overpressure factors, Cd, for walls of height equal to three times the device depth (centered about the device) be at least 50 % higher than shown by Table 2-4. Safarian recommends that the effect of eccentric
29
JENIKE'S APPROACH FOR COMPUTING TOTAL PRE$SURE
In a paper presented to the Norwegian Society of Chartered Engineers.?" Jenike introduced a method of computing total pressures in granular and· powdery materials in mass-flow silos. This approach was suggested for use with silo shapes shown by Figs. 2-28 . and 2-29. For computing pressure, Jenike divides the silo into three zones, as follows: I. Top zone-from the top to distance D (di~meter) below the top 2. Lower zone-balance of the cylindrical silo below the top zone 3. Hopper In the top zone, Jenike suggests that total lateral pressure be computed as IS times the Janssen static pressure, but using:
k = (I - sin p)/(l
+
sin p)
(2-45)
or:
k = 0.4 whichever is larger. For the lower portion of the silo cylinder, pressure is computed by the principle of minimum strain energy. The graphs shown by Figs. 2-30 through 2°33 show information for various ratios of HID. Ratios of H/D
f.r -.·_ . ."1
30
SILOS AND BUNKERS ·
Table 2~2.Values of Factors Kd and Kb for Use with Reimbert's · Pressures. A-I
A·2
A-3
A-4
i
• A:.5
l for a single, circular cement storage silo· or bunker: The principle, however, should apply also for structures for storing other hot granular .or powdery materials. The following assumptions are made:
L Tensile strength-of the concrete is negligible. 2. Wall temperatures vary only radially. (T emperature differences between shady and sunny sides and between. points. of .different elevations, and the effect of wind are all neglected.) 3. In buildings, the usual practice is to ignore a certain amount of inside/outside temperature dif. ference. For silos and bunkers, the authors usually · neglect ·not, more than 80°F (44.5°C) of this difference. The inside design temperature (in °F and °C, respectively) of stored material having temperature T; is then: · T;,des
or
T;,des
(3-6)
= T; - 80°F
= (T; - 44.5°C).
The temperature of· hot granular material in silos is not uniform, but· drops appreciably near the inside surface of the wall. This drop may be considered when 'determining the design temperature difference.-Aj", between inner and outer wall faces. For example, with hot cerrient, the authors suggest that an 8-in. thickness of cement adjacent· to the inside face of the wall be considered as: insulating material, and that the tem, perature -varies-Iinearly across this strip .. Fig. 3-l(b) shows-the temperature.variation through .the 8Lin. thickness of cement and the silo wall. The temperature difference Ll T between the inside and outside faces is: ,j
!). T =; T2· .._
T1
(3- 7)
T1 and Tf may, be calculated by· heat transfer equation Q = UAbT, substituting !).T, for the temperature difference [)Tso that:
I
Q
= UA(/),.T)
.'t
(3-8)
where:
Q = heat transfer, Btu/hr (kg-cal/hr) U = heat transfer coefficient
The temperat~re drop !)T with~n the 'wallis a .portion of the total.design temperaturedifference, corresponding to K,, the ratio .of the thermal .resistance, of the ~all alone to that of the cement, wall, and ~utslde air combined. Drop !).Tis then: · (3-9) The determination of K1 is by heat transfer principles. FactorX, for various wall thicknesses is given (for stored cement) by the curve of Fig. J-1 (a). This curve is based oh the assumptions listed. Bending moment due to temperature gradient is derived for an uncracked section. The added reinforcing steel, however, is chosen for a cracked section. The horizontal ultimate thermal bending rriorrient due to LlT, using plane-strain analysis, Poisson's ratio v = 0.2, and a load factor K9 is: (3-10)
The authors suggest using 1.4 for the load factor K 9 . Application of the method is shown in Chapter 4. The required area of additional horizontal steel may be easily calculated using the ultimate strength method. This calculated steel area is to be added to that required for material pressure alone. The added steel A. 1 should be located near the outer (colder) face. In wall~ with two-layer reinforcetnent, the entire amount, A,,, should be added to the outer layer. For simplicity, when silos are constructed by the slipform method, an equal amount is usually added to the inner layer to avoid having bar sizes or spacings differ from one. layer to the other unless the added amount of reinforcing is substantial and not justified economically. Vertical tensile thermal stress is usually offset by vertical dead load compressive stress, so that added vertical temperature steel for the effect of hot stored material is normally not: needed. ' The hot-stored-material effect should be considered in the design of silo and bunker roof and bottom structures, as well as walls. ·, Bohm!" proposes a slightly different method for computing the temperature differential, !). T, between the inside and outside walls of cement storage. silos, not allowing neglect of the first 80°F of difference, as shown above. Under Bohm's approach:
A~ area1ofcross section of wall through which trans·. fer occurs
T;,des
= T; - To
(3-11)
SILO AND BUNKER LOADS
x; .c,LUES
\.
Taconite pellets y='l30 moisture: 0% µ =.18°.!. p 7 33°,. (estirnatedj"
(6°
=
K0}'B
• .300
86
73
RANGE OF INDUSTRY CALCULATIONS
AT OPENING,
· q=CyB 3y
HYDROSTATIC
I,.
. 2,600
236
.' 555
I
, ,
q = 0.40
ff= 1.4
76
256
270
(C)_~ li\1
::\•,.
212
)lt
1,1,8?0,
• ,390
·' ·'j
down slope) J .
;260. , (level).
Limestone in.) )'.=.100 ··' moisture; .4 % µ = 25° p =45°'
170 (6° down slope)
Mesabi ore lines (-1/4 in.) .)' = 140 , , moisture: 7 % µ s=' 30° 'p ='50°
160 (6° down slope)
(-2
Note; Width of hopper opening:B
Q
WAU I PRESSURE
1•Bff cr1 = m+ I
JENI KE,
280 (6° dow~1s_I?Pf)
250 • .(level)
LOADS
Feeder Tests. Net Feeder Load in psf underBin.Openinq during Flow ( Reisner). 6
SYNTRON AVG.
AND.BUNKER·
155 (level)
ti!:
q = 0.50
ff=.).7
(9) = 1,4
38
150
1'05
300 I
q
= 0.33
ff=
52
q =.
1,400
L3
(C)
= 0.32
= 0.90
. 122
194
ff= 1.2
·(C)
l;il20
= 0.75
1.16 ft.
under steady flow. According to Reisner, the filling pres, sures at_ the discharge opening are -usually two to :four times as large as the steady-flow discharge pressures on the feeder, depending on the point of impact and the filling rate. Reisner. suggests leaving an 8- to lfl-ft (2,4,to 3, 1 m) depth of material in the silo when the feeder stops, and then refilling the silo. This would avoid the impact of material directly over the hopper opening during filling, thus reducing the filling pressures to only 10 to 20% higher than the pressures due to steady flow. This suggestion, however, -seems. impractical for computing feede~ _ loads or for computing pressures for bar and slide gates, Therefore, for design pressures, for either feeders or gates, .the authors prefer .to use .maximum pressure ,values at the discharge opening caused by filling. If such values.are not available (which usually is the case); the autho~s suggest using . four times. the value computed by either eq. (3-19) or eq. (3-20), suggested by Jenike, or, by.using.eq. (3s2l),and.eq. (3-22);-suggested by Reisner.
Broersma 11 .gives a unit pressure value qb on th
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